From 40796a7eb9059610a7f9994b43a6d8513a6ae84a Mon Sep 17 00:00:00 2001
From: Aswin P Kumar <130536278+The-APK@users.noreply.github.com>
Date: Sat, 21 Oct 2023 14:24:48 +0530
Subject: [PATCH] Added code for Matrix Chain Multiplication

---
 Coding/Matrix_Chain_Multiplication.py | 51 +++++++++++++++++++++++++++
 1 file changed, 51 insertions(+)
 create mode 100644 Coding/Matrix_Chain_Multiplication.py

diff --git a/Coding/Matrix_Chain_Multiplication.py b/Coding/Matrix_Chain_Multiplication.py
new file mode 100644
index 0000000..a5e8463
--- /dev/null
+++ b/Coding/Matrix_Chain_Multiplication.py
@@ -0,0 +1,51 @@
+def matrix_chain_order(p):
+    """
+    Compute the minimum number of scalar multiplications needed to
+    multiply a sequence of matrices with given dimensions.
+
+    :param p: A list of matrix dimensions where p[i] is the number of rows of the i-th matrix,
+              and p[i+1] is the number of columns of the i-th matrix.
+    :return: A tuple (m, s) where m[i][j] contains the minimum number of scalar multiplications
+             required to compute the product of matrices i through j, and s[i][j] contains the
+             index of the matrix where the split should occur to achieve this minimum.
+    """
+    n = len(p) - 1  # Number of matrices
+    m = [[0] * (n + 1) for _ in range(n + 1)]  # Minimum scalar multiplications
+    s = [[0] * n for _ in range(n)]  # Splitting points
+
+    # Chain length l varies from 2 to n
+    for l in range(2, n + 1):
+        for i in range(n - l + 1):
+            j = i + l - 1
+            m[i][j] = float('inf')  # Initialize to positive infinity
+            for k in range(i, j):
+                # Calculate the cost of the multiplication
+                cost = m[i][k] + m[k + 1][j] + p[i] * p[k + 1] * p[j + 1]
+                if cost < m[i][j]:
+                    m[i][j] = cost
+                    s[i][j] = k
+
+    return m, s
+
+def print_optimal_parentheses(s, i, j):
+    """
+    Print the optimal parentheses for matrix chain multiplication.
+
+    :param s: The splitting points computed by the matrix_chain_order function.
+    :param i: The start index of the matrices to consider.
+    :param j: The end index of the matrices to consider.
+    """
+    if i == j:
+        print(f'Matrix {i}', end='')
+    else:
+        print('(', end='')
+        print_optimal_parentheses(s, i, s[i][j])
+        print_optimal_parentheses(s, s[i][j] + 1, j)
+        print(')', end='')
+
+# Example usage:
+matrix_dimensions = [30, 35, 15, 5, 10, 20, 25]
+m, s = matrix_chain_order(matrix_dimensions)
+print("Minimum number of scalar multiplications:", m[0][-1])
+print("Optimal Parentheses:", end=' ')
+print_optimal_parentheses(s, 0, len(matrix_dimensions) - 2)