LeetCode-in-All

62. Unique Paths

Medium

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?

Example 1:

Input: m = 3, n = 7

Output: 28

Example 2:

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 -> Down -> Down
2. Down -> Down -> Right
3. Down -> Right -> Down 

Example 3:

Input: m = 7, n = 3

Output: 28

Example 4:

Input: m = 3, n = 3

Output: 6

Constraints:

Solution

# @param {Integer} m
# @param {Integer} n
# @return {Integer}
def unique_paths(m, n)
  dp = Array.new(m) {Array.new(n, 0)}

  m.times {|i| dp[i][0] = 1}
  n.times {|j| dp[0][j] = 1}

  (1...m).each do |i|
    (1...n).each do |j|
      dp[i][j] = dp[i - 1][j] + dp[i][j - 1]
    end
  end

  dp[m - 1][n - 1]
end