[swift] LeetCode 62. Unique Paths

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?

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

Note: m and n will be at most 100.

func uniquePaths(_ m: Int, _ n: Int) -> Int {
    pathMatrix = Array(repeating: Array(repeating: 0, count: n+1), count: m+1)
    return pathMatrix(m, n)
}
 
private var pathMatrix: [[Int]]!
private func pathMatrix(_ m: Int, _ n: Int) -> Int {
    if m <= 0 || n <= 0 { return 0 }
    if m < 2 || n < 2 { pathMatrix[m][n] = 1; return 1 }
 
    if pathMatrix[m-1][n] == 0 {
        pathMatrix[m-1][n] = pathMatrix(m-1, n)
    }
    if pathMatrix[m][n-1] == 0 {
        pathMatrix[m][n-1] = pathMatrix(m, n-1)
    }
    return pathMatrix[m-1][n] + pathMatrix[m][n-1]
}

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