Unique Paths II

• Lintcode : 115 / Leetcode : 63
• Level : Easy

Problem

Follow up for "Unique Paths":

Now consider if some obstacles are added to the grids. How many unique paths would there be?

An obstacle and empty space is marked as 1 and 0 respectively in the grid.

Example
Example 1:
    Input: [[0]]
    Output: 1

Example 2:
    Input:  [[0,0,0],[0,1,0],[0,0,0]]
    Output: 2

    Explanation:
    Only 2 different path.


Notice
m and n will be at most 100.

Concept & Algorithm

筆記

Time Complexity & Space Complexity

time : O(m n)
space: O(m n)

Answer

class Solution {
public:
    int uniquePathsWithObstacles(vector<vector<int>> &obstacleGrid) {
        int m = obstacleGrid.size(), n = obstacleGrid[0].size();
        vector<vector<int>> dp(m, vector<int>(n, 0));
        dp[0][0] = 1;
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                if (obstacleGrid[i][j] == 1) {
                    dp[i][j] = 0;
                }else if (i == 0 && j == 0) {
                    continue;
                }else if (i == 0) {
                    dp[i][j] = dp[i][j - 1];
                }else if (j == 0) {
                    dp[i][j] = dp[i - 1][j];
                }else {
                    dp[i][j] = dp[i - 1][j] + dp[i][j - 1];
                }
            }
        }
        return dp[m - 1][n - 1];
    }
};

tags: DP

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