Skip to content
Snippets Groups Projects
Verified Commit 8e8cbebc authored by orestis.malaspin's avatar orestis.malaspin
Browse files

updated tri par tas

parent 081a23f2
Branches
Tags
No related merge requests found
Show whitespace changes
Inline Side-by-side
slides/figs/heap_tree.svg 0 → 100644
+ 498
− 0
View file @ 8e8cbebc
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!-- Created with Inkscape (http://www.inkscape.org/) -->
<svg
width="159.01459mm"
height="65.378784mm"
viewBox="0 0 159.01459 65.378784"
version="1.1"
id="svg5"
inkscape:version="1.1.2 (0a00cf5339, 2022-02-04)"
sodipodi:docname="heap_tree.svg"
xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
xmlns="http://www.w3.org/2000/svg"
xmlns:svg="http://www.w3.org/2000/svg">
<sodipodi:namedview
id="namedview7"
pagecolor="#ffffff"
bordercolor="#666666"
borderopacity="1.0"
inkscape:pageshadow="2"
inkscape:pageopacity="0.0"
inkscape:pagecheckerboard="0"
inkscape:document-units="mm"
showgrid="true"
inkscape:zoom="0.67081229"
inkscape:cx="168.45249"
inkscape:cy="78.263325"
inkscape:window-width="1920"
inkscape:window-height="1080"
inkscape:window-x="0"
inkscape:window-y="0"
inkscape:window-maximized="1"
inkscape:current-layer="layer1"
fit-margin-top="0"
fit-margin-left="0"
fit-margin-right="0"
fit-margin-bottom="0">
<inkscape:grid
type="xygrid"
id="grid824"
originx="-26.326043"
originy="-41.90753" />
</sodipodi:namedview>
<defs
id="defs2">
<marker
style="overflow:visible"
id="Arrow2Lend"
refX="0"
refY="0"
orient="auto"
inkscape:stockid="Arrow2Lend"
inkscape:isstock="true">
<path
transform="matrix(-1.1,0,0,-1.1,-1.1,0)"
d="M 8.7185878,4.0337352 -2.2072895,0.01601326 8.7185884,-4.0017078 c -1.7454984,2.3720609 -1.7354408,5.6174519 -6e-7,8.035443 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:context-stroke;stroke-width:0.625;stroke-linejoin:round"
id="path17053" />
</marker>
<marker
style="overflow:visible"
id="Arrow2Lend-8"
refX="0"
refY="0"
orient="auto"
inkscape:stockid="Arrow2Lend"
inkscape:isstock="true">
<path
transform="matrix(-1.1,0,0,-1.1,-1.1,0)"
d="M 8.7185878,4.0337352 -2.2072895,0.01601326 8.7185884,-4.0017078 c -1.7454984,2.3720609 -1.7354408,5.6174519 -6e-7,8.035443 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:context-stroke;stroke-width:0.625;stroke-linejoin:round"
id="path17053-7" />
</marker>
<marker
style="overflow:visible"
id="Arrow2Lend-2"
refX="0"
refY="0"
orient="auto"
inkscape:stockid="Arrow2Lend"
inkscape:isstock="true">
<path
transform="matrix(-1.1,0,0,-1.1,-1.1,0)"
d="M 8.7185878,4.0337352 -2.2072895,0.01601326 8.7185884,-4.0017078 c -1.7454984,2.3720609 -1.7354408,5.6174519 -6e-7,8.035443 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:context-stroke;stroke-width:0.625;stroke-linejoin:round"
id="path17053-0" />
</marker>
<marker
style="overflow:visible"
id="Arrow2Lend-8-2"
refX="0"
refY="0"
orient="auto"
inkscape:stockid="Arrow2Lend"
inkscape:isstock="true">
<path
transform="matrix(-1.1,0,0,-1.1,-1.1,0)"
d="M 8.7185878,4.0337352 -2.2072895,0.01601326 8.7185884,-4.0017078 c -1.7454984,2.3720609 -1.7354408,5.6174519 -6e-7,8.035443 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:context-stroke;stroke-width:0.625;stroke-linejoin:round"
id="path17053-7-3" />
</marker>
<marker
