斐波那契数列-递归的优化

实现斐波那契数列:

1 1 2 3 5 8 13 21 34 55 ···

• fib(1) = 1
• fib(2) = 1
• fib(n) = fib(n-1) + fib(n-2)

for循环实现

function fib(n){
    let val1 = 1, val2 = 1, temp
    if(n === 1) return val1
    for(let i=3; i<=n; i++){
        temp = val1 + val2        val1 = val2
        val2 = temp    }
    return val2
}

递归实现

function fib(){
    if(n === 1 || n === 2) return 1    return fib(n-1) + fib(n-2)
}

用空间换效率

function fib(n) {
  let arr = [0, 1, 1]
  for(i=3; i<=n; i++) {
    arr[i] = arr[i-1] + arr[i-2]
  }
  return arr[n]
}

使用缓存提升效率

function fib(n) {
  let cache = [0, 1, 1]
  function _fib(n) {
    if(cache[n]) return cache[n]
    cache[n] = _fib(n-1) + _fib(n-2)
    return cache[n]
  }
  return _fib(n)
}