mirror of
https://github.com/krahets/hello-algo.git
synced 2024-12-26 12:16:27 +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
68 lines
1.8 KiB
Dart
68 lines
1.8 KiB
Dart
/**
|
|
* File: coin_change.dart
|
|
* Created Time: 2023-08-11