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diff --git a/www/lang_with.html b/www/lang_with.html new file mode 100644 index 0000000..aafca54 --- /dev/null +++ b/www/lang_with.html @@ -0,0 +1,3195 @@ +<!DOCTYPE html> +<html><head> +<meta name="viewport" content="width=device-width, initial-scale=1.0"> +<meta http-equiv="content-type" content="text/html; charset=UTF-8"> +<link href="sqlite.css" rel="stylesheet"> +<title>The WITH Clause</title> +<!-- path= --> +</head> +<body> +<div class=nosearch> +<a href="index.html"> +<img class="logo" src="images/sqlite370_banner.gif" alt="SQLite" border="0"> +</a> +<div><!-- IE hack to prevent disappearing logo --></div> +<div class="tagline desktoponly"> +Small. Fast. 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Overview</a></div> +<div class="fancy-toc1"><a href="#ordinary_common_table_expressions">2. Ordinary Common Table Expressions</a></div> +<div class="fancy-toc1"><a href="#recursive_common_table_expressions">3. Recursive Common Table Expressions</a></div> +<div class="fancy-toc2"><a href="#recursive_query_examples">3.1. Recursive Query Examples</a></div> +<div class="fancy-toc2"><a href="#hierarchical_query_examples">3.2. Hierarchical Query Examples</a></div> +<div class="fancy-toc2"><a href="#queries_against_a_graph">3.3. Queries Against A Graph</a></div> +<div class="fancy-toc2"><a href="#controlling_depth_first_versus_breadth_first_search_of_a_tree_using_order_by">3.4. Controlling Depth-First Versus Breadth-First Search Of a Tree +Using ORDER BY</a></div> +<div class="fancy-toc2"><a href="#outlandish_recursive_query_examples">3.5. Outlandish Recursive Query Examples</a></div> +<div class="fancy-toc1"><a href="#materialization_hints">4. Materialization Hints</a></div> +<div class="fancy-toc1"><a href="#limitations_and_caveats">5. Limitations And Caveats</a></div> +</div> +</div> +<script> +function toggle_toc(){ +var sub = document.getElementById("toc_sub") +var mk = document.getElementById("toc_mk") +if( sub.style.display!="block" ){ +sub.style.display = "block"; +mk.innerHTML = "▼"; +} else { +sub.style.display = "none"; +mk.innerHTML = "►"; +} +} +</script> +</div> + + + + +<h1 id="overview"><span>1. </span>Overview</h1> +<p><b><a href="syntax/with-clause.html">with-clause:</a></b> +<button id='x2257' onclick='hideorshow("x2257","x2258")'>hide</button></p> + <div id='x2258' class='imgcontainer'> + <div style="max-width:1056px"><svg xmlns='http://www.w3.org/2000/svg' class="pikchr" viewBox="0 0 1056.72 140.4"> +<circle cx="5" cy="85" r="3.6" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<polygon points="32,85 20,89 20,81" style="fill:rgb(0,0,0)"/> +<path d="M9,85L26,85" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<path d="M47,100L78,100A15 15 0 0 0 93 85A15 15 0 0 0 78 70L47,70A15 15 0 0 0 32 85A15 15 0 0 0 47 100Z" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<text x="62" y="85" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">WITH</text> +<polygon points="134,55 123,59 123,50" style="fill:rgb(0,0,0)"/> +<path d="M93,85 L 100,85 Q 108,85 108,70 L 108,70 Q 108,55 118,55 L 129,55" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<path d="M150,70L235,70A15 15 0 0 0 250 55L250,55A15 15 0 0 0 235 39L150,39A15 15 0 0 0 134 55L134,55A15 15 0 0 0 150 70Z" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<text x="192" y="55" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">RECURSIVE</text> +<path d="M250,55 L 258,55 Q 265,55 265,70 L 265,70 Q 265,85 273,85 L 280,85" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<polygon points="307,85 295,89 295,81" style="fill:rgb(0,0,0)"/> +<path d="M280,85L301,85" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<path d="M307,100L444,100L444,70L307,70Z" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<text x="375" y="85" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">cte-table-name</text> +<polygon points="467,85 455,89 455,81" style="fill:rgb(0,0,0)"/> +<path d="M444,85L461,85" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<path d="M482,100L486,100A15 15 0 0 0 501 85A15 15 0 0 0 486 70L482,70A15 15 0 0 0 467 85A15 15 0 0 0 482 100Z" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<text x="484" y="85" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">AS</text> +<polygon points="542,17 531,21 531,12" style="fill:rgb(0,0,0)"/> +<path d="M501,85 L 508,85 Q 516,85 516,70 L 516,32 Q 516,17 526,17 L 537,17" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<path d="M558,32L578,32A15 15 0 0 0 593 17L593,17A15 15 0 0 0 578 2L558,2A15 15 0 0 0 542 17L542,17A15 15 0 0 0 558 32Z" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<text x="568" y="17" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">NOT</text> +<polygon points="610,17 599,21 599,12" style="fill:rgb(0,0,0)"/> +<path d="M593,17L604,17" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<path d="M625,32L743,32A15 15 0 0 0 759 17L759,17A15 15 0 0 0 743 2L625,2A15 15 0 0 0 610 17L610,17A15 15 0 0 0 625 32Z" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<text x="684" y="17" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">MATERIALIZED</text> +<polygon points="800,85 789,89 789,81" style="fill:rgb(0,0,0)"/> +<path d="M759,17 L 766,17 Q 774,17 774,32 L 774,70 Q 774,85 784,85 L 794,85" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<path d="M815,100A15 15 0 0 0 830 85A15 15 0 0 0 815 70A15 15 0 0 0 800 85A15 15 0 0 0 815 100Z" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<text x="815" y="85" text-anchor="middle" font-weight="bold" fill="rgb(0,0,0)" dominant-baseline="central">(</text> +<polygon points="853,85 842,89 842,81" style="fill:rgb(0,0,0)"/> +<path d="M830,85L848,85" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<path d="M853,100L958,100L958,70L853,70Z" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<text x="905" y="85" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">select-stmt</text> +<polygon points="981,85 969,89 969,81" style="fill:rgb(0,0,0)"/> +<path d="M958,85L975,85" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<path d="M996,100A15 15 0 0 0 1011 85A15 15 0 0 0 996 70A15 15 0 0 0 981 85A15 15 0 0 0 996 