style="overflow:visible"
id="Arrow2Lend-8-2-9"
refX="0"
refY="0"
orient="auto"
inkscape:stockid="Arrow2Lend"
inkscape:isstock="true">
<path
transform="matrix(-1.1,0,0,-1.1,-1.1,0)"
d="M 8.7185878,4.0337352 -2.2072895,0.01601326 8.7185884,-4.0017078 c -1.7454984,2.3720609 -1.7354408,5.6174519 -6e-7,8.035443 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:context-stroke;stroke-width:0.625;stroke-linejoin:round"
id="path17053-7-3-2" />
</marker>
<marker
style="overflow:visible"
id="Arrow2Lend-2-2"
refX="0"
refY="0"
orient="auto"
inkscape:stockid="Arrow2Lend"
inkscape:isstock="true">
<path
transform="matrix(-1.1,0,0,-1.1,-1.1,0)"
d="M 8.7185878,4.0337352 -2.2072895,0.01601326 8.7185884,-4.0017078 c -1.7454984,2.3720609 -1.7354408,5.6174519 -6e-7,8.035443 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:context-stroke;stroke-width:0.625;stroke-linejoin:round"
id="path17053-0-8" />
</marker>
<marker
style="overflow:visible"
id="Arrow2Lend-8-3"
refX="0"
refY="0"
orient="auto"
inkscape:stockid="Arrow2Lend"
inkscape:isstock="true">
<path
transform="matrix(-1.1,0,0,-1.1,-1.1,0)"
d="M 8.7185878,4.0337352 -2.2072895,0.01601326 8.7185884,-4.0017078 c -1.7454984,2.3720609 -1.7354408,5.6174519 -6e-7,8.035443 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:context-stroke;stroke-width:0.625;stroke-linejoin:round"
id="path17053-7-6" />
</marker>
<marker
style="overflow:visible"
id="Arrow2Lend-1"
refX="0"
refY="0"
orient="auto"
inkscape:stockid="Arrow2Lend"
inkscape:isstock="true">
<path
transform="matrix(-1.1,0,0,-1.1,-1.1,0)"
d="M 8.7185878,4.0337352 -2.2072895,0.01601326 8.7185884,-4.0017078 c -1.7454984,2.3720609 -1.7354408,5.6174519 -6e-7,8.035443 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:context-stroke;stroke-width:0.625;stroke-linejoin:round"
id="path17053-2" />
</marker>
<marker
style="overflow:visible"
id="Arrow2Lend-1-9"
refX="0"
refY="0"
orient="auto"
inkscape:stockid="Arrow2Lend"
inkscape:isstock="true">
<path
transform="matrix(-1.1,0,0,-1.1,-1.1,0)"
d="M 8.7185878,4.0337352 -2.2072895,0.01601326 8.7185884,-4.0017078 c -1.7454984,2.3720609 -1.7354408,5.6174519 -6e-7,8.035443 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:context-stroke;stroke-width:0.625;stroke-linejoin:round"
id="path17053-2-4" />
</marker>
<marker
style="overflow:visible"
id="Arrow2Lend-8-3-7"
refX="0"
refY="0"
orient="auto"
inkscape:stockid="Arrow2Lend"
inkscape:isstock="true">
<path
transform="matrix(-1.1,0,0,-1.1,-1.1,0)"
d="M 8.7185878,4.0337352 -2.2072895,0.01601326 8.7185884,-4.0017078 c -1.7454984,2.3720609 -1.7354408,5.6174519 -6e-7,8.035443 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:context-stroke;stroke-width:0.625;stroke-linejoin:round"
id="path17053-7-6-8" />
</marker>
<marker
style="overflow:visible"
id="Arrow2Lend-1-0"
refX="0"
refY="0"
orient="auto"
inkscape:stockid="Arrow2Lend"
inkscape:isstock="true">
<path
transform="matrix(-1.1,0,0,-1.1,-1.1,0)"
d="M 8.7185878,4.0337352 -2.2072895,0.01601326 8.7185884,-4.0017078 c -1.7454984,2.3720609 -1.7354408,5.6174519 -6e-7,8.035443 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:context-stroke;stroke-width:0.625;stroke-linejoin:round"
id="path17053-2-3" />
</marker>
<marker
style="overflow:visible"
id="Arrow2Lend-8-3-6"
refX="0"
refY="0"
