Added multistage-graph in dynamic programming

Algorithms_and_Data_Structures/Dynamic-Programming-Series/Medium-DP-Problems/multistage-graph.py

@@ -0,0 +1,46 @@
+INF = 99
+
+def shortestDist(graph, n, source, target):
+    dist = [INF] * (n + 1)
+    path = [-1] * (n + 1)
+
+    dist[target] = 0
+    path[target] = target
+
+    for i in range(target - 1, 0, -1):
+        for j in range(i + 1, n + 1):
+            if graph[i][j] != INF and dist[i] > graph[i][j] + dist[j]:
+                dist[i] = graph[i][j] + dist[j]
+                path[i] = j
+
+    if dist[source] == INF:
+        print(f"There is no path from node {source} to node {target}")
+        return
+
+    print(f"The shortest path distance from node {source} to node {target} is: {dist[source]}")
+
+    print("Path:", source, end="")
+    current = source
+    while current != target:
+        current = path[current]
+        print(f" -> {current}", end="")
+    print()
+
+def main():
+    n = int(input("Enter the number of vertices in the graph: "))
+
+    graph = [[INF] * (n + 1) for _ in range(n + 1)]
+
+    print(f"Enter the adjacency matrix (use {INF} for INF):")
+    for i in range(1, n + 1):
+        row = list(map(int, input(f"Row {i}: ").split()))
+        for j in range(1, n + 1):
+            graph[i][j] = row[j - 1]
+
+    source = int(input("Enter the source node: "))
+    target = int(input("Enter the target node: "))
+
+    shortestDist(graph, n, source, target)
+
+if __name__ == "__main__":
+    main()

Project-Structure.md

@@ -79,6 +79,7 @@
     * Medium-Dp-Problems
       * [Coin-Change](Algorithms_and_Data_Structures/Dynamic-Programming-Series/Medium-DP-Problems/coin-change.py)
       * [Longest-Inc-Subseq](Algorithms_and_Data_Structures/Dynamic-Programming-Series/Medium-DP-Problems/longest-inc-subseq.py)
+      * [Multistage-Graph](Algorithms_and_Data_Structures/Dynamic-Programming-Series/Medium-DP-Problems/multistage-graph.py)
       * [Partition-Subset-Sum](Algorithms_and_Data_Structures/Dynamic-Programming-Series/Medium-DP-Problems/partition-subset-sum.py)
       * [Unique-Paths](Algorithms_and_Data_Structures/Dynamic-Programming-Series/Medium-DP-Problems/unique-paths.py)
   * Heapsort