100Z" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<text x="996" y="85" text-anchor="middle" font-weight="bold" fill="rgb(0,0,0)" dominant-baseline="central">)</text> +<polygon points="1047,85 1035,89 1035,81" style="fill:rgb(0,0,0)"/> +<path d="M1011,85L1041,85" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<circle cx="1050" cy="85" r="3.6" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<polygon points="542,56 531,60 531,52" style="fill:rgb(0,0,0)"/> +<path d="M501,85 L 508,85 Q 516,85 516,70 Q 516,56 526,56 L 537,56" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<path d="M558,71L676,71A15 15 0 0 0 691 56A15 15 0 0 0 676 41L558,41A15 15 0 0 0 542 56A15 15 0 0 0 558 71Z" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<text x="617" y="56" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">MATERIALIZED</text> +<polygon points="759,56 747,60 747,52" style="fill:rgb(0,0,0)"/> +<path d="M691,56L753,56" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<path d="M759,56 L 766,56 Q 774,56 774,64 L 774,71" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<polygon points="617,85 605,89 605,81" style="fill:rgb(0,0,0)"/> +<path d="M501,85L611,85" 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onclick='hideorshow("x2259","x2260")'>show</button></p> + <div id='x2260' style='display:none;' class='imgcontainer'> + <div style="max-width:475px"><svg xmlns='http://www.w3.org/2000/svg' class="pikchr" viewBox="0 0 475.949 91.8"> +<circle cx="5" cy="36" r="3.6" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<polygon points="32,36 20,41 20,32" style="fill:rgb(0,0,0)"/> +<path d="M9,36L26,36" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<path d="M47,51L122,51A15 15 0 0 0 137 36A15 15 0 0 0 122 21L47,21A15 15 0 0 0 32 36A15 15 0 0 0 47 51Z" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<text x="85" y="36" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">table-name</text> +<polygon points="173,36 162,41 162,32" style="fill:rgb(0,0,0)"/> +<path d="M137,36L168,36" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<path d="M188,51A15 15 0 0 0 204 36A15 15 0 0 0 188 21A15 15 0 0 0 173 36A15 15 0 0 0 188 51Z" 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onclick='hideorshow("x2283","x2284")'>show</button></p> + <div id='x2284' style='display:none;' class='imgcontainer'> + <div style="max-width:793px"><svg xmlns='http://www.w3.org/2000/svg' class="pikchr" viewBox="0 0 793.282 84.24"> +<circle cx="5" cy="17" r="3.6" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<polygon points="32,17 20,21 20,12" style="fill:rgb(0,0,0)"/> +<path d="M9,17L26,17" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<path d="M32,32L193,32L193,2L32,2Z" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<text x="112" y="17" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">table-or-subquery</text> +<polygon points="259,47 247,51 247,43" style="fill:rgb(0,0,0)"/> +<path d="M193,17 L 200,17 Q 208,17 208,32 L 208,32 Q 208,47 223,47 L 238,47 L 253,47" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<path d="M259,62L380,62L380,32L259,32Z" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<text x="319" 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style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<text x="617" y="395" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">CURRENT</text> +<polygon points="690,395 678,399 678,390" style="fill:rgb(0,0,0)"/> +<path d="M667,395L684,395" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<path d="M705,410L729,410A15 15 0 0 0 744 395A15 15 0 0 0 729 380L705,380A15 15 0 0 0 690 395A15 15 0 0 0 705 410Z" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<text x="717" y="395" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">ROW</text> +<polygon points="767,395 756,399 756,390" style="fill:rgb(0,0,0)"/> +<path d="M744,395L762,395" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<path d="M767,395 L 775,395 Q 782,395 782,402 L 782,410" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<path d="M461,448L529,448A15 15 0 0 0 544 433A15 15 0 0 0 529 417L461,417A15 15 0 0 0 446 433A15 15 0 0 0 461 448Z" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<text x="495" y="433" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">EXCLUDE</text> +<polygon points="567,433 555,437 555,428" style="fill:rgb(0,0,0)"/> +<path d="M544,433L561,433" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<path d="M582,448L625,448A15 15 0 0 0 640 433A15 15 0 0 0 625 417L582,417A15 15 0 0 0 567 433A15 15 0 0 0 582 448Z" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<text x="604" y="433" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">GROUP</text> +<polygon points="767,433 756,437 756,428" style="fill:rgb(0,0,0)"/> +<path d="M640,433L762,433" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<path d="M767,433 L 775,433 Q 782,433 782,440 L 782,448" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<path d="M461,486L529,486A15 15 0 0 0 544 470A15 15 0 0 0 529 455L461,455A15 15 0 0 0 446 470A15 15 0 0 0 461 486Z" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<text x="495" y="470" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">EXCLUDE</text> +<polygon points="567,470 555,475 555,466" style="fill:rgb(0,0,0)"/> +<path d="M544,470L561,470" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<path d="M582,486L604,486A15 15 0 0 0 619 470A15 15 0 0 0 604 455L582,455A15 15 0 0 0 567 470A15 15 0 0 0 582 486Z" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<text x="593" y="470" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">TIES</text> +<polygon points="767,470 756,475 756,466" style="fill:rgb(0,0,0)"/> +<path d="M619,470L762,470" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<path d="M767,470 L 775,470 Q 782,470 782,478 L 782,485" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<path d="M461,372L529,372A15 15 0 0 0 544 357A15 15 0 0 0 529 342L461,342A15 15 0 0 0 446 357A15 15 0 0 0 461 372Z" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<text x="495" y="357" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">EXCLUDE</text> +<polygon points="567,357 555,361 555,353" style="fill:rgb(0,0,0)"/> +<path