Goldmine problem dp added

Algorithms/Dynamic Problems/C++/Gold_mine.cpp

@@ -0,0 +1,46 @@
+/*
+ Problem : We are given a gold mine of n*m dimensions.
+ Each field in mine contains a positive integer which is the amount of gold in tons. Initially the miner can start from any row in the first column. From a given cell, the miner can move
+
+ 1. to the cell diagonally up towards the right 
+ 2. to the right
+ 3. to the cell diagonally down towards the right
+ we need to find out maximum amount of gold which he can collect.
+
+ Sample I/p : 4 4
+              1 3 1 5 2 2 4 1 5 0 2 3 0 6 1 2
+ Sample O/P : 16
+ */
+
+ #include <bits/stdc++.h>
+ using namespace std;
+
+ int maxGold(int n, int m, vector<vector<int> > gold_mine) {
+         int ans = INT_MIN;
+         vector<vector<int> > dp(n+2, vector<int> (m+1, 0));
+         for(int j = 1;  j <= m; j++){
+             for(int i = 1; i <= n; i++){
+                 dp[i][j] = max(dp[i-1][j-1], max(dp[i][j-1], dp[i+1][j-1])) + gold_mine[i-1][j-1];
+             }
+         }
+
+         for(int i = 0;i <= n;i++)
+             ans = max(dp[i][m], ans);
+
+         return ans;
+ }
+
+ int main() {
+     int m,n;
+     cin >> n >> m;
+     vector<vector<int> > gold_mine(n, vector<int>(m, 0));
+     for (int i = 0; i < n; i++) {
+         for (int j = 0; j < m; j++) {
+             cin >> gold_mine[i][j];
+         }
+     }
+
+     cout<< maxGold(n, m, gold_mine) <<"\n";
+     return 0;
+
+ }