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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
object Solution {
def uniquePaths(m: Int, n: Int): Int = {
val dp = Array.ofDim[Int](m, n)
for (i <- 0 until m) {
dp(i)(0) = 1
}
for (j <- 0 until n) {
dp(0)(j) = 1
}
for (i <- 1 until m) {
for (j <- 1 until n) {
dp(i)(j) = dp(i - 1)(j) + dp(i)(j - 1)
}
}
dp(m - 1)(n - 1)
}
}