d="M544,357L561,357" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<path d="M582,372L591,372A15 15 0 0 0 606 357A15 15 0 0 0 591 342L582,342A15 15 0 0 0 567 357A15 15 0 0 0 582 372Z" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<text x="586" y="357" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">NO</text> +<polygon points="629,357 617,361 617,353" style="fill:rgb(0,0,0)"/> +<path d="M606,357L623,357" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<path d="M644,372L700,372A15 15 0 0 0 715 357A15 15 0 0 0 700 342L644,342A15 15 0 0 0 629 357A15 15 0 0 0 644 372Z" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<text x="672" y="357" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">OTHERS</text> +<polygon points="767,357 756,361 756,353" style="fill:rgb(0,0,0)"/> +<path d="M715,357L762,357" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<polygon points="890,516 879,520 879,511" style="fill:rgb(0,0,0)"/> +<path d="M767,357 L 775,357 Q 782,357 782,372 L 782,501 Q 782,516 797,516 L 870,516 L 885,516" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<circle cx="894" cy="516" r="3.6" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<polygon points="710,304 722,300 722,308" style="fill:rgb(0,0,0)"/> +<path d="M1001,304L716,304" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<polygon points="527,516 516,520 516,511" style="fill:rgb(0,0,0)"/> +<path d="M710,304 L 434,304 Q 419,304 419,319 L 419,501 Q 419,516 434,516 L 507,516 L 522,516" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<path d="M527,516L797,516" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<polygon points="446,357 434,361 434,353" style="fill:rgb(0,0,0)"/> +<path d="M419,342 L 419,349 Q 419,357 430,357 L 440,357" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<polygon points="446,395 434,399 434,390" style="fill:rgb(0,0,0)"/> +<path d="M419,380 L 419,387 Q 419,395 430,395 L 440,395" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<polygon points="446,433 434,437 434,428" style="fill:rgb(0,0,0)"/> +<path d="M419,417 L 419,425 Q 419,433 430,433 L 440,433" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<polygon points="446,470 434,475 434,466" style="fill:rgb(0,0,0)"/> +<path d="M419,455 L 419,463 Q 419,470 430,470 L 440,470" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +</svg> +</div> +</div> +</div> +</div> +</div> + + +<p>Common Table Expressions or CTEs act like temporary <a href="lang_createview.html">views</a> that exist +only for the duration of a single SQL statement. There are two kinds of +common table expressions: "ordinary" and "recursive". Ordinary +common table expressions are helpful for making +queries easier to understand by factoring +subqueries out of the main SQL statement. +Recursive common table expressions +provide the ability to do hierarchical or +recursive queries of trees and graphs, a capability +that is not otherwise available in the SQL language. + +</p><p>All common table expressions (ordinary and recursive) are +created by prepending a WITH clause in front of a <a href="lang_select.html">SELECT</a>, <a href="lang_insert.html">INSERT</a>, <a href="lang_delete.html">DELETE</a>, +or <a href="lang_update.html">UPDATE</a> statement. A single WITH clause can specify one or more +common table expressions, some of which are ordinary and some of which +are recursive. + +<a name="ordinarycte"></a> + +</p><h1 id="ordinary_common_table_expressions"><span>2. </span>Ordinary Common Table Expressions</h1> + +<p>An ordinary common table expression works as if it were a <a href="lang_createview.html">view</a> that +exists for the duration of a single statement. Ordinary common table +expressions are useful for factoring out subqueries and making the overall +SQL statement easier to read and understand. + +</p><p>A WITH clause can contain ordinary common table expressions even if +it includes the RECURSIVE keyword. The use of RECURSIVE does not force +common table expressions to be recursive. + +<a name="recursivecte"></a> + +</p><h1 id="recursive_common_table_expressions"><span>3. </span>Recursive Common Table Expressions</h1> + +<p>A recursive common table expression can be used to write a query that +walks a tree or graph. A recursive common table expression has the same +basic syntax as an ordinary common table expression, but with the following +additional attributes: + +</p><ol> +<li> The "<a href="syntax/select-stmt.html">select-stmt</a>" must be a <a href="lang_select.html#compound">compound select</a>. That is to say, + the CTE body must be two or more individual SELECT statements + separated by compound operators like UNION, UNION ALL, INTERSECT, + or EXCEPT. +</li><li> One or more of the individual SELECT statements that make up + the compound must be + "recursive". A SELECT statement is a recursive if + its FROM clause contains exactly one reference to the + the CTE table (the table named on the left-hand side of the + AS clause). +</li><li> One or more of the SELECT statements in the compound must be + non-recursive. +</li><li> All non-recursive SELECT statements must occur before any + recursive SELECT statements. +</li><li> The recursive SELECT statements must be separated from the + non-recursive SELECT statements + and from each other by the UNION or UNION ALL operators. + If there are two or more recursive SELECT statements, they all must + be separated from each other using the same operator that separates + the first recursive SELECT from the last non-recursive SELECT statement. +</li><li> Recursive SELECT statements may not use + <a href="lang_aggfunc.html">aggregate functions</a> or <a href="windowfunctions.html">window functions</a>. +</li></ol> + +<p>To put it another way, a recursive common table expression must +look something like the following: + +<p><b><a href="syntax/recursive-cte.html">recursive-cte:</a></b> +<button id='x2299' onclick='hideorshow("x2299","x2300")'>hide</button></p> + <div id='x2300' class='imgcontainer'> + <div style="max-width:874px"><svg xmlns='http://www.w3.org/2000/svg' class="pikchr" viewBox="0 0 874.291 72.36"> +<circle cx="5" cy="17" r="3.6" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<polygon