https://leetcode.com/problems/unique-paths/

unique_paths.go

func uniquePaths(m int, n int) int {
    // we are going to memorize all previous steps
    moves := make([][]int, n)
    
    for i, _ := range moves {
        moves[i] = make([]int, m)
    }
    
    // we are already located at the top-left corner.
    // There is only one way to be at this cell.
    moves[0][0] = 1
    
    for i := 0; i < n; i++ {
        for j := 0; j < m; j++ {
            // Can we come from left cell to the right?
            if j > 0 {
                moves[i][j] += moves[i][j - 1]
            }
            
            // Can we come from the top cell to the down?
            if i > 0 {
                moves[i][j] += moves[i - 1][j]
            }
        }
    }
    
    // Return the total number of unique paths
    return moves[n - 1][m - 1]
}