MatrixChainOrder

Author: shivg7706

dynamic_programming/matrix_chain_order.py

@@ -0,0 +1,46 @@
+import sys
+'''
+Dynamic Programming
+Implementation of Matrix Chain Multiplication
+Time Complexity: O(n^3)
+Space Complexity: O(n^2)
+'''
+def MatrixChainOrder(array):
+    N=len(array)
+    Matrix=[[0 for x in range(N)] for x in range(N)]
+    Sol=[[0 for x in range(N)] for x in range(N)]
+    for i in range(1,N):
+        Matrix[i][i]=0
+
+    for ChainLength in range(2,N):
+        for a in range(1,N-ChainLength+1):
+            b = a+ChainLength-1
+
+            Matrix[a][b] = sys.maxsize
+            for c in range(a , b):
+                cost = Matrix[a][c] + Matrix[c+1][b] + array[a-1]*array[c]*array[b]
+                if cost < Matrix[a][b]:
+                    Matrix[a][b] = cost
+                    Sol[a][b] = c
+    return Matrix , Sol
+#Print order of matrix with Ai as Matrix
+def PrintOptimalSolution(OptimalSolution,i,j):
+    if i==j:
+        print("A" + str(i),end = " ")
+    else:
+        print("(",end = " ")
+        PrintOptimalSolution(OptimalSolution,i,OptimalSolution[i][j])
+        PrintOptimalSolution(OptimalSolution,OptimalSolution[i][j]+1,j)
+        print(")",end = " ")
+
+def main():
+    array=[30,35,15,5,10,20,25]
+    n=len(array)
+    #Size of matrix created from above array will be
+    # 30*35 35*15 15*5 5*10 10*20 20*25
+    Matrix , OptimalSolution = MatrixChainOrder(array)
+
+    print("No. of Operation required: "+str((Matrix[1][n-1])))
+    PrintOptimalSolution(OptimalSolution,1,n-1)
+if __name__ == '__main__':
+    main()