Create dp-on-matrices.cpp

Author: rachitiitr

dp-on-matrices.cpp

@@ -0,0 +1,59 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+const int N = 1003;
+int n, m, a[N][N], dp[N][N], vis[N][N];
+
+//Returns the max sum you can achieve 
+//when you start at (i,j) and end at (n-1, m-1)
+//and move only in down and right directions
+int go(int i, int j){
+    if(i == n-1 and j == m-1)
+        return a[i][j];
+    
+    if(vis[i][j]) return dp[i][j];
+    
+    vis[i][j] = 1;
+    
+    int &ans = dp[i][j];
+    
+    if(i<n-1 and j<m-1)
+        ans = a[i][j] + max(go(i, j+1), go(i+1, j));
+    else if(i == n-1)
+            ans = a[i][j]+ go(i, j+1);
+    else 
+        ans = a[i][j] + go(i+1, j);
+    
+	return ans;
+}
+
+int main() {
+	int i, j;
+	cin >> n >> m;
+	
+	for(i = 0; i < n; i++)
+		for(j = 0; j < m; j++)
+			cin >> a[i][j];
+			
+	//Display the matrix
+	for(i = 0; i < n; i++){
+		for(j = 0; j < m; j++)
+			cout << a[i][j] << "\t";
+		cout << endl;
+	}
+			
+	//Print the answer
+	cout << go(0, 0) << endl;
+	//It should be 73 i.e 1+5+9+13+14+15+16
+	
+	
+	return 0;
+    
+}
+
+//Input:
+//4 4
+//1 2 3 4
+//5 6 7 8
+//9 10 11 12
+//13 14 15 16