orient="auto"
inkscape:stockid="Arrow2Lend"
inkscape:isstock="true">
<path
transform="matrix(-1.1,0,0,-1.1,-1.1,0)"
d="M 8.7185878,4.0337352 -2.2072895,0.01601326 8.7185884,-4.0017078 c -1.7454984,2.3720609 -1.7354408,5.6174519 -6e-7,8.035443 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:context-stroke;stroke-width:0.625;stroke-linejoin:round"
id="path17053-7-6-1" />
</marker>
</defs>
<g
inkscape:label="Layer 1"
inkscape:groupmode="layer"
id="layer1"
transform="translate(-26.326042,-41.907531)">
<text
xml:space="preserve"
style="font-size:10.5833px;line-height:0;font-family:sans-serif;letter-spacing:0px;stroke-width:0.264583"
x="31.369009"
y="64.637695"
id="text2487"><tspan
sodipodi:role="line"
id="tspan2485"
style="stroke-width:0.264583"
x="31.369009"
y="64.637695">0</tspan></text>
<path
style="fill:none;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 26.458333,68.791666 h 15.875 V 52.916667 h -15.875 v 15.875"
id="path15418" />
<g
id="g15829"
transform="translate(-5.2916667,-26.458334)">
<text
xml:space="preserve"
style="font-size:10.5833px;line-height:0;font-family:sans-serif;letter-spacing:0px;stroke-width:0.264583"
x="53.213009"
y="91.090736"
id="text4987"><tspan
sodipodi:role="line"
id="tspan4985"
style="stroke-width:0.264583"
x="53.213009"
y="91.090736">1</tspan></text>
<path
style="fill:none;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="M 47.625,95.25 H 63.5 V 79.375001 H 47.625 v 15.875"
id="path15418-3" />
</g>
<g
id="g15834"
transform="translate(-37.041667,-52.916673)">
<text
xml:space="preserve"
style="font-size:10.5833px;line-height:0;font-family:sans-serif;letter-spacing:0px;stroke-width:0.264583"
x="100.18185"
y="117.60199"
id="text5981"><tspan
sodipodi:role="line"
id="tspan5979"
style="stroke-width:0.264583"
x="100.18185"
y="117.60199">2</tspan></text>
<path
style="fill:none;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 95.25,121.70833 h 15.875 V 105.83334 H 95.25 v 15.87499"
id="path15418-6" />
</g>
<g
id="g15839"
transform="translate(-58.208327,-58.208333)">
<text
xml:space="preserve"
style="font-size:10.5833px;line-height:0;font-family:sans-serif;letter-spacing:0px;stroke-width:0.264583"
x="137.26584"
y="122.84074"
id="text6887"><tspan
sodipodi:role="line"
id="tspan6885"
style="stroke-width:0.264583"
x="137.26584"
y="122.84074">3</tspan></text>
<path
style="fill:none;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 132.29166,127 h 15.875 v -15.875 h -15.875 V 127"
id="path15418-7" />
</g>
<g
id="g15844"
transform="translate(-42.333327,-74.083333)">
<text
xml:space="preserve"
style="font-size:10.5833px;line-height:0;font-family:sans-serif;letter-spacing:0px;stroke-width:0.264583"
x="137.19705"
y="138.73691"
id="text7815"><tspan
sodipodi:role="line"
id="tspan7813"
style="stroke-width:0.264583"
x="137.19705"
y="138.73691">4</tspan></text>
<path
style="fill:none;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 132.29166,142.875 h 15.875 V 127 h -15.875 v 15.875"
id="path15418-5" />
</g>
<g
id="g15854"
transform="translate(111.125,-68.791663)">
<text
xml:space="preserve"
style="font-size:10.5833px;line-height:0;font-family:sans-serif;letter-spacing:0px;stroke-width:0.264583"
x="15.451676"
y="133.42407"
id="text9407"><tspan
sodipodi:role="line"
