uniquePaths.go

/* https://leetcode.com/problems/unique-paths/description/
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?

https://leetcode.com/static/images/problemset/robot_maze.png

Above is a 3 x 7 grid. How many possible unique paths are there?

Note: m and n will be at most 100.
*/

package ldp

func uniquePaths(m int, n int) int {
	dp := make([][]int, m)
	for i := range dp {
		dp[i] = make([]int, n, n)
		dp[i][0] = 1
	}
	for i := 0; i < n; i++ {
		dp[0][i] = 1
	}

	for i := 1; i < m; i++ {
		for j := 1; j < n; j++ {
			dp[i][j] = dp[i-1][j] + dp[i][j-1]
		}
	}
	return dp[m-1][n-1]
}