Added minimum path sum problem solution in cpp

Author: sunilkumarmaurya786693

leetcode/dynamic programming/minimum-path-sum.cpp

@@ -0,0 +1,55 @@
+// 64. Minimum Path Sum
+// Medium
+
+// 8794
+
+// 113
+
+// Add to List
+
+// Share
+// Given a m x n grid filled with non-negative numbers, find a path from top left to bottom right, which minimizes the sum of all numbers along its path.
+
+// Note: You can only move either down or right at any point in time.
+
+ 
+
+// Example 1:
+
+
+// Input: grid = [[1,3,1],[1,5,1],[4,2,1]]
+// Output: 7
+// Explanation: Because the path 1 → 3 → 1 → 1 → 1 minimizes the sum.
+// Example 2:
+
+// Input: grid = [[1,2,3],[4,5,6]]
+// Output: 12
+ 
+
+// Constraints:
+
+// m == grid.length
+// n == grid[i].length
+// 1 <= m, n <= 200
+// 0 <= grid[i][j] <= 100
+
+class Solution {
+public:
+    int solve(vector<vector<int>>&grid,int n,int m, int i,int j, vector<vector<int>>&dp){
+        if(i<0 || j<0 || i>=n || j>=m)return 100000000;
+        if(dp[i][j]!=-1)return dp[i][j];
+        if(i==n-1 && j==m-1){
+            return grid[i][j];
+        }
+        int ans=solve(grid,n,m,i,j+1, dp)+grid[i][j];
+        ans=min(ans,solve(grid,n,m,i+1,j, dp)+grid[i][j]);
+        dp[i][j]=ans;
+        return ans;
+    }
+    int minPathSum(vector<vector<int>>& grid) {
+        int n=grid.size();
+        int m=grid[0].size();
+        vector<vector<int>>dp(n,vector<int>(m,-1));
+        return solve(grid,n,m,0,0,dp);
+    }
+};