points="32,17 20,21 20,12" style="fill:rgb(0,0,0)"/> +<path d="M9,17L26,17" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<path d="M32,32L169,32L169,2L32,2Z" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<text x="100" y="17" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">cte-table-name</text> +<polygon points="192,17 180,21 180,12" style="fill:rgb(0,0,0)"/> +<path d="M169,17L186,17" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<path d="M207,32L211,32A15 15 0 0 0 226 17A15 15 0 0 0 211 2L207,2A15 15 0 0 0 192 17A15 15 0 0 0 207 32Z" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<text x="209" y="17" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">AS</text> +<polygon points="249,17 237,21 237,12" style="fill:rgb(0,0,0)"/> +<path d="M226,17L243,17" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<path d="M264,32A15 15 0 0 0 279 17A15 15 0 0 0 264 2A15 15 0 0 0 249 17A15 15 0 0 0 264 32Z" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<text x="264" y="17" text-anchor="middle" font-weight="bold" fill="rgb(0,0,0)" dominant-baseline="central">(</text> +<polygon points="302,17 291,21 291,12" style="fill:rgb(0,0,0)"/> +<path d="M279,17L296,17" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<path d="M317,32L403,32A15 15 0 0 0 418 17A15 15 0 0 0 403 2L317,2A15 15 0 0 0 302 17A15 15 0 0 0 317 32Z" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<text x="360" y="17" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">initial-select</text> +<polygon points="459,55 448,59 448,50" style="fill:rgb(0,0,0)"/> +<path d="M418,17 L 425,17 Q 433,17 433,32 L 433,40 Q 433,55 443,55 L 454,55" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<path d="M474,70L518,70A15 15 0 0 0 533 55L533,55A15 15 0 0 0 518 39L474,39A15 15 0 0 0 459 55L459,55A15 15 0 0 0 474 70Z" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<text x="496" y="55" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">UNION</text> +<polygon points="556,55 545,59 545,50" style="fill:rgb(0,0,0)"/> +<path d="M533,55L550,55" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<path d="M571,70L586,70A15 15 0 0 0 601 55L601,55A15 15 0 0 0 586 39L571,39A15 15 0 0 0 556 55L556,55A15 15 0 0 0 571 70Z" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<text x="579" y="55" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">ALL</text> +<polygon points="643,17 631,21 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style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<circle cx="868" cy="17" r="3.6" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<polygon points="459,17 448,21 448,12" style="fill:rgb(0,0,0)"/> +<path d="M418,17L454,17" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<path d="M474,32L518,32A15 15 0 0 0 533 17A15 15 0 0 0 518 2L474,2A15 15 0 0 0 459 17A15 15 0 0 0 474 32Z" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<text x="496" y="17" text-anchor="middle" fill="rgb(0,0,0)" dominant-baseline="central">UNION</text> +<path d="M533,17L631,17" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +</svg> +</div> +<p><b><a href="syntax/cte-table-name.html">cte-table-name:</a></b> +<button id='x2301' onclick='hideorshow("x2301","x2302")'>show</button></p> + <div id='x2302' style='display:none;' class='imgcontainer'> + <div style="max-width:475px"><svg xmlns='http://www.w3.org/2000/svg' class="pikchr" viewBox="0 0 475.949 91.8"> +<circle 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style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<path d="M302,89A15 15 0 0 0 317 74L317,74A15 15 0 0 0 302 59A15 15 0 0 0 287 74L287,74A15 15 0 0 0 302 89Z" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<text x="302" y="74" text-anchor="middle" font-weight="bold" fill="rgb(0,0,0)" dominant-baseline="central">,</text> +<polygon points="317,74 328,70 328,78" style="fill:rgb(0,0,0)"/> +<path d="M364,36 L 371,36 Q 379,36 379,51 L 379,59 Q 379,74 364,74 L 338,74 L 323,74" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<path d="M287,74 L 232,74 Q 217,74 217,59 L 217,51 Q 217,36 224,36 L 232,36" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<polygon points="302,6 290,10 290,2" style="fill:rgb(0,0,0)"/> +<path d="M137,36 L 145,36 Q 152,36 152,21 L 152,21 Q 152,6 167,6 L 281,6 L 296,6" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +<path d="M302,6 L 422,6 Q 437,6 437,21 L 437,21 Q 437,36 445,36 L 452,36" style="fill:none;stroke-width:2.16;stroke:rgb(0,0,0);" /> +</svg> +</div> +</div> +</div> + + +</p><p>In the diagram above, <span class='yyterm'>initial-select</span> means one or more +non-recursive SELECT statements and <span class='yyterm'>recursive-select</span> means +one or more recursive SELECT statements. The most common case is for there +to be exactly one <span class='yyterm'>initial-select</span> and exactly one +<span class='yyterm'>recursive-select</span> but more than one of each is allowed.</p> + +<p>Call the table named by the <a href="syntax/cte-table-name.html">cte-table-name</a> in a recursive +common table expression the "recursive table". +In the <a href="syntax/recursive-cte.html">recursive-cte</a> bubble diagram above, the recursive +table must appear exactly once in the FROM clause of each +top-level SELECT statement in the <span class='yyterm'>recursive-select</span> +and must not appear anywhere else in either the +<span class='yyterm'>initial-select</span> or the +<span class='yyterm'>recursive-select</span>, including subqueries. +The <span class='yyterm'>initial-select</span> may be +a <a href="lang_select.html#compound">compound select</a>, but it may not include an ORDER BY, LIMIT, or OFFSET. +The <span class='yyterm'>recursive-select</span> may also be a <a href="lang_select.html#compound">compound select</a> with +the restriction that all elements of that compound must be separated by +the same UNION or UNION ALL operator that separates +<span class='yyterm'>initial-select</span> from <span class='yyterm'>recursive-select</span>. +The <span class='yyterm'>recursive-select</span> is allowed to include an +ORDER BY, LIMIT, and/or OFFSET but may not use +<a href="lang_aggfunc.html">aggregate functions</a> or <a href="windowfunctions.html">window functions</a>. + +</p><p>The ability for the <span class='yyterm'>recursive-select</span> to be a compound +was added in <a href="releaselog/3_34_0.html">version 3.34.0</a> (2020-12-01). In earlier versions of +SQLite, the <span class='yyterm'>recursive-select</span> could only be a single +simple SELECT statement.