UniquePathsII.java

Author: 李文超

README.md

@@ -85,6 +85,7 @@ This is leetcode solution in Java with eplaination and generalization.
 |---| ----- | -------- | ---------- | ----------- |
 | 5 | [Longest Palindromic Substring](https://leetcode.com/problems/longest-palindromic-substring/) | dp | Medium | [LongestPalindromicSubstring.java](https://github.com/venciallee/leetcode-in-Java/blob/master/algorithm/app/src/main/java/com/bytecode/leetcode/dp/LongestPalindromicSubstring.java) |
 | 62 | [Unique Paths](https://leetcode.com/problems/unique-paths/) | dp | Medium | [UniquePaths.java](https://github.com/venciallee/leetcode-in-Java/blob/master/algorithm/app/src/main/java/com/bytecode/leetcode/dp/UniquePaths.java) |
+| 63 | [Unique Paths II](https://leetcode.com/problems/unique-paths-ii/) | dp | Medium | [UniquePathsII.java](https://github.com/venciallee/leetcode-in-Java/blob/master/algorithm/app/src/main/java/com/bytecode/leetcode/dp/UniquePathsII.java) |
 
 ## Design
 

algorithm/app/src/main/java/com/bytecode/leetcode/dp/UniquePathsII.java

@@ -0,0 +1,80 @@
+package com.bytecode.leetcode.dp;
+
+/**
+ * 63. Unique Paths II
+ * <p>
+ * A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).
+ * <p>
+ * The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked 'Finish' in the diagram below).
+ * <p>
+ * Now consider if some obstacles are added to the grids. How many unique paths would there be?
+ * <p>
+ * An obstacle and empty space is marked as 1 and 0 respectively in the grid.
+ * <p>
+ * Note: m and n will be at most 100.
+ * <p>
+ * Example 1:
+ * <p>
+ * Input:
+ * [
+ * [0,0,0],
+ * [0,1,0],
+ * [0,0,0]
+ * ]
+ * Output: 2
+ * Explanation:
+ * There is one obstacle in the middle of the 3x3 grid above.
+ * There are two ways to reach the bottom-right corner:
+ * 1. Right -> Right -> Down -> Down
+ * 2. Down -> Down -> Right -> Right
+ * <p>
+ * <a href="https://leetcode.com/problems/unique-paths-ii/">63. Unique Paths II</a>
+ * <p>
+ * <a href="https://leetcode-cn.com/problems/unique-paths-ii/">63. 不同路径 II</a>
+ * Created by vencial on 2019-09-10.
+ */
+public class UniquePathsII {
+
+    /**
+     * 1. 设dp为每格可能路径的总数, 如果无路障则第一行和第一列均为1, 否则为0
+     * 2. 如果obstacleGrid[i][j]是路障, 则dp[i][j]为0, 否则dp[i][j]则为dp[i - 1][j] 加上dp[i][j - 1]的总和
+     * <p>
+     * 1. let dp is the sum of possible unique paths, as we know dp of the first row and column is 1 if there is no obstacles
+     * 2. if obstacleGrid[i][j] is obstacles, dp[i][j] should be 0, else dp[i][j] is the sum of left dp and the top dp, that is dp[i - 1][j] + dp[i][j - 1]
+     *
+     * @param obstacleGrid obstacleGrid
+     * @return int
+     */
+    public int uniquePathsWithObstacles(int[][] obstacleGrid) {
+        if (obstacleGrid.length == 0) return 0;
+        if (obstacleGrid[0][0] == 1) {
+            return 0;
+        }
+        int row = obstacleGrid.length;
+        int column = obstacleGrid[0].length;
+        int dp[][] = new int[row][column];
+        dp[0][0] = 1;
+        for (int i = 1; i < row; i++) {
+            if (obstacleGrid[i][0] != 1 && dp[i - 1][0] == 1) {
+                dp[i][0] = 1;
+            }
+        }
+
+        for (int i = 1; i < column; i++) {
+            if (obstacleGrid[0][i] != 1 && dp[0][i - 1] == 1) {
+                dp[0][i] = 1;
+            }
+        }
+
+        for (int i = 1; i < row; i++) {
+            for (int j = 1; j < column; j++) {
+                if (obstacleGrid[i][j] == 1) {
+                    dp[i][j] = 0;
+                    continue;
+                }
+                dp[i][j] = dp[i - 1][j] + dp[i][j - 1];
+            }
+        }
+        return dp[row - 1][column - 1];
+    }
+}