From 92932f4e5b639393c95da4ca583f6fd1add34c77 Mon Sep 17 00:00:00 2001
From: Soumyakanta Barik <soumyakantabarik@gmail.com>
Date: Sun, 31 Oct 2021 22:46:58 +0530
Subject: [PATCH] Remove array end element to maximize the sum

Remove array end element to maximize the sum of product using dynamic programming
---
 ...element to maximize the sum of product.cpp | 39 +++++++++++++++++++
 1 file changed, 39 insertions(+)
 create mode 100644 Remove array end element to maximize the sum of product.cpp

diff --git a/Remove array end element to maximize the sum of product.cpp b/Remove array end element to maximize the sum of product.cpp
new file mode 100644
index 0000000..9b49358
--- /dev/null
+++ b/Remove array end element to maximize the sum of product.cpp	
@@ -0,0 +1,39 @@
+// CPP program to find maximum score we can get
+// by removing elements from either end.
+#include <bits/stdc++.h>
+#define MAX 50
+using namespace std;
+
+int solve(int dp[][MAX], int a[], int low, int high,
+										int turn)
+{
+	// If only one element left.
+	if (low == high)
+		return a[low] * turn;
+
+	// If already calculated, return the value.
+	if (dp[low][high] != 0)
+		return dp[low][high];
+
+	// Computing Maximum value when element at
+	// index i and index j is to be choosed.
+	dp[low][high] = max(a[low] * turn + solve(dp, a,
+							low + 1, high, turn + 1),
+						a[high] * turn + solve(dp, a,
+						low, high - 1, turn + 1));
+
+	return dp[low][high];
+}
+
+// Driven Program
+int main()
+{
+	int arr[] = { 1, 3, 1, 5, 2 };
+	int n = sizeof(arr) / sizeof(arr[0]);
+
+	int dp[MAX][MAX];
+	memset(dp, 0, sizeof(dp));
+
+	cout << solve(dp, arr, 0, n - 1, 1) << endl;
+	return 0;
+}