数据结构之递归

1. 概念

函数内部调用函数自身就是递归。在编写递归的函数的时候原则：

1. 找到最小单元。
2. 找到终止条件

2. 实例

2.1 数字阶乘

// 数字阶乘, 0的阶乘是1
// 1. 迭代方式
function factorialInteractive(num) {
  if (typeof num !== 'number' || num < 0) return undefined;

  let total = 1;
  for(let i = num; i > 1; i--) {
    total *= i;
  }
  return total;
}

// 2. 递归
function factorialRecursion(num) {
  if (num === 0 || num === 1) {
    return 1;
  }
  return num * factorialRecursion(num - 1);
}

let a = factorialInteractive(10);
let b = factorialRecursion(10);
console.log('a:', a);
console.log('b:', b);

2.2 斐波那契数

裴波那契数 0,1,1,2,3,5,8,13,21,34…

// 1. 迭代
function fibonacciInteractive(n) {
  if (n < 1) return 0;
  if (n <= 2) return 1;

  let fibNMinus1 = 0;
  let fibNMinus2 = 1;
  let fibB = 2;

  for (let i = 2; i <= n; i++) {
    fibB = fibNMinus1 + fibNMinus2;
    fibNMinus1 = fibNMinus2;
    fibNMinus2 = fibB;
  }
  return fibB;
}

// 递归
function fibonacciRecursion(n) {
  if (n < 1) return 0;
  if (n <= 2) return 1;

  return fibonacciRecursion(n - 1) + fibonacciRecursion(n - 2);
}

let c = fibonacciInteractive(10);
let d = fibonacciRecursion(10);
console.log('c:', c);
console.log('d:', d);

2.3 记忆化斐波那契数

function fibonacciMemoization(n) {
  const memo = [0, 1]; 
  const fibonacci = (n) => {
    if (memo[n] != null) return memo[n]; 
    return memo[n] = fibonacci(n -1, memo) + fibonacci(n -2, memo); 
  };
  return fibonacci;
}