id="tspan9405"
style="stroke-width:0.264583"
x="15.451676"
y="133.42407">6</tspan></text>
<path
style="fill:none;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 10.583333,137.58333 h 15.875 v -15.87499 h -15.875 v 15.87499"
id="path15418-35" />
</g>
<g
id="g15849"
transform="translate(79.375,-58.208333)">
<text
xml:space="preserve"
style="font-size:10.5833px;line-height:0;font-family:sans-serif;letter-spacing:0px;stroke-width:0.264583"
x="31.337259"
y="122.78782"
id="text8479"><tspan
sodipodi:role="line"
id="tspan8477"
style="stroke-width:0.264583"
x="31.337259"
y="122.78782">5</tspan></text>
<path
style="fill:none;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 26.458333,127 h 15.875 v -15.875 h -15.875 V 127"
id="path15418-62" />
</g>
<g
id="g15859"
transform="translate(58.208333,-100.54167)">
<text
xml:space="preserve"
style="font-size:10.5833px;line-height:0;font-family:sans-serif;letter-spacing:0px;stroke-width:0.264583"
x="84.312134"
y="165.17407"
id="text10533"><tspan
sodipodi:role="line"
id="tspan10531"
style="stroke-width:0.264583"
x="84.312134"
y="165.17407">7</tspan></text>
<path
style="fill:none;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="M 79.375,169.33334 H 95.25 v -15.875 H 79.375 v 15.875"
id="path15418-9" />
</g>
<g
id="g15864"
transform="translate(121.70833,-111.125)">
<text
xml:space="preserve"
style="font-size:10.5833px;line-height:0;font-family:sans-serif;letter-spacing:0px;stroke-width:0.264583"
x="36.66597"
y="175.7574"
id="text11329"><tspan
sodipodi:role="line"
id="tspan11327"
style="stroke-width:0.264583"
x="36.66597"
y="175.7574">8</tspan></text>
<path
style="fill:none;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 31.75,179.91667 h 15.875 v -15.875 H 31.75 v 15.875"
id="path15418-1" />
</g>
<g
id="g15869"
transform="translate(153.45833,-116.41667)">
<text
xml:space="preserve"
style="font-size:10.5833px;line-height:0;font-family:sans-serif;letter-spacing:0px;stroke-width:0.264583"
x="20.796259"
y="181.04907"
id="text13137"><tspan
sodipodi:role="line"
id="tspan13135"
style="stroke-width:0.264583"
x="20.796259"
y="181.04907">9</tspan></text>
<path
style="fill:none;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="M 15.875,185.20834 H 31.75 v -15.875 H 15.875 v 15.875"
id="path15418-2" />
</g>
<path
style="fill:none;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 26.458333,68.791666 v 21.166666 l 158.749997,10e-7 V 68.791667"
id="path15904" />
<path
style="fill:none;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="M 42.333333,68.791666 V 89.958332"
id="path15906" />
<path
style="fill:none;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 58.208333,68.791667 v 21.16666"
id="path15906-7" />
<path
style="fill:none;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="M 74.083333,68.791667 V 89.958329"
id="path15906-0" />
<path
style="fill:none;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 89.958333,68.791667 v 21.16666"
id="path15906-9" />
<path
style="fill:none;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 121.70833,68.791667 v 21.16666"
id="path15906-3" />
<path
style="fill:none;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 137.58333,68.791667 v 21.16666"
id="path15906-6" />
<path
