DP GRID Minimum cost

Author: Dhananjay Nagargoje

Diff for: src/main/java/problems/onRecursionAndDp/dp/MinimumCostInGrid.java

@@ -0,0 +1,59 @@
+package problems.onRecursionAndDp.dp;
+
+public class MinimumCostInGrid {
+
+    public int minPathSum(int[][] grid) {
+        int[][] dp = new int[grid.length][grid.length];
+        dp[0][0] = grid[0][0];
+
+        //fill the first row as there is only one way to visit row from right side
+        //so cost will be cost till previous cell + current grid cost
+        for (int i=1;i<grid.length;i++) dp[0][i] = dp[0][i-1] + grid[0][i];
+
+        //same for first column there is only  one way to visit by from top.
+        for (int i=1;i<grid.length;i++) dp[i][0] = dp[i-1][0] + grid[i][0];
+
+        //for remaining each cell there are two possibilities from top  and from right
+        //so to minimize cost take minimum at each step > optimal substructure
+        //final minimum depends on minimum at each step.
+        for (int i=1;i<grid.length;i++){
+            for (int j=1;j<grid.length;j++) {
+                dp[i][j] = Math.min(dp[i-1][j], dp[i][j-1]) + grid[i][j];
+            }
+        }
+
+        return dp[grid.length-1][grid.length-1];
+    }
+
+    public static void main(String[] args) {
+       int[][] grid = {{1,2,3},{4,5,6}};
+        System.out.println(grid.length);
+        System.out.println(grid[0].length);
+    }
+}
+/**
+ 64. Minimum Path Sum
+ Medium
+
+ 1878
+
+ 46
+
+ 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:
+
+ Input:
+ [
+ [1,3,1],
+ [1,5,1],
+ [4,2,1]
+ ]
+ Output: 7
+ Explanation: Because the path 1→3→1→1→1 minimizes the sum.
+ */