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Verified Commit b52413ad authored by orestis.malaspin's avatar orestis.malaspin
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added lossless compression

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slides/cours_20.md
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View file @ b52413ad
......@@ -642,12 +642,151 @@ arbre symétrie(arbre)
. . .
```C
arbre symétrie(arbre)
rien rotation_gauche(arbre)
si !est_feuille(arbre))
échange_cyclique_gauche(arbre.enfant)
pour i de 0 à 3
rotation_gauche(arbre.enfant[i])
```
# Rotation d'un quart de cercle
\footnotesize
## Comment faire sur un arbre?
```
SG=0 | SD=1 SG=0 | SD=1
21 | 12 | 4 | 4 4 | 4 | 31 | 27
9 | 7 | 4 | 4 4 | 4 | 0 | 3
----------------- => -----------------
1 | 1 | 0 | 31 12 | 7 | 1 | 1
1 | 1 | 3 | 27 21 | 9 | 1 | 1
IG=2 | ID=3 IG=2 | ID=3
```
* Écrire le vrai (5min, matrix)
. . .
```C
void rotate(node *qt) {
if (!is_leaf(qt)) {
node *tmp = qt->child[2];
qt->child[2] = qt->child[0];
qt->child[0] = qt->child[1];
qt->child[1] = qt->child[3];
qt->child[3] = tmp;
for (int i=0;i < 4; i++) {
rotate(qt->child[i]);
}
}
}
```
# Compression sans perte (1/N)
## Idée générale
* Regrouper les pixels par valeur
```
SG=0 | SD=1 SG=0 | SD=1
21 | 12 | 4 | 4 21 | 12 | 4
9 | 7 | 4 | 4 9 | 7 |
----------------- => -----------------
1 | 1 | 0 | 31 1 | 0 | 31
1 | 1 | 3 | 27 | 3 | 27
IG=2 | ID=3 IG=2 | ID=3
```
* Comment faire?
# Compression sans perte (2/N)
## Que devient l'arbre suivant?
![](figs/quad_img_simple.svg)
. . .
## Arbre compressé
![](figs/quad_img_simple_comp.svg)
# Compression sans perte (3/N)
* Si un noeud a tous ses enfants égaux:
* Donner la valeur au noeud,
* Supprimer les enfants.
* Remonter jusqu'à la racine.
## Écrire le pseudo-code (5min, matrix)
```C
rien compression_sans_perte(arbre)
si !est_feuille(arbre)
échanger(arbre.enfant[0], arbre.enfant[1])
échanger(arbre.enfant[2], arbre.enfant[3])
pour i de 0 à 3
symétrie(arbre.enfant[i])
retourne arbre
compression_sans_perte(arbre.enfant[i])
si derniere_branche(arbre)
valeur, toutes_égales = valeur_enfants(arbre)
si toutes_egales
arbre.info = valeur
detruire_enfants(arbre)
```
# Compression sans perte (4/N)
\footnotesize
## Écrire le code C (5min, matrix)
. . .
```C
void lossless_compression(node *qt) {
if (!is_leaf(qt)) {
for (int i = 0; i < CHILDREN; i++) {
lossless_compression(qt->child[i]);
}
}
if (is_last_branch(qt)) {
int val = -1;
if (last_value(qt, &val)) {
qt->info = val;
for (int i = 0; i < 4; ++i) {
free(qt->child[i]);
qt->child[i] = NULL;
}
}
}
}
```
# Compression sans perte (5/N)
\footnotesize
```C
bool is_last_branch(node *qt) {
for (int i = 0; i < 4; ++i) {
if (!is_leaf(qt)) {
return false;
}
}
return true;
}
bool last_value(node *qt, int *val) {
int info = qt->child[0];
for (int i = 1; i < 4; ++i) {
if (info != qt->child[i]) {
return false;
}
}
*val = info;
return true;
}
```
slides/figs/quad_img_simple_comp.svg 0 → 100644
+ 161
− 0
View file @ b52413ad
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<text text-anchor="middle" x="171" y="-85.8" font-family="Times,serif" font-size="14.00" fill="#000000">SG</text>
</g>
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<g id="edge1" class="edge">
<title>0-&gt;sg1</title>
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</g>
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<g id="edge2" class="edge">
<title>0-&gt;sd1</title>
<path fill="none" stroke="#000000" d="M270.2854,-144.5708C266.0403,-136.0807 260.8464,-125.6929 256.1337,-116.2674"/>
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</g>
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<g id="node4" class="node">
<title>ig1</title>
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<text text-anchor="middle" x="315" y="-85.8" font-family="Times,serif" font-size="14.00" fill="#000000">1</text>
</g>
<!-- 0&#45;&gt;ig1 -->
<g id="edge3" class="edge">
<title>0-&gt;ig1</title>
<path fill="none" stroke="#000000" d="M287.7146,-144.5708C291.9597,-136.0807 297.1536,-125.6929 301.8663,-116.2674"/>
<polygon fill="#000000" stroke="#000000" points="305.024,-117.7782 306.3657,-107.2687 298.763,-114.6477 305.024,-117.7782"/>
</g>
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<g id="node5" class="node">
<title>id1</title>
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<text text-anchor="middle" x="387" y="-85.8" font-family="Times,serif" font-size="14.00" fill="#000000">ID</text>
</g>
<!-- 0&#45;&gt;id1 -->
<g id="edge4" class="edge">
<title>0-&gt;id1</title>
<path fill="none" stroke="#000000" d="M298.3082,-149.1278C315.3555,-137.763 340.4019,-121.0654 359.5344,-108.3104"/>