</p> + +<p>The basic algorithm for computing the content of the recursive table +is as follows: + +</p><ol> +<li> Run the <span class='yyterm'>initial-select</span> and add the results to a queue. +</li><li> While the queue is not empty: +<ol type="a"> +<li> Extract a single row from the queue. +</li><li> Insert that single row into the recursive table +</li><li> Pretend that the single row just extracted is the only + row in the recursive table and run the recursive-select, + adding all results to the queue. +</li></ol> +</li></ol> + +<p>The basic procedure above may modified by the following additional rules: + +</p><ul> +<li><p> + If a UNION operator connects the <span class='yyterm'>initial-select</span> with the + <span class='yyterm'>recursive-select</span>, then only add rows to the queue if + no identical row has + been previously added to the queue. Repeated rows are discarded before being + added to the queue even if the repeated rows have already been extracted + from the queue by the recursion step. If the operator is UNION ALL, + then all rows generated by both the <span class='yyterm'>initial-select</span> and the + <span class='yyterm'>recursive-select</span> are always added to the queue even if + they are repeats. + When determining if a row is repeated, NULL values compare + equal to one another and not equal to any other value. +</p></li><li><p> + The LIMIT clause, if present, determines the maximum number of rows that + will ever be added to the recursive table in step 2b. + Once the limit is reached, the recursion stops. + A limit of zero means that no rows are ever added to the + recursive table, and a negative limit means an unlimited number of rows + may be added to the recursive table. +</p></li><li><p> + The OFFSET clause, if it is present and has a positive value N, prevents the + first N rows from being added to the recursive table. + The first N rows are still processed + by the <span class='yyterm'>recursive-select</span> — they + just are not added to the recursive table. Rows are not counted toward + fulfilling the LIMIT until all OFFSET rows have been skipped. +</p></li><li><p> + If an ORDER BY clause is present, it determines the order in which rows + are extracted from the queue in step 2a. If there is no ORDER BY clause, + then the order in which rows are extracted is undefined. (In the current + implementation, the queue becomes a FIFO if the ORDER BY clause is omitted, + but applications should not depend on that fact since it might change.) +</p></li></ul> + +<a name="rcex1"></a> + +<h2 id="recursive_query_examples"><span>3.1. </span>Recursive Query Examples</h2> + +<p>The following query returns all integers between 1 and 1000000: + +</p><blockquote><pre> +WITH RECURSIVE + cnt(x) AS (VALUES(1) UNION ALL SELECT x+1 FROM cnt WHERE x<1000000) +SELECT x FROM cnt; +</pre></blockquote> + +<p>Consider how this query works. The initial-select +runs first and returns a single row +with a single column "1". This one row is added to the queue. In +step 2a, that one row is extracted from the queue and added to "cnt". +Then the recursive-select is run in accordance with step 2c generating +a single new row with value "2" to add to the queue. The queue still +has one row, so step 2 repeats. The "2" row is extracted and added to the +recursive table by steps 2a and 2b. Then the row containing 2 is used +as if it were the complete content of the recursive table and the +recursive-select is run again, resulting in a row with value "3" being added +to the queue. This repeats 999999 times until finally at step 2a the +only value on the queue is a row containing 1000000. That row is +extracted and added to the recursive table. But this time, the +WHERE clause causes the recursive-select to return no rows, so the +queue remains empty and the recursion stops. + +</p><p><b>Optimization note:</b> +In the discussion above, statements like "insert the row into +the recursive table" should be understood conceptually, not literally. +It sounds as if SQLite is accumulating a huge table +containing one million rows, then going back and scanning that table +from top to bottom to generate the result. What really happens +is that the query optimizer sees that values in the +"cnt" recursive table are only used once. So as each row is added to +the recursive table, that row is immediately returned as a result of the main +SELECT statement and then discarded. SQLite does <em>not</em> accumulate +a temporary table containing a million rows. Very little memory is +needed to run the above example. However, if the example had used +UNION instead of UNION ALL, then SQLite would have had to keep around +all previously generated content in order to check for duplicates. +For this reason, programmers should strive to use UNION ALL instead +of UNION when feasible. + +</p><p>Here is a variation on the previous example: + +</p><blockquote><pre> +WITH RECURSIVE + cnt(x) AS ( + SELECT 1 + UNION ALL + SELECT x+1 FROM cnt + LIMIT 1000000 + ) +SELECT x FROM cnt; +</pre></blockquote> + +<p>There are two differences in this variation. The initial-select is +"SELECT 1" instead of "VALUES(1)". But those are just different +syntaxes for saying exactly the same thing. The other change is that the +recursion is stopped by a LIMIT rather than a WHERE clause. The use of +LIMIT means that when the one-millionth row is added to the "cnt" table +(and returned by the main SELECT, thanks to the query optimizer) +then the recursion stops immediately regardless of how many rows might be +left in the queue. On more complex queries, it can sometimes be +difficult to ensure that the WHERE clause will eventually cause the +queue to drain and the recursion to terminate. But the LIMIT clause will +always stop the recursion. So it is good practice to always include a +LIMIT clause