style="fill:none;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 153.45833,68.791667 v 21.16666"
id="path15906-06" />
<path
style="fill:none;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 169.33333,68.791667 v 21.16666"
id="path15906-2" />
<path
style="fill:none;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 105.83333,68.791667 v 21.16667"
id="path15906-61" />
<path
style="fill:none;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;marker-end:url(#Arrow2Lend)"
d="m 34.395833,50.270833 c 0,0 7.9375,-10.583334 15.875,0"
id="path16437"
sodipodi:nodetypes="cc" />
<path
style="fill:none;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;marker-end:url(#Arrow2Lend-8)"
d="m 34.395833,50.270833 c 0,0 14.552084,-18.520833 31.75,0"
id="path16437-9"
sodipodi:nodetypes="cc" />
<path
style="fill:none;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;marker-end:url(#Arrow2Lend-1)"
d="m 161.39583,91.28125 c 0,0 -38.36458,35.71875 -79.374997,0"
id="path16437-93"
sodipodi:nodetypes="cc" />
<path
style="fill:none;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;marker-end:url(#Arrow2Lend-8-3)"
d="m 145.52083,91.28125 c 0,0 -31.75,21.16667 -60.854163,0"
id="path16437-9-1"
sodipodi:nodetypes="cc" />
<path
style="fill:none;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;marker-end:url(#Arrow2Lend-1-0)"
d="m 129.64583,91.28125 c 0,0 -31.749997,34.39583 -62.17708,0"
id="path16437-93-0"
sodipodi:nodetypes="cc" />
<path
style="fill:none;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;marker-end:url(#Arrow2Lend-8-3-6)"
d="m 113.77083,91.28125 c 0,0 -23.812497,21.16667 -43.656247,0"
id="path16437-9-1-6"
sodipodi:nodetypes="cc" />
<path
style="fill:none;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;marker-end:url(#Arrow2Lend-2)"
d="m 50.270836,50.270833 c 0,0 15.874997,-10.583333 31.749997,0"
id="path16437-7"
sodipodi:nodetypes="cc" />
<path
style="fill:none;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;marker-end:url(#Arrow2Lend-8-2)"
d="m 50.270836,50.270833 c 0,0 23.812497,-18.520833 47.624997,0"
id="path16437-9-5"
sodipodi:nodetypes="cc" />
<path
style="fill:none;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;marker-end:url(#Arrow2Lend-2-2)"
d="m 66.145833,50.270833 c 0,0 23.8125,-11.90625 47.624997,1.322917"
id="path16437-7-9"
sodipodi:nodetypes="cc" />
<path
style="fill:none;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;marker-end:url(#Arrow2Lend-8-2-9)"
d="m 66.145833,50.270833 c 0,0 31.75,-18.520833 62.177087,0"
id="path16437-9-5-7"
sodipodi:nodetypes="cc" />
</g>
</svg>
slides/tri_par_tas.md
+ 381
− 0
View file @ 8e8cbebc
......@@ -24,6 +24,387 @@ date: "2022-03-02"
# Visuellement
::: columns
:::: column
* Où vont les indices correspondant du tableau?
```{.mermaid format=pdf width=400 loc=figs/}
graph TD;
id0(( ))-->id1(( ));
id0-->id2(( ));
id1-->id3(( ));
id1-->id4(( ));
id2-->id5(( ));
id2-->id6(( ));
id3-->id7(( ));
id3-->id8(( ));
id4-->id9(( ));
id4-->id10(( ));
style id10 fill:#fff,stroke:#fff
```
::::
:::: column
* Les flèche de gauche à droite, parent -> enfants.
* Les flèche de droite à gauche, enfants -> parent.
![Dualité tableau arbre binaire.](figs/heap_tree.svg)
::::
:::
**Propriétés:**
1. les feuilles sont toutes sur l'avant dernier ou dernier niveau.
