Leetcode 63:Unique Paths II

Datetime:2016-08-23 01:21:26          Topic: LeetCode           Share

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.

For example,

There is one obstacle in the middle of a 3x3 grid as illustrated below.

[
  [0,0,0],
  [0,1,0],
  [0,0,0]
]

The total number of unique paths is 2 .

Note: m and  n will be at most 100.

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//这道题跟 Unique Paths 差不多,只是这道题给机器人加了障碍,不是每次都有两个选择(向右,向下)了。
//因为有了这个条件,所以 Unique Paths 中最后一个直接求组合的方法就不适用了,这里最好的解法就是用动态规划了。
//递推式还是跟 Unique Paths 一样,只是每次我们要判断一下是不是障碍,如果是,则dp[i][j] = 0,
//否则还是dp[i][j] = dp[i - 1][j] + dp[i][j - 1]。
class Solution {
public:
	int uniquePathsWithObstacles(vector<vector<int>>& obstacleGrid) {
		int m = obstacleGrid.size(), n = obstacleGrid[0].size();
		if (m== 0 || n == 0)
			return 0;

		vector<int> dp(n);
		dp[0] = 1;
		for (int i = 0; i < obstacleGrid.size(); ++i)
		{
			for (int j = 0; j < obstacleGrid[0].size();++j)
			{
				if (obstacleGrid[i][j] == 1)
					dp[j] = 0;
				else
				{
					if (j>0)   dp[j] = dp[j] + dp[j - 1];
				}
			}
		}
		return dp[n - 1];
	}
};




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