From 4a0930e3abc7abc29448dd4f6797c8ccf3eb6d8f Mon Sep 17 00:00:00 2001
From: Omprakash <59120734+opeeyum@users.noreply.github.com>
Date: Mon, 17 Oct 2022 22:11:41 +0530
Subject: [PATCH] Matrix Chain Multiplications

---
 C++/matrix_chain_multiplication.cpp | 90 +++++++++++++++++++++++++++++
 1 file changed, 90 insertions(+)
 create mode 100644 C++/matrix_chain_multiplication.cpp

diff --git a/C++/matrix_chain_multiplication.cpp b/C++/matrix_chain_multiplication.cpp
new file mode 100644
index 0000000..afaf069
--- /dev/null
+++ b/C++/matrix_chain_multiplication.cpp
@@ -0,0 +1,90 @@
+// MCM -> Recursive
+//  -> Recursive memomized
+// No Top down appraoch, it doesn't help.
+
+// FORMAT
+// 1. -> Decide i and j
+// 2. -> Set range of K
+// 3. -> Find funtion/operation to apply on temp_val
+
+// Printing MCM
+// Evaluate Expression to True or Boolean Parenthesis
+// Min/Max value of an expression
+// Palindrome Partitioning
+// Scramble string
+// Egg Droping Problem
+
+#include <iostream>
+#include <climits>
+#include <vector>
+using namespace std;
+
+typedef vector<vector<int>> tdvec;
+
+int mcm(int *arr, int i, int j, tdvec &ds)
+{
+    // Base condition
+    if (i >= j)
+        return 0;
+
+    // Memomisation
+    if (ds[i][j] != -1)
+        return ds[i][j];
+
+    int cost = INT_MAX;
+
+    for (int k = i; k < j; k++)
+    {
+        int temp = mcm(arr, i, k, ds) + mcm(arr, k + 1, j, ds);
+        temp += (arr[i - 1] * arr[k] * arr[j]);
+
+        cost = cost > temp ? temp : cost;
+    }
+
+    return ds[i][j] = cost;
+}
+
+bool is_palindrome(string str, int left, int right)
+{
+    while (left < right)
+    {
+        if (str[left] != str[right])
+            return false;
+
+        left++;
+        right--;
+    }
+    return true;
+}
+int palindrominc_partioning(string str, int left, int right)
+{
+    // Base condtion
+    // 1. Length of string either 0 or 1
+    if (left >= right)
+        return 0;
+
+    // 2. Given string is palindrome
+    if (is_palindrome(str, left, right))
+        return 0;
+
+    int ans = 1000001;
+    // Computation
+    for (int k = left; k < right; k++)
+    {
+        int temp_cost = palindrominc_partioning(str, left, k) + palindrominc_partioning(str, k + 1, right);
+        temp_cost += 1;
+
+        ans = temp_cost < ans ? temp_cost : ans;
+    }
+    return ans;
+}
+
+int main()
+{
+    int arr[] = {40, 20, 30, 10, 30};
+    int n = sizeof(arr) / sizeof(arr[0]);
+    tdvec ds(n + 1, vector<int>(n + 1, -1));
+    cout << mcm(arr, 1, n - 1, ds) << endl;
+
+    cout << palindrominc_partioning("abcde", 0, 4) << endl;
+}
\ No newline at end of file