2. les feuilles de profondeur maximale sont "tassée" à gauche.
# Le tas (ou heap)
## Définition
* Un arbre est un tas, si la valeur de chacun de ses descendants est inférieure
ou égale à sa propre valeur.
## Exemples (ou pas)
```
16 8 14 6 2 10 12 4 5 # Tas
16 14 8 6 2 10 12 4 5 # Non-tas, 10 > 8 et 12 > 8
```
## Exercices (ou pas)
```
19 18 12 12 17 1 13 4 5 # Tas ou pas tas?
19 18 16 12 17 1 12 4 5 # Tas ou pas tas?
```
. . .
```
19 18 12 12 17 1 13 4 5 # Pas tas! 13 > 12
19 18 16 12 17 1 12 4 5 # Tas!
```
# Exemple de tri par tas (1/N)
```
| 1 | 16 | 5 | 12 | 4 | 2 | 8 | 10 | 6 | 7 |
```
::: columns
:::: column
* Quel est l'arbre que cela représente?
. . .
```{.mermaid format=pdf width=400 loc=figs/}
graph TD;
id0((1))-->id1((16));
id0-->id2((5));
id1-->id3((12));
id1-->id4((4));
id2-->id5((2));
id2-->id6((8));
id3-->id7((10));
id3-->id8((6));
id4-->id9((7));
id4-->id10(( ));
style id10 fill:#fff,stroke:#fff
```
::::
:::: column
**But:** Transformer l'arbre en tas.
* On commence à l'indice $N/2 = 5$: `7`.
* `7 > 4` (enfant `>` parent).
* intervertir `4` et `7`.
```{.mermaid format=pdf width=400 loc=figs/}
graph TD;
id0((1))-->id1((16));
id0-->id2((5));
id1-->id3((12));
id1-->id4((7));
id2-->id5((2));
id2-->id6((8));
id3-->id7((10));
id3-->id8((6));
id4-->id9((4));
id4-->id10(( ));
style id10 fill:#fff,stroke:#fff
```
::::
:::
. . .
```
* *
| 1 | 16 | 5 | 12 | 7 | 2 | 8 | 10 | 6 | 4 |
```
# Exemple de tri par tas (2/N)
```
| 1 | 16 | 5 | 12 | 7 | 2 | 8 | 10 | 6 | 4 |
```
::: columns
:::: column
**But:** Transformer l'arbre en tas.
* On continue à l'indice $N/2-1 = 4$: `12`.
* Déjà un tas, rien à faire.
```{.mermaid format=pdf width=400 loc=figs/}
graph TD;
id0((1))-->id1((16));
id0-->id2((5));
id1-->id3((12));
id1-->id4((7));
id2-->id5((2));
id2-->id6((8));
id3-->id7((10));
id3-->id8((6));
id4-->id9((4));
id4-->id10(( ));
style id10 fill:#fff,stroke:#fff
```
::::
:::: column
**But:** Transformer l'arbre en tas.
* On continue à l'indice $N/2-2 = 3$: `5`.
* `5 < 8`, échanger `8` et `5` (aka `max(2, 5, 8)`)
```{.mermaid format=pdf width=400 loc=figs/}
graph TD;
id0((1))-->id1((16));
id0-->id2((8));
id1-->id3((12));
id1-->id4((7));
id2-->id5((2));
id2-->id6((5));
id3-->id7((10));
id3-->id8((6));
id4-->id9((4));
id4-->id10(( ));
style id10 fill:#fff,stroke:#fff
```
::::
:::
. . .
```
| 1 | 16 | 8 | 12 | 7 | 2 | 5 | 10 | 6 | 4 |
```
# Exemple de tri par tas (3/N)
```
| 1 | 16 | 5 | 12 | 7 | 2 | 8 | 10 | 6 | 4 |
```
::: columns
:::: column
**But:** Transformer l'arbre en tas.
* Indice $N/2-1 = 4$: `12`.
* Déjà un tas, rien à faire.
