diff --git a/TD Yanis Darius.pdf b/TD Yanis Darius.pdf
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diff --git a/ex3_TD4_V2.py b/ex3_TD4_V2.py
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+def heapify(array, n, i):
+
+    largest = i  
+    left = 2 * i + 1 
+    right = 2 * i + 2  
+
+    if left < n and array[left] > array[largest]:
+        largest = left
+
+    if right < n and array[right] > array[largest]:
+        largest = right
+
+    if largest != i:
+        array[i], array[largest] = array[largest], array[i]  
+        heapify(array, n, largest)
+
+def heap_sort(array):
+    n = len(array)
+
+    # Construire un tas max
+    for i in range(n // 2 - 1, -1, -1):
+        heapify(array, n, i)
+
+    
+    for i in range(n - 1, 0, -1):
+        array[i], array[0] = array[0], array[i]  
+        heapify(array, i, 0)  
+
+    return array
+
+def total_sum(array):
+    if isinstance(array[0], int):  
+        return sum(array)
+    return sum(total_sum(subarray) for subarray in array)  # Si tableau multidimensionnel
+
+
+def sort_with_sum(array):
+    for i in range(1, len(array)):
+        key = array[i]
+        key_sum = total_sum(key)
+        j = i - 1
+        # Réorganise les sous-tableaux en fonction de leur somme
+        while j >= 0 and total_sum(array[j]) > key_sum:
+            array[j + 1] = array[j]
+            j -= 1
+        array[j + 1] = key
+        
+    return  array
+    
+
+
+def sort_nd_array(array):
+    # Si le tableau est de dimension 1, tri simple par insertion
+    if isinstance(array[0], int):
+        return heap_sort(array)
+
+    # Si le tableau est multidimensionnel, on trie récursivement les sous-tableaux
+    sorted_subarrays = [sort_nd_array(subarray) for subarray in array]
+
+    sorted_subarrays = sort_with_sum(sorted_subarrays)
+
+    return sorted_subarrays
+
+
+def print_nd_array(array, level=0):
+    """
+    Affiche un tableau N-dimensionnel de manière lisible.
+    """
+    if isinstance(array[0], int):  # Si tableau 1D  
+        print("  " * level + str(array))
+    else:  # Tableau multidimensionnel
+        print("  " * level + "[")
+        for subarray in array:
+            print_nd_array(subarray, level + 1)
+        print("  " * level + "]")
+
+
+def main():
+    # Exemple 1 : Tableau 2D
+    array_2d = [[0, 3, 2], [9, 4, 5], [4, 1, 3]]
+    print("Tableau 2D avant tri :")
+    print_nd_array(array_2d)
+    result_2d = sort_nd_array(array_2d)
+    print("Tableau 2D après tri :")
+    print_nd_array(result_2d)
+
+    # Exemple 2 : Tableau 3D
+    array_3d = [
+        [[3, 1], [4, 2], [1, 3]],
+        [[5, 7], [2, 8], [9, 4]],
+        [[0, 0], [1, 1], [1, 0]]
+    ]
+    print("\nTableau 3D avant tri :")
+    print_nd_array(array_3d)
+    result_3d = sort_nd_array(array_3d)
+    print("Tableau 3D après tri :")
+    print_nd_array(result_3d)
+
+    # Exemple 3 : Tableau 4D
+    array_4d = [
+        [
+            [[1, 3], [4, 5], [2, 2]],
+            [[7, 8], [5, 6], [3, 4]]
+        ],
+        [
+            [[9, 1], [6, 7], [8, 3]],
+            [[2, 5], [7, 3], [9, 9]]
+        ],
+        [
+            [[3, 3], [2, 1], [5, 6]],
+            [[4, 2], [8, 7], [3, 9]]
+        ]
+    ]
+    print("\nTableau 4D avant tri :")
+    print_nd_array(array_4d)
+    result_4d = sort_nd_array(array_4d)
+    print("Tableau 4D après tri :")
+    print_nd_array(result_4d)
+    
+if __name__ == "__main__":
+    main()