爬楼梯

/**
* 时间复杂度O(2^n)
*/

const climbStairsByRecursion = (n) => {
    if(n === 1) return 1
    if(n === 2) return 2
    return climbStairsByRecursion(n - 1) + climbStairsByRecursion(n - 2)
}

/**

* 记忆化斐波那契

*/

const climbStairsByMemory = (n) => {
    const memory = [1,1]
    const fibonacci = (n) => {
        if(memory[n]) return memory[n]
        return memory[n] = fibonacci(n - 1, memory) + fibonacci(n - 2, memory)
    }
    return fibonacci
}

/**
* 动态规划
* 时间复杂度O(n)
* 空间复杂度O(n)
*/

const climbStairsByDynamic = (n) => {
    const arr = [0,1,2]
    if(n < 3){
        return arr[n]
    }
    for(let i = 3; i <= n; i++){
        arr[i] = arr[i - 1] + arr[i - 2]
    }
    return arr[n]
}

/**
* 斐波那契
* 时间复杂度O(n)
* 空间复杂度O(1)
*/

const climbStairsByFibonacci = (n) => {
    let x = 1,y = 1
    while(--n > 0){
        y = x + y
        x = y - x
    }
    return y
}