Merge pull request #1 from tusharnain4578/tusharnain4578-patch-1

Added Matrix Chain Multiplication program

Matrix_Chain_Multiplication.py

@@ -0,0 +1,59 @@
+def matrix_product(p):
+
+    length = len(p) # len(p) = number of matrices + 1
+
+    m = [[-1]*length for _ in range(length)]
+    s = [[-1]*length for _ in range(length)]
+
+    matrix_product_helper(p, 1, length - 1, m, s)
+
+    return m, s
+
+
+def matrix_product_helper(p, start, end, m, s):
+
+    if m[start][end] >= 0:
+        return m[start][end]
+
+    if start == end:
+        q = 0
+    else:
+        q = float('inf')
+        for k in range(start, end):
+            temp = matrix_product_helper(p, start, k, m, s) \
+                   + matrix_product_helper(p, k + 1, end, m, s) \
+                   + p[start - 1]*p[k]*p[end]
+            if q > temp:
+                q = temp
+                s[start][end] = k
+
+    m[start][end] = q
+    return q
+
+
+def print_parenthesization(s, start, end):
+
+    if start == end:
+        print('A[{}]'.format(start), end='')
+        return
+
+    k = s[start][end]
+
+    print('(', end='')
+    print_parenthesization(s, start, k)
+    print_parenthesization(s, k + 1, end)
+    print(')', end='')
+
+
+n = int(input('Enter number of matrices: '))
+p = []
+for i in range(n):
+    temp = int(input('Enter number of rows in matrix {}: '.format(i + 1)))
+    p.append(temp)
+temp = int(input('Enter number of columns in matrix {}: '.format(n)))
+p.append(temp)
+
+m, s = matrix_product(p)
+print('The number of scalar multiplications needed:', m[1][n])
+print('Optimal parenthesization: ', end='')
+print_parenthesization(s, 1, n)