题目:楼梯有n阶台阶，每次可以上1阶、2阶或3阶,计算上楼梯的方式有多少种.

解法一

<pre><code>` func countStepWays(n:Int) -> Int {

    if n < 0 {
        return 0
    } else if n == 0 {
        return 1
    } else {
        return countStepWays(n:n - 1) + countStepWays(n: n - 2) + countStepWays(n: n - 3)
    }
}`</code></pre>

解法二

<pre><code>` func countStepWays2(n:Int,map:inout [Int]) -> Int {

    if n < 0 {
        return 0
    } else if n == 0 {
        return 1
    } else if map[n] > -1 {
        return map[n]
    } else {
        map[n] = countStepWays2(n: n - 1, map: &map) + countStepWays2(n: n - 2, map: &map) + countStepWays2(n: n - 3, map: &map)
        return map[n]
    }
}`</code></pre>

测试代码:
<pre><code>var steps:Int = recursion.countStepWays(n: 10) var map:[Int] = [Int].init(repeating: -1, count: 11) var steps2:Int = recursion.countStepWays2(n: 10, map: &map) print("FlyElephant--跳10级台阶的跳法---\(steps)-----\(steps2)")</code></pre>

FlyElephant.png