as a safety if an upper bound on the size of the recursion +is known. + +<a name="rcex2"></a> + +</p><h2 id="hierarchical_query_examples"><span>3.2. </span>Hierarchical Query Examples</h2> + +<p>Consider a table that describes the members of an organization as +well as the chain-of-command within that organization: + +</p><blockquote><pre> +CREATE TABLE org( + name TEXT PRIMARY KEY, + boss TEXT REFERENCES org, + height INT, + -- other content omitted +); +</pre></blockquote> + +<p>Every member in the organization has a name, and most members have +a single boss. (The head of the whole organization has a NULL +"boss" field.) The rows of the "org" table form a tree. + +</p><p>Here is a query that computes the average height over everyone +in Alice's organization, including Alice: + +</p><blockquote><pre> +WITH RECURSIVE + works_for_alice(n) AS ( + VALUES('Alice') + UNION + SELECT name FROM org, works_for_alice + WHERE org.boss=works_for_alice.n + ) +SELECT avg(height) FROM org + WHERE org.name IN works_for_alice; +</pre></blockquote> + +<p>The next example uses two +common table expressions in a single WITH clause. +The following table records a family tree: + +</p><blockquote><pre> +CREATE TABLE family( + name TEXT PRIMARY KEY, + mom TEXT REFERENCES family, + dad TEXT REFERENCES family, + born DATETIME, + died DATETIME, -- NULL if still alive + -- other content +); +</pre></blockquote> + +<p>The "family" table is similar to the earlier "org" table except that +now there are two parents to each member. +We want to know all living ancestors of Alice, from oldest to youngest. +An ordinary common table expression, "parent_of", is defined first. That +ordinary CTE is a view that can be used to find all parents of any +individual. That ordinary CTE is then used in the "ancestor_of_alice" +recursive CTE. The recursive CTE is then used in the final query: + +</p><blockquote><pre> +WITH RECURSIVE + parent_of(name, parent) AS + (SELECT name, mom FROM family UNION SELECT name, dad FROM family), + ancestor_of_alice(name) AS + (SELECT parent FROM parent_of WHERE name='Alice' + UNION ALL + SELECT parent FROM parent_of JOIN ancestor_of_alice USING(name)) +SELECT family.name FROM ancestor_of_alice, family + WHERE ancestor_of_alice.name=family.name + AND died IS NULL + ORDER BY born; +</pre></blockquote> + +<a name="rcex3"></a> + +<h2 id="queries_against_a_graph"><span>3.3. </span>Queries Against A Graph</h2> + +<p>Suppose you have an undirected graph where each node is +identified by an integer and edges are defined by a table like +this: + +</p><blockquote><pre> +CREATE TABLE edge(aa INT, bb INT); +CREATE INDEX edge_aa ON edge(aa); +CREATE INDEX edge_bb ON edge(bb); +</pre></blockquote> + +<p>The indexes are not required, but they do help performance +for large graphs. +To find all nodes of the graph that are connected to +node 59, use a query similar to the following: + +</p><blockquote><pre> +WITH RECURSIVE nodes(x) AS ( + SELECT 59 + UNION + SELECT aa FROM edge JOIN nodes ON bb=x + UNION + SELECT bb FROM edge JOIN nodes ON aa=x +) +SELECT x FROM nodes; +</pre></blockquote> + +<p> +The <span class='yyterm'>initial-select</span> in this case is the simple query +"SELECT 59". This establishes the base case. The +<span class='yyterm'>recursive-select</span> consists of the other two +SELECT statements. The first recursive SELECT follows edges +in the bb-to-aa direction and the second recursive SELECT follows +edges in the aa-to-bb direction. UNION is used instead of +UNION ALL to prevent the recursion from entering an infinite +loop if the graph contains cycles. +</p> + +<p>Here is a real-world example of using a graph query against a +directed graph: +A version control system (VCS) will typically store the evolving +versions of a project as a directed acyclic graph (DAG). Call each +version of the project a "checkin". A single +checkin can have zero or more parents. Most checkins (except the +first) have a single parent, but in the case of a merge, a checkin +might have two or three or more parents. A schema to keep track of +checkins and the order in which they occur might look something like +this: + +</p><blockquote><pre> +CREATE TABLE checkin( + id INTEGER PRIMARY KEY, + mtime INTEGER -- timestamp when this checkin occurred +); +CREATE TABLE derivedfrom( + xfrom INTEGER NOT NULL REFERENCES checkin, -- parent checkin + xto INTEGER NOT NULL REFERENCES checkin, -- derived checkin + PRIMARY KEY(xfrom,xto) +); +CREATE INDEX derivedfrom_back ON derivedfrom(xto,xfrom); +</pre></blockquote> + +<p>This graph is acyclic. And we assume that the mtime of every +child checkin is no less than the mtime of all its parents. But +unlike the earlier examples, this graph might have multiple paths of +differing lengths between any two checkins. + +</p><p>We want to know the twenty most recent ancestors in time (out of +the thousands and thousands of ancestors in the whole DAG) for +checkin "@BASELINE". (A query similar to this is used +by the <a href="http://www.fossil-scm.org/">Fossil</a> VCS to +show the N most recent ancestors of a checkin. For example: +<a href="http://www.sqlite.org/src/timeline?p=trunk&n=30">http://www.sqlite.org/src/timeline?p=trunk&n=30</a>.) + +</p><blockquote><pre> +WITH RECURSIVE + ancestor(id,mtime) AS ( + SELECT id, mtime FROM checkin WHERE id=@BASELINE + UNION + SELECT derivedfrom.xfrom, checkin.mtime + FROM ancestor, derivedfrom, checkin + WHERE ancestor.id=derivedfrom.xto + AND checkin.id=derivedfrom.xfrom + ORDER BY checkin.mtime DESC + LIMIT 20 + ) +SELECT * FROM checkin JOIN ancestor USING(id); +</pre></blockquote> + +<p> +The "ORDER BY checkin.mtime DESC" term in the recursive-select makes +the query run much faster by preventing it from following +branches that merge checkins +from long ago. The ORDER BY forces the recursive-select to focus +on the most recent checkins, the ones we want. Without the ORDER BY +on the recursive-select, one would be forced to compute the complete set of +thousands of ancestors, sort them all by mtime, then take the top twenty. +The ORDER BY essentially sets up a priority queue that +forces the recursive query to look at the most recent ancestors first, +allowing