DP typical problems

Author: zhongn2

Diff for: Minimum Path Sum.cpp

@@ -0,0 +1,26 @@
+//Minimum Path Sum
+
+//f[i][j] = min(f[i-1][j], f[i][j-1]) + grid[i][j]; 
+class Solution {
+public:
+    int minPathSum(vector<vector<int> > &grid) {
+        int m = grid.size();
+        int n = grid[0].size();
+        int path[m][n];
+		//initialization
+        path[0][0] = grid[0][0];
+        for(int i = 1; i < m; i++){
+            path[i][0] = path[i-1][0] + grid[i][0];
+        }
+        for(int i = 1; i < n; i++){
+            path[0][i] = path[0][i - 1] + grid[0][i];
+        }
+		
+        for(int i = 1; i < m; i++){
+            for(int k = 1; k < n; k++){
+                path[i][k] = min(path[i-1][k], path[i][k-1]) + grid[i][k];
+            }
+        }
+        return path[m-1][n-1];
+    }
+};