MinimumPathSum

Change-Id: If5ffcb57ecfdab8d54a0fca6fba7d11dea0e1a76

Author: applewjg

MinimumPathSum.java

@@ -0,0 +1,32 @@
+/*
+ Author:     King, [email protected]
+ Date:       Dec 26, 2014
+ Problem:    Minimum Path Sum
+ Difficulty: Easy
+ Source:     https://oj.leetcode.com/problems/minimum-path-sum/
+ Notes:
+ 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.
+
+ Solution: Dynamic Programming. Space O(N).
+ */
+public class Solution {
+    public int minPathSum(int[][] grid) {
+        if (grid.length == 0) return Integer.MIN_VALUE;
+        int M = grid.length, N = grid[0].length;
+        int[] dp = new int[N];
+        dp[0] = grid[0][0];
+        for (int i = 1; i < N; ++i)
+            dp[i] = grid[0][i] + dp[i-1];
+        
+        for (int i = 1; i < M; ++i)
+        {
+            dp[0] += grid[i][0];
+            for (int j = 1; j < N; ++j)
+                dp[j] = Math.min(dp[j-1], dp[j]) + grid[i][j];
+        }
+        
+        return dp[N-1];  
+    }
+}