the use of a LIMIT clause to restrict the scope of the +query to just the checkins of interest. + +<a name="withorderby"></a> + +</p><h2 id="controlling_depth_first_versus_breadth_first_search_of_a_tree_using_order_by"><span>3.4. </span>Controlling Depth-First Versus Breadth-First Search Of a Tree +Using ORDER BY</h2> + +<p>An ORDER BY clause on the recursive-select can be used to control +whether the search of a tree is depth-first or breadth-first. To +illustrate, we will use a variation on the "org" table from an example +above, without the "height" column, and with some real data inserted: + +</p><blockquote><pre> +CREATE TABLE org( + name TEXT PRIMARY KEY, + boss TEXT REFERENCES org +) WITHOUT ROWID; +INSERT INTO org VALUES('Alice',NULL); +INSERT INTO org VALUES('Bob','Alice'); +INSERT INTO org VALUES('Cindy','Alice'); +INSERT INTO org VALUES('Dave','Bob'); +INSERT INTO org VALUES('Emma','Bob'); +INSERT INTO org VALUES('Fred','Cindy'); +INSERT INTO org VALUES('Gail','Cindy'); +</pre></blockquote> + +<p>Here is a query to show the tree structure in a breadth-first pattern: + +</p><blockquote><pre> +WITH RECURSIVE + under_alice(name,level) AS ( + VALUES('Alice',0) + UNION ALL + SELECT org.name, under_alice.level+1 + FROM org JOIN under_alice ON org.boss=under_alice.name + ORDER BY 2 + ) +SELECT substr('..........',1,level*3) || name FROM under_alice; +</pre></blockquote> + +<p>The "ORDER BY 2" (which means the same as "ORDER BY under_alice.level+1") +causes higher levels in the organization chart (with smaller "level" values) +to be processed first, resulting in a breadth-first search. The output is: + +</p><blockquote><pre> +Alice +...Bob +...Cindy +......Dave +......Emma +......Fred +......Gail +</pre></blockquote> + +<p>But if we change the ORDER BY clause to add the "DESC" modifier, that will +cause lower levels in the organization (with larger "level" values) to be +processed first by the recursive-select, resulting in a depth-first search: + +</p><blockquote><pre> +WITH RECURSIVE + under_alice(name,level) AS ( + VALUES('Alice',0) + UNION ALL + SELECT org.name, under_alice.level+1 + FROM org JOIN under_alice ON org.boss=under_alice.name + ORDER BY 2 <b>DESC</b> + ) +SELECT substr('..........',1,level*3) || name FROM under_alice; +</pre></blockquote> + +<p>The output of this revised query is: + +</p><blockquote><pre> +Alice +...Bob +......Dave +......Emma +...Cindy +......Fred +......Gail +</pre></blockquote> + +<p>When the ORDER BY clause is omitted from the recursive-select, the +queue behaves as a FIFO, which results in a breadth-first search. + + +<a name="mandelbrot"></a> + +</p><h2 id="outlandish_recursive_query_examples"><span>3.5. </span>Outlandish Recursive Query Examples</h2> + +<p>The following query computes an approximation of the Mandelbrot Set +and outputs the result as ASCII-art: + +</p><blockquote><pre> +WITH RECURSIVE + xaxis(x) AS (VALUES(-2.0) UNION ALL SELECT x+0.05 FROM xaxis WHERE x<1.2), + yaxis(y) AS (VALUES(-1.0) UNION ALL SELECT y+0.1 FROM yaxis WHERE y<1.0), + m(iter, cx, cy, x, y) AS ( + SELECT 0, x, y, 0.0, 0.0 FROM xaxis, yaxis + UNION ALL + SELECT iter+1, cx, cy, x*x-y*y + cx, 2.0*x*y + cy FROM m + WHERE (x*x + y*y) < 4.0 AND iter<28 + ), + m2(iter, cx, cy) AS ( + SELECT max(iter), cx, cy FROM m GROUP BY cx, cy + ), + a(t) AS ( + SELECT group_concat( substr(' .+*#', 1+min(iter/7,4), 1), '') + FROM m2 GROUP BY cy + ) +SELECT group_concat(rtrim(t),x'0a') FROM a; +</pre></blockquote> + +<p>In this query, the "xaxis" and "yaxis" CTEs define the grid of points for +which the Mandelbrot Set will be approximated. Each row in the +"m(iter,cx,cy,x,y)" CTE means that after "iter" iterations, the Mandelbrot +iteration starting at cx,cy has reached point x,y. The number of iterations +in this example is limited to 28 (which severely limits the resolution of +the computation, but is sufficient for low-resolution ASCII-art output). +The "m2(iter,cx,cy)" CTE holds the maximum number of iterations reached when +starting at point cx,cy. +Finally, each row in the "a(t)" CTE holds a string +which is a single line of the output ASCII-art. +The SELECT statement at the end just queries the "a" CTE to +retrieve all lines of ASCII-art, one by one. + +</p><p>Running the query above in an SQLite <a href="cli.html">command-line shell</a> results +in the following output: + +</p><blockquote><pre> + ....# + ..#*.. + ..+####+. + .......+####.... + + ..##+*##########+.++++ + .+.##################+. + .............+###################+.+ + ..++..#.....*#####################+. + ...+#######++#######################. + ....+*################################. + #############################################... + ....+*################################. + ...+#######++#######################. + ..++..#.....*#####################+. + .............+###################+.+ + .+.##################+. + ..##+*##########+.++++ + .......+####.... + + ..+####+. + ..#*.. + ....# + +. +</pre></blockquote> + +<a name="sudoku"></a> + +<p>This next query solves a Sudoku puzzle. The state of the puzzle is +defined by an 81-character string formed by reading entries from the +puzzle box row by row from left to right and then from top to bottom. +Blank squares in the puzzle are denoted by a "." character. +Thus the input string: + +</p><blockquote> +53..7....6..195....98....6.8...6...34..8.3..17...2...6.6....28....419..5....8..79 +</blockquote> + +<p>Corresponds to a puzzle like this: + +</p><blockquote> +<table border="1" cellpadding="5"> +<tr><td>5</td><td>3</td><td> </td><td> </td><td>7</td><td> </td><td> </td><td> </td><td> +</td></tr><tr><td>6</td><td> </td><td> </td><td>1</td><td>9</td><td>5</td><td> </td><td> </td><td> +</td></tr><tr><td> </td><td>9</td><td>8</td><td> </td><td> </td><td> </td><td> </td><td>6</td><td> +</td></tr><tr><td>8</td><td> </td><td> </td><td> </td><td>6</td><td> </td><td> </td><td> </td><td>3 +</td></tr><tr><td>4</td><td> </td><td> </td><td>8</td><td> </td><td>3</td><td> </td><td> </td><td>1 +</td></tr><tr><td>7</td><td> </td><td> </td><td> </td><td>2</td><td> </td><td> </td><td> </td><td>6 +</td></tr><tr><td> </td><td>6</td><td> </td><td> </td><td> </td><td> </td><td>2</td><td>8</td><td> +</td></tr><tr><td> </td><td> </td><td> </td><td>4</td><td>1</td><td>9</td><td> </td><td> </td><td>5 +</td></tr><tr><td> </td><td> </td><td> </td><td> </td><td>8</td><td> </td><td> </td><td>7</td><td>9 +</td></tr></table> +</blockquote> + +<p>This is the query that solves the puzzle: + +</p><blockquote><pre> +WITH RECURSIVE + input(sud) AS ( + VALUES('53..7....6..195....98....6.8...6...34..8.3..17...2...6.6....28....419..5....8..79') + ), + digits(z, lp) AS ( + VALUES('1', 1) + UNION ALL SELECT + CAST(lp+1 AS TEXT), lp+1 FROM digits WHERE lp<9 + ), + x(s, ind) AS ( + SELECT sud, instr(sud, '.') FROM input + UNION ALL + SELECT + substr(s, 1, ind-1) || z || substr(s, ind+1), + instr( substr(s, 1, ind-1) || z || substr(s, ind+1), '.' ) + FROM x, digits AS z + WHERE ind>0 + AND NOT EXISTS ( + SELECT 1 + FROM digits AS lp + WHERE z.z = substr(s, ((ind-1)/9)*9 + lp, 1) + OR z.z = substr(s, ((ind-1)%9) + (lp-1)*9 + 1, 1) + OR z.z = substr(s, (((ind-1)/3) % 3) * 3 + + ((ind-1)/27) * 27 + lp + + ((lp-1) / 3) * 6, 1) + ) + ) +SELECT s FROM x WHERE ind=0; +</pre></blockquote> + +<p>The "input" CTE defines the input puzzle. +The "digits" CTE defines a table that holds all digits between 1 and 9. +The work of solving the puzzle is undertaken by the "x" CTE. +An entry in x(s,ind) means that the 81-character string "s" is a valid +sudoku puzzle (it has no conflicts) and that the first unknown character +is at position "ind", or ind==0 if all character positions are filled in. +The goal, then, is to compute entries for "x" with an "ind" of 0. + +</p><p>The solver works by adding new entries to the "x" recursive table. +Given prior entries, the recursive-select tries to fill in a single new +position with all values between 1 and 9 that actually work in that +position. The complicated "NOT EXISTS" subquery is the magic that +figures out whether or not each candidate "s" string is a valid +sudoku puzzle or not. + +</p><p>The final answer is found by looking for a string with ind==0. +If the original sudoku problem did not have a unique solution, then +the query will return all possible solutions. If the original problem +was unsolvable, then no rows will be returned. In this case, the unique +answer is: + +</p><blockquote> +534678912672195348198342567859761423426853791713924856961537284287419635345286179 +</blockquote> + +<p>The solution was computed in less than 300 milliseconds on a modern +workstation. + +<a name="mathint"></a> + +</p><h1 id="materialization_hints"><span>4. </span>Materialization Hints</h1> + +<p> +The "AS MATERIALIZED" and "AS NOT MATERIALIZED" forms of a common table expression +are non-standard SQL syntax copied from PostgreSQL. Using MATERIALIZED or +NOT MATERIALIZED after the AS keyword provides non-binding hints to the query +planner about how the CTE should be implemented. + +</p><p> +If the MATERIALIZED phrase is used, then <span class='yynonterm'>select-stmt</span> is +likely evaluated to generate an ephemeral table that is held in memory or a +temporary disk file, to be used in place of the +CTE table name whenever that table name appears in the subsequent SQL. +Because the <span class='yynonterm'>select-stmt</span> is evaluated immediately, +the opportunity to apply optimizations such as +<a href="optoverview.html#flattening">query flattening</a> or the <a href="optoverview.html#pushdown">push-down optimization</a>, is lost. +(The CTE then acts as an "optimization fence".) + +</p><p> +If the NOT MATERIALIZED phrase is used, then <span class='yynonterm'>select-stmt</span> +is substituted as a subquery in place of every occurrence of the CTE +table name. Optimizations such as <a href="optoverview.html#flattening">flattening</a> and +<a href="optoverview.html#pushdown">push-down</a> are then applied to the subquery as if +the subquery had by used in directly. In spite of its name, the NOT MATERIALIZED +phrase does not prohibit the use of materialization. The query planner +is still free to implement the subquery using materialization if +it feels that is the best solution. The true meaning of NOT MATERIALIZED +is closer to "TREAT LIKE ANY ORDINARY VIEW OR SUBQUERY". + +</p><p> +If neither hint is present, then SQLite 3.35.0 (2021-03-12) and +later process the CTE as if the MATERIALIZED phrase were present if the +CTE is used more than once, or as if the NOT MATERIALIZED phrase were +present if the CTE is used only once. Prior to SQLite 3.35.0, all +CTEs where treated as if the NOT MATERIALIZED phrase was present. +The decision of whether to treat a specific CTE as MATERIALIZED or +as NOT MATERIALIZED based on the number of uses is a heuristic that +is subject to change in future releases, if we come up with a better +query planning strategy. The difference is purely a matter of +performance. Equivalent answers should be computed either way. + +</p><p> +Applications should not depend upon the semantic effects of this hint +with respect to when or how often user-defined functions are called. +Future versions of the query planner may disregard this hint. + +</p><p> +The MATERIALIZED and NOT MATERIALIZED hints are only available in +SQLite version 3.35.0 (2021-03-12) and later. + +</p><h1 id="limitations_and_caveats"><span>5. </span>Limitations And Caveats</h1> + +<ul> +<li><p> +The WITH clause cannot be used within a <a href="lang_createtrigger.html">CREATE TRIGGER</a>. +</p></li><li><p> +The WITH clause must appear at the beginning of a top-level <a href="lang_select.html">SELECT</a> statement +or at the beginning of a subquery. The WITH clause cannot be prepended to +the second or subsequent SELECT statement of a <a href="lang_select.html#compound">compound select</a>. +</p></li><li><p> +The SQL:1999 spec requires that the RECURSIVE keyword follow WITH in any +WITH clause that includes a recursive common table expression. However, for +compatibility with SqlServer and Oracle, SQLite does not enforce this rule. +</p></li></ul> +<p align="center"><small><i>This page last modified on <a href="https://sqlite.org/docsrc/honeypot" id="mtimelink" data-href="https://sqlite.org/docsrc/finfo/pages/lang_with.in?m=b11c4b9e6087ba2a2">2022-01-17 12:21:35</a> UTC </small></i></p> + |