A robot is located at the top-left corner of a m x n grid (marked ‘Start’ in the diagram below).
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).
How many possible unique paths are there?
Above is a 7 x 3 grid. How many possible unique paths are there?
Note:m and n will be at most 100.
Example 1:
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Input: m = 3, n = 2 Output: 3 Explanation: From the top-left corner, there are a total of 3 ways to reach the bottom-right corner: 1\. Right -> Right -> Down 2\. Right -> Down -> Right 3\. Down -> Right -> Right
Example 2:
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Input: m = 7, n = 3 Output: 28
Solution
Language: Java
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classSolution{ publicintuniquePaths(int m, int n){ int[][] dp = newint[m][n]; Arrays.fill(dp[0], 1); for (int i = 0; i < m; i++) { dp[i][0] = 1; } for (int i = 1; i < m; i++) { for (int j = 1; j < n; j++) { dp[i][j] = dp[i - 1][j] + dp[i][j - 1]; } } return dp[m - 1][n - 1]; } }
滚动数组优化
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classSolution{ publicintuniquePaths(int m, int n){ if (m <= 1 || n <= 1) { return1; } int[][] dp = newint[2][n]; Arrays.fill(dp[0], 1); dp[1][0] = 1; for (int i = 1; i < m; i++) { for (int j = 1; j < n; j++) { dp[i % 2][j] = dp[(i - 1) % 2][j] + dp[i % 2][j - 1]; } } return dp[(m - 1) % 2][n - 1]; } }