mirror of
https://github.com/krahets/hello-algo.git
synced 2024-12-26 11:16:28 +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
69 lines
2.1 KiB
Swift
69 lines
2.1 KiB
Swift
/**
|
||
* File: coin_change.swift
|
||
* Created Time: 2023-07-15
|
||
* Author: nuomi1 (nuomi1@qq.com)
|
||
*/
|
||
|
||
/* 零钱兑换：动态规划 */
|
||
func coinChangeDP(coins: [Int], amt: Int) -> Int {
|
||
let n = coins.count
|
||
let MAX = amt + 1
|
||
// 初始化 dp 表
|
||
var dp = Array(repeating: Array(repeating: 0, count: amt + 1), count: n + 1)
|
||
// 状态转移：首行首列
|
||
for a in stride(from: 1, through: amt, by: 1) {
|
||
dp[0][a] = MAX
|
||
}
|
||
// 状态转移：其余行和列
|
||
for i in stride(from: 1, through: n, by: 1) {
|
||
for a in stride(from: 1, through: amt, by: 1) {
|
||
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] = 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：空间优化后的动态规划 */
|
||
func coinChangeDPComp(coins: [Int], amt: Int) -> Int {
|
||
let n = coins.count
|
||
let MAX = amt + 1
|
||
// 初始化 dp 表
|
||
var dp = Array(repeating: MAX, count: amt + 1)
|
||
dp[0] = 0
|
||
// 状态转移
|
||
for i in stride(from: 1, through: n, by: 1) {
|
||
for a in stride(from: 1, through: amt, by: 1) {
|
||
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] = min(dp[a], dp[a - coins[i - 1]] + 1)
|
||
}
|
||
}
|
||
}
|
||
return dp[amt] != MAX ? dp[amt] : -1
|
||
}
|
||
|
||
@main
|
||
enum CoinChange {
|
||
/* Driver Code */
|
||
static func main() {
|
||
let coins = [1, 2, 5]
|
||
let amt = 4
|
||
|
||
// 动态规划
|
||
var res = coinChangeDP(coins: coins, amt: amt)
|
||
print("凑到目标金额所需的最少硬币数量为 \(res)")
|
||
|
||
// 空间优化后的动态规划
|
||
res = coinChangeDPComp(coins: coins, amt: amt)
|
||
print("凑到目标金额所需的最少硬币数量为 \(res)")
|
||
}
|
||
}
|