文章直达地址: https://labuladong.gitee.io/algo/%E5%8A%A8%E6%80%81%E8%A7%84%E5%88%92%E7%B3%BB%E5%88%97/%E5%8A%A8%E6%80%81%E8%A7%84%E5%88%92%E8%AF%A6%E8%A7%A3%E8%BF%9B%E9%98%B6.html

本系列为labuladong的算法小抄的javascript实现版本，实现原理参考labuladong的算法小抄。
本文为第0章第2小节《动态规划》所涉及的代码，直接上代码

//斐波那契数列
/**
 * @param {number} n
 * @return {number}
 */
// var fib = function (n) {
//   if (n < 1) return 0;
//   const mp = {};
//   return helper(n, mp);
// };

// var helper = function (n, mp) {
//   if (n == 1 || n == 2) return 1;
//   if (mp[n] != undefined) {
//     return mp[n];
//   }
//   mp[n] = helper(n - 1, mp) + helper(n - 2, mp);
//   return mp[n];
// };

var fib = function (n) {
  if (n < 1) return 0;
  if (n == 2 || n == 1) return 1;
  let prev = 1;
  let curr = 1;
  for (let i = 2; i < n; i++) {
    let sum = prev + curr;
    prev = curr;
    curr = sum;
  }
  return curr;
};

// console.log(fib(3));

/**
 * 凑零钱问题v1.0 暴力穷举
 * @param {number[]} coins
 * @param {number} amount
 * @return {number}
 */
var coinChange = function (coins, amount) {
  function dp(n) {
    if (n == 0) return 0;
    if (n < 0) return -1;
    let res = Infinity;
    for (let index in coins) {
      let sb = dp(n - coins[index]);
      if (sb == -1) continue;
      res = Math.min(res, 1 + sb);
    }
    return res;
  }
  let num = dp(amount);
  return num == Infinity ? -1 : num;
};

// /**
//  * 凑零钱问题v2.0 备忘录
//  * @param {number[]} coins
//  * @param {number} amount
//  * @return {number}
//  */
// var coinChange = function (coins, amount) {
//   let mp = {};
//   function dp(n) {
//     if (mp[n]) return mp[n];
//     if (n == 0) return 0;
//     if (n < 0) return -1;
//     let res = Infinity;
//     for (let index in coins) {
//       let sb = dp(n - coins[index]);
//       if (sb == -1) continue;
//       res = Math.min(res, 1 + sb);
//     }
//     if (res != Infinity) {
//       mp[n] = res;
//     } else {
//       mp[n] = -1;
//     }
//     return res;
//   }
//   let num = dp(amount);
//   return num == Infinity ? -1 : num;
// };

/**
 * 凑零钱问题v2.0 备忘录
 * @param {number[]} coins
 * @param {number} amount
 * @return {number}
 */
var coinChange = function (coins, amount) {
  let infos = new Array(amount + 1);
  infos.fill(amount + 1);
  infos[0] = 0;
  for (let i = 0; i < infos.length; i++) {
    for (let index in coins) {
      if (i - coins[index] < 0) continue;
      infos[i] = Math.min(infos[i], 1 + infos[i - coins[index]]);
    }
  }
  return infos[amount] == amount + 1 ? -1 : infos[amount];
};

console.log(coinChange([1, 2, 5], 11));