<polygon fill="#000000" stroke="#000000" points="361.4799,-111.2199 367.8589,-102.7607 357.5969,-105.3956 361.4799,-111.2199"/>
</g>
<!-- sg2 -->
<g id="node6" class="node">
<title>sg2</title>
<ellipse fill="none" stroke="#000000" cx="27" cy="-18" rx="27" ry="18"/>
<text text-anchor="middle" x="27" y="-13.8" font-family="Times,serif" font-size="14.00" fill="#000000">21</text>
</g>
<!-- sg1&#45;&gt;sg2 -->
<g id="edge5" class="edge">
<title>sg1-&gt;sg2</title>
<path fill="none" stroke="#000000" d="M149.1295,-79.0647C124.7778,-66.8889 85.238,-47.119 57.7715,-33.3858"/>
<polygon fill="#000000" stroke="#000000" points="59.114,-30.1439 48.6045,-28.8022 55.9835,-36.4049 59.114,-30.1439"/>
</g>
<!-- sd2 -->
<g id="node7" class="node">
<title>sd2</title>
<ellipse fill="none" stroke="#000000" cx="99" cy="-18" rx="27" ry="18"/>
<text text-anchor="middle" x="99" y="-13.8" font-family="Times,serif" font-size="14.00" fill="#000000">12</text>
</g>
<!-- sg1&#45;&gt;sd2 -->
<g id="edge6" class="edge">
<title>sg1-&gt;sd2</title>
<path fill="none" stroke="#000000" d="M155.7307,-74.7307C145.803,-64.803 132.6847,-51.6847 121.5637,-40.5637"/>
<polygon fill="#000000" stroke="#000000" points="123.7933,-37.8436 114.2473,-33.2473 118.8436,-42.7933 123.7933,-37.8436"/>
</g>
<!-- ig2 -->
<g id="node8" class="node">
<title>ig2</title>
<ellipse fill="none" stroke="#000000" cx="171" cy="-18" rx="27" ry="18"/>
<text text-anchor="middle" x="171" y="-13.8" font-family="Times,serif" font-size="14.00" fill="#000000">9</text>
</g>
<!-- sg1&#45;&gt;ig2 -->
<g id="edge7" class="edge">
<title>sg1-&gt;ig2</title>
<path fill="none" stroke="#000000" d="M171,-71.8314C171,-64.131 171,-54.9743 171,-46.4166"/>
<polygon fill="#000000" stroke="#000000" points="174.5001,-46.4132 171,-36.4133 167.5001,-46.4133 174.5001,-46.4132"/>
</g>
<!-- id2 -->
<g id="node9" class="node">
<title>id2</title>
<ellipse fill="none" stroke="#000000" cx="243" cy="-18" rx="27" ry="18"/>
<text text-anchor="middle" x="243" y="-13.8" font-family="Times,serif" font-size="14.00" fill="#000000">7</text>
</g>
<!-- sg1&#45;&gt;id2 -->
<g id="edge8" class="edge">
<title>sg1-&gt;id2</title>
<path fill="none" stroke="#000000" d="M186.2693,-74.7307C196.197,-64.803 209.3153,-51.6847 220.4363,-40.5637"/>
<polygon fill="#000000" stroke="#000000" points="223.1564,-42.7933 227.7527,-33.2473 218.2067,-37.8436 223.1564,-42.7933"/>
</g>
<!-- sg5 -->
<g id="node10" class="node">
<title>sg5</title>
<ellipse fill="none" stroke="#000000" cx="315" cy="-18" rx="27" ry="18"/>
<text text-anchor="middle" x="315" y="-13.8" font-family="Times,serif" font-size="14.00" fill="#000000">0</text>
</g>
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<g id="edge9" class="edge">
<title>id1-&gt;sg5</title>
<path fill="none" stroke="#000000" d="M371.7307,-74.7307C361.803,-64.803 348.6847,-51.6847 337.5637,-40.5637"/>
<polygon fill="#000000" stroke="#000000" points="339.7933,-37.8436 330.2473,-33.2473 334.8436,-42.7933 339.7933,-37.8436"/>
</g>
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<g id="node11" class="node">
<title>sd5</title>
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<text text-anchor="middle" x="387" y="-13.8" font-family="Times,serif" font-size="14.00" fill="#000000">31</text>
</g>
<!-- id1&#45;&gt;sd5 -->
<g id="edge10" class="edge">
<title>id1-&gt;sd5</title>
<path fill="none" stroke="#000000" d="M387,-71.8314C387,-64.131 387,-54.9743 387,-46.4166"/>
<polygon fill="#000000" stroke="#000000" points="390.5001,-46.4132 387,-36.4133 383.5001,-46.4133 390.5001,-46.4132"/>
</g>
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<title>ig5</title>
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</g>
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<g id="edge11" class="edge">
<title>id1-&gt;ig5</title>
<path fill="none" stroke="#000000" d="M402.2693,-74.7307C412.197,-64.803 425.3153,-51.6847 436.4363,-40.5637"/>
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<g id="edge12" class="edge">
<title>id1-&gt;id5</title>
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</g>
</g>
</svg>
\ No newline at end of file
slides/graphviz/quad_img_simple_comp.dot 0 → 100644
+ 18
− 0
View file @ b52413ad
digraph G {
0 [label=" "]
sg1 [label="SG"]
sd1 [label="4"]
ig1 [label="1"]
id1 [label="ID"]
sg2 [label="21"]
sd2 [label="12"]
ig2 [label="9"]
id2 [label="7"]
sg5 [label="0"]
sd5 [label="31"]
ig5 [label="3"]
id5 [label="27"]
0->{sg1, sd1, ig1, id1} [quadtree = "normal"]
sg1->{sg2, sd2, ig2, id2} [quadtree = "normal"]
id1->{sg5, sd5, ig5, id5} [quadtree = "normal"]
}
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