add solution of problem 64: minimun path sum

Author: ppulse

MinimunPathSum64/README.md

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+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.

MinimunPathSum64/Solution.java

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+public class Solution {
+    public int minPathSum(int[][] grid) {
+        if (grid == null || grid.length == 0 || grid[0].length == 0)
+            return 0;
+        
+        int rowLen = grid.length;
+        int colLen = grid[0].length;
+        int[][] pathSum = new int[rowLen][colLen];
+        int lastRowIdx = rowLen - 1;
+        int lastColIdx = colLen - 1;
+        int lastButOneRowIdx = lastRowIdx - 1;
+        int lastButOneColIdx = lastColIdx - 1;
+
+        pathSum[lastRowIdx][lastColIdx] = grid[lastRowIdx][lastColIdx];
+        
+        for (int row = lastRowIdx, col = lastButOneColIdx; col >= 0; col--) {
+            pathSum[row][col] += pathSum[row][col+1] + grid[row][col];
+        }
+
+        for (int row = lastButOneRowIdx, col = lastColIdx; row >= 0; row--) {
+            pathSum[row][col] += pathSum[row+1][col] + grid[row][col];
+        }
+
+        for (int row = lastButOneRowIdx; row >= 0; row--) {
+            for (int col = lastButOneColIdx; col >= 0; col--) {
+                int rowBelow = row + 1;
+                int colRight = col + 1;
+                int minValue = pathSum[rowBelow][col] < pathSum[row][colRight] ? pathSum[rowBelow][col] : pathSum[row][colRight];
+                pathSum[row][col] += grid[row][col] + minValue;
+            }
+        }
+        
+        return pathSum[0][0];
+    }
+}