added 2,3,4 reines

slides/cours_7.md

@@ -55,7 +55,7 @@ void tri_insertion(int size, int tab[size]) {
 
 . . .
 
-* Parcous de tous les éléments (ordre $N$); placer (ordre $N$).
+* Parcours de tous les éléments (ordre $N$); placer (ordre $N$).
 * Moyenne: $\mathcal{O}(N^2)$.
 
 . . .
@@ -315,7 +315,7 @@ int ppcm(int m, int n) {
     -   `ppcm(mult_n,mult_m) = mult_n`      
         si `mult_n = mult_m`   (condition d’arrêt)
 
-#  Problème des 8-reines
+# Problème des 8-reines
 
 * Placer 8 reines d'un jeu d'échecs sur un échiquier de $8 \times 8$
 * Sans que les reines ne puissent se menacer mutuellement. 
@@ -323,6 +323,7 @@ int ppcm(int m, int n) {
 ## Conséquence
 
 * Deux reines ne partagent pas la même rangée, colonne, ou diagonale.
+* Donc chaque solution a **une** reine **par colonne** ou **ligne**.
 
 ## Généralisation
 
@@ -333,3 +334,26 @@ int ppcm(int m, int n) {
 ![Problème des 8-reines. Source:
 [wikipedia](https://fr.wikipedia.org/wiki/Problème_des_huit_dames)](./figs/fig_recursivite_8_reines.png){width=40%}
 
+# Problème des 2-reines
+
+![Le problème des 2 reines n'a pas de solution.](figs/2reines.svg)
+
+# Problème des 3-reines
+
+![Le problème des 3 reines n'a pas de solution non plus.](figs/3reines.svg)
+
+# Problème des 4-reines
+
+![Le problème des 4 reines a une solution.](figs/4reines.svg)
+
+# Problème des 4-reines, symétrie
+
+![Le problème des 4 reines a une autre solution (symétrie
+horizontale).](figs/4reines_sym.svg)
+
+
+
+
+
+
+

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