Merge pull request #640 from saanidhi-git/add-floyd-warshall-python

[REQUEST] Add Floyd-Warshall Algorithm in Python ((#629)

Author: Karanjot786

Python/algorithms/graph_algorithms/floyd_warshall.py

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+"""
+Floyd Warshall Algorithm:
+
+The Floyd Warshall algorithm finds the shortest distances between
+every pair of vertices in a weighted graph (both directed and undirected).
+
+Time Complexity: O(V^3)
+Space Complexity: O(V^2)
+"""
+
+def floyd_warshall(graph):
+    """
+    graph: 2D list (adjacency matrix)
+           graph[i][j] = weight from i → j or float('inf') if no edge.
+
+    Returns: dist - 2D list of shortest path distances.
+    """
+    V = len(graph)
+    dist = [row[:] for row in graph]
+
+    for k in range(V):
+        for i in range(V):
+            for j in range(V):
+                if dist[i][k] + dist[k][j] < dist[i][j]:
+                    dist[i][j] = dist[i][k] + dist[k][j]
+    return dist
+
+
+if __name__ == "__main__":
+    INF = float('inf')
+    graph = [
+        [0, 3, INF, 5],
+        [2, 0, INF, 4],
+        [INF, 1, 0, INF],
+        [INF, INF, 2, 0]
+    ]
+
+    result = floyd_warshall(graph)
+    print("All-Pairs Shortest Paths:")
+    for row in result:
+        print(row)

Python/algorithms/graph_algorithms/floyd_warshall_README.md

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+### 3. Floyd-Warshall Algorithm - `floyd_warshall.py`
+**Description**: Computes shortest paths between **all pairs of vertices** in a weighted graph.  
+It can handle **negative edge weights** (but no negative cycles) and works for both directed and undirected graphs.
+
+**Key Features**:
+- Finds shortest paths between every pair of vertices
+- Supports graphs with negative edge weights
+- Simple and easy-to-understand matrix-based implementation
+- Includes example usage for testing
+
+**Time Complexity**: O(V³), where V is the number of vertices  
+**Space Complexity**: O(V²), for storing the distance matrix  
+
+**Applications**:
+- Network routing and optimization
+- Finding shortest paths in road networks
+- Game AI pathfinding
+- All-pairs shortest distance analysis
+
+**Code Highlights**:
+```python
+from floyd_warshall import floyd_warshall
+
+graph = [
+    [0, 3, float('inf'), 7],
+    [8, 0, 2, float('inf')],
+    [5, float('inf'), 0, 1],
+    [2, float('inf'), float('inf'), 0]
+]
+
+shortest_paths = floyd_warshall(graph)
+print("All pairs shortest path matrix:")
+for row in shortest_paths:
+    print(row)
+
+
+All pairs shortest path matrix:
+[0, 3, 5, 7]
+[5, 0, 2, 4]
+[3, 6, 0, 1]
+[2, 5, 7, 0]
+
+
+Graph represented as adjacency matrix:
+- graph[i][j] = weight of edge from vertex i to j
+- float('inf') = no edge between i and j