Unique Paths.py

# https://leetcode.com/problems/unique-paths/
# Hak Soo Kim
# 2/28/2022

class Solution(object):
    def uniquePaths(self, m, n):
        arr = [[1] * n] * m
        for i in range(1, m):
            for j in range(1, n):
                arr[i][j] = arr[i - 1][j] + arr[i][j - 1]
        return arr[m - 1][n - 1]
        """
        :type m: int
        :type n: int
        :rtype: int
        """

# There is a robot on an m x n grid. The robot is initially located at the top-left corner (i.e., grid[0][0]). The robot tries to move to the bottom-right corner (i.e., grid[m - 1][n - 1]). The robot can only move either down or right at any point in time.
#
# Given the two integers m and n, return the number of possible unique paths that the robot can take to reach the bottom-right corner.
#
# The test cases are generated so that the answer will be less than or equal to 2 * 109.
#
# 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
#
# Constraints:
#
# 1 <= m, n <= 100