mirror of
https://github.com/krahets/hello-algo.git
synced 2024-12-25 13:46:30 +08:00
e720aa2d24
* Sync recent changes to the revised Word. * Revised the preface chapter * Revised the introduction chapter * Revised the computation complexity chapter * Revised the chapter data structure * Revised the chapter array and linked list * Revised the chapter stack and queue * Revised the chapter hashing * Revised the chapter tree * Revised the chapter heap * Revised the chapter graph * Revised the chapter searching * Reivised the sorting chapter * Revised the divide and conquer chapter * Revised the chapter backtacking * Revised the DP chapter * Revised the greedy chapter * Revised the appendix chapter * Revised the preface chapter doubly * Revised the figures
66 lines
2 KiB
JavaScript
66 lines
2 KiB
JavaScript
/**
|
|
* File: coin_change.js
|
|
* Created Time: 2023-08-23
|
|
* Author: Gaofer Chou (gaofer-chou@qq.com)
|
|
*/
|
|
|
|
/* 零钱兑换：动态规划 */
|
|
function coinChangeDP(coins, amt) {
|
|
const n = coins.length;
|
|
const MAX = amt + 1;
|
|
// 初始化 dp 表
|
|
const dp = Array.from({ length: n + 1 }, () =>
|
|
Array.from({ length: amt + 1 }, () => 0)
|
|
);
|
|
// 状态转移：首行首列
|
|
for (let a = 1; a <= amt; a++) {
|
|
dp[0][a] = MAX;
|
|
}
|
|
// 状态转移：其余行和列
|
|
for (let i = 1; i <= n; i++) {
|
|
for (let a = 1; a <= amt; a++) {
|
|
if (coins[i - 1] > a) {
|
|
// 若超过目标金额，则不选硬币 i
|
|
dp[i][a] = dp[i - 1][a];
|
|
} else {
|
|
// 不选和选硬币 i 这两种方案的较小值
|
|
dp[i][a] = Math.min(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1);
|
|
}
|
|
}
|
|
}
|
|
return dp[n][amt] !== MAX ? dp[n][amt] : -1;
|
|
}
|
|
|
|
/* 零钱兑换：状态压缩后的动态规划 */
|
|
function coinChangeDPComp(coins, amt) {
|
|
const n = coins.length;
|
|
const MAX = amt + 1;
|
|
// 初始化 dp 表
|
|
const dp = Array.from({ length: amt + 1 }, () => MAX);
|
|
dp[0] = 0;
|
|
// 状态转移
|
|
for (let i = 1; i <= n; i++) {
|
|
for (let a = 1; a <= amt; a++) {
|
|
if (coins[i - 1] > a) {
|
|
// 若超过目标金额，则不选硬币 i
|
|
dp[a] = dp[a];
|
|
} else {
|
|
// 不选和选硬币 i 这两种方案的较小值
|
|
dp[a] = Math.min(dp[a], dp[a - coins[i - 1]] + 1);
|
|
}
|
|
}
|
|
}
|
|
return dp[amt] !== MAX ? dp[amt] : -1;
|
|
}
|
|
|
|
/* Driver Code */
|
|
const coins = [1, 2, 5];
|
|
const amt = 4;
|
|
|
|
// 动态规划
|
|
let res = coinChangeDP(coins, amt);
|
|
console.log(`凑到目标金额所需的最少硬币数量为 ${res}`);
|
|
|
|
// 状态压缩后的动态规划
|
|
res = coinChangeDPComp(coins, amt);
|
|
console.log(`凑到目标金额所需的最少硬币数量为 ${res}`);
|