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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:
1 <= m, n <= 100- It’s guaranteed that the answer will be less than or equal to
2 * 109.
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