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+# TD2
+
+## Algorythme dichotomique en C
+
+```c
+int f(int t[], int target, int len) {
+    int min = 0;
+    int max = len-1;
+    while (min < max) {
+        int i = (min+max)/2
+        int val = t[i];
+        if (target < val) {
+            max = i;
+        } else if (target > val) {
+            min = i;
+        } else {
+            min = i;
+            max = i;
+        }
+    }
+    return min;
+}
+```
+
+Preuve de terminaison :
+
+- **variant :** $\lfloor log_2(\frac{max-min}{2}) \rfloor$
+
+Preuve de correction :
+
+- **invariant :** $min \leq i_{target} \leq max$
+- **après la boucle :** $min = max$
+
+  donc $min \leq i_{target} \leq min$
+
+  donc $i_{target} = min$
+
+Complexité : $O(log_2(n))$
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