```{.mermaid format=pdf width=400 loc=figs/}
graph TD;
id0((1))-->id1((16));
id0-->id2((5));
id1-->id3((12));
id1-->id4((7));
id2-->id5((2));
id2-->id6((8));
id3-->id7((10));
id3-->id8((6));
id4-->id9((4));
id4-->id10(( ));
style id10 fill:#fff,stroke:#fff
```
::::
:::: column
**But:** Transformer l'arbre en tas.
* Indice $N/2-2 = 3$: `5`.
* `5 < 8`, `5 <=> max(2, 5, 8)`
```{.mermaid format=pdf width=400 loc=figs/}
graph TD;
id0((1))-->id1((16));
id0-->id2((8));
id1-->id3((12));
id1-->id4((7));
id2-->id5((2));
id2-->id6((5));
id3-->id7((10));
id3-->id8((6));
id4-->id9((4));
id4-->id10(( ));
style id10 fill:#fff,stroke:#fff
```
::::
:::
```
* *
| 1 | 16 | 8 | 12 | 7 | 2 | 5 | 10 | 6 | 4 |
```
# Exemple de tri par tas (4/N)
```
| 1 | 16 | 8 | 12 | 7 | 2 | 5 | 10 | 6 | 4 |
```
::: columns
:::: column
**But:** Transformer l'arbre en tas.
* Indice $N/2-3 = 1$: `16`.
* Déjà un tas, rien à faire.
```{.mermaid format=pdf width=400 loc=figs/}
graph TD;
id0((1))-->id1((16));
id0-->id2((5));
id1-->id3((12));
id1-->id4((7));
id2-->id5((2));
id2-->id6((8));
id3-->id7((10));
id3-->id8((6));
id4-->id9((4));
id4-->id10(( ));
style id10 fill:#fff,stroke:#fff
```
::::
:::: column
**But:** Transformer l'arbre en tas.
* Indice $N/2-4 = 1$: `1`.
* `1 < 16 && 1 < 8`, `1 <=> max(1, 16, 8)`
```{.mermaid format=pdf width=400 loc=figs/}
graph TD;
id0((16))-->id1((1));
id0-->id2((8));
id1-->id3((12));
id1-->id4((7));
id2-->id5((2));
id2-->id6((5));
id3-->id7((10));
id3-->id8((6));
id4-->id9((4));
id4-->id10(( ));
style id10 fill:#fff,stroke:#fff
```
::::
:::
```
* *
| 16 | 1 | 8 | 12 | 7 | 2 | 5 | 10 | 6 | 4 |
```
# Exemple de tri par tas (5/N)
```
| 16 | 1 | 8 | 12 | 7 | 2 | 5 | 10 | 6 | 4 |
```
::: columns
:::: column
**But:** Transformer l'arbre en tas.
* Recommencer avec `1`.
* `1 <=> max(1, 12, 7)`.
```{.mermaid format=pdf width=400 loc=figs/}
graph TD;
id0((16))-->id1((12));
id0-->id2((5));
id1-->id3((1));
id1-->id4((7));
id2-->id5((2));
id2-->id6((8));
id3-->id7((10));
id3-->id8((6));
id4-->id9((4));
id4-->id10(( ));
style id10 fill:#fff,stroke:#fff
```
::::
:::: column
**But:** Transformer l'arbre en tas.
* Recommencer avec `1`.
* `1 <=> max(1, 10, 6)`.
```{.mermaid format=pdf width=400 loc=figs/}
graph TD;
id0((16))-->id1((12));
id0-->id2((8));
id1-->id3((10));
id1-->id4((7));
id2-->id5((2));
id2-->id6((5));
id3-->id7((1));
id3-->id8((6));
id4-->id9((4));
id4-->id10(( ));
style id10 fill:#fff,stroke:#fff
```
::::
:::
```
* * *
| 16 | 12 | 8 | 10 | 7 | 2 | 5 | 1 | 6 | 4 |
```
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Please register or to comment