added DP solution to max grid problem.

Author: swapnilnarad2000

20. Dynamic Programming/finding_max_grid_problem.cpp

@@ -0,0 +1,69 @@
+#include <iostream>
+#include <bits/stdc++.h>
+
+typedef long long ll;
+
+using namespace std;
+
+// DP, Kadane's Algorithm
+
+int MaxSumSubArray(vector<int> &list)
+{
+    int n = list.size();
+    int sumNow = 0;
+    int maxSum = INT16_MIN;
+    for (int i = 0; i < n; i++)
+    {
+        sumNow = sumNow + list[i];
+        if (sumNow < 0)
+            sumNow = 0;
+        if (maxSum < sumNow)
+            maxSum = sumNow;
+    }
+    for (int i = 0; i < n; i++)
+    {
+        if (list[i] > maxSum)
+            maxSum = list[i];
+    }
+    return maxSum;
+}
+
+int main()
+{
+    int n, m;
+    cin >> n >> m;
+    vector<vector<int>> matrix(n, vector<int>(m, 0));
+    // taking input
+    for (int i = 0; i < n; i++)
+    {
+        for (int j = 0; j < m; j++)
+        {
+            int num;
+            cin >> num;
+            matrix[i][j] = num;
+        }
+    }
+    int maxGridSum = 0;
+    // making DP array
+    // appending first column to it
+    vector<int> DP(n, 0);
+    // configuring L and R for grids
+    for (int i = 0; i < m; i++)
+    {
+        DP.assign(n, 0);
+        for (int j = i; j < m; j++)
+        {
+            for (int k = 0; k < n; k++)
+            {
+                DP[k] += matrix[k][j];
+            }
+            int calculate = MaxSumSubArray(DP);
+            cout << "sum at : " << i << " and " << j << " : " << calculate << endl;
+            if (calculate > maxGridSum)
+                maxGridSum = calculate;
+        }
+    }
+    // vector<int> arr{1, -4, 2, -9, 2};
+    cout << maxGridSum << endl;
+    return 0;
+}