minimum path sum

fishercoder1534 · fishercoder1534 · commit a8ecd7215991 · 2016-07-31T13:34:39.000-07:00
diff --git a/MEDIUM/src/medium/MinimumPathSum.java b/MEDIUM/src/medium/MinimumPathSum.java
@@ -0,0 +1,65 @@
+package medium;
+
+import utils.CommonUtils;
+
+/**64. Minimum Path Sum
+
+    Total Accepted: 78724
+    Total Submissions: 219899
+    Difficulty: Medium
+
+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.*/
+public class MinimumPathSum {
+    /**Same idea as ClimbingStairs, also typical trick:
+     * have to initialize the first row and the first column and start the for loop from i==1 and j==1 for the rest
+     * of the matrix.*/
+    public int minPathSum(int[][] grid) {
+        if(grid == null || grid.length == 0) return 0;
+        
+        int height = grid.length, width = grid[0].length;
+        int[][] dp = new int[height][width];
+        dp[0][0] = grid[0][0];
+        for(int i = 1; i < height; i++){
+            dp[i][0] = dp[i-1][0] + grid[i][0];
+        }
+        for(int j = 1; j < width; j++){
+            dp[0][j] = dp[0][j-1] + grid[0][j];
+        }
+        for(int i = 1; i < height; i++){
+            for(int j = 1; j < width; j++){
+                dp[i][j] = Math.min(dp[i-1][j], dp[i][j-1]) + grid[i][j];
+            }
+        }
+        CommonUtils.printMatrix(dp);
+        return dp[height-1][width-1];
+    }
+    
+    public static void main(String...strings){
+        MinimumPathSum test = new MinimumPathSum();
+//        int[][] grid = new int[2][2];
+//        grid[0][0] = 1;
+//        grid[0][1] = 2;
+//        grid[1][0] = 1;
+//        grid[1][1] = 1;
+        
+//        int[][] grid = new int[1][1];
+//        grid[0][0] = 1;
+        
+        int[][] grid = new int[3][3];
+        grid[0][0] = 1;
+        grid[0][1] = 3;
+        grid[0][2] = 1;
+        grid[1][0] = 1;
+        grid[1][1] = 5;
+        grid[1][2] = 1;
+        grid[2][0] = 4;
+        grid[2][1] = 2;
+        grid[2][2] = 1;
+        
+        
+        CommonUtils.printMatrix(grid);
+        System.out.println(test.minPathSum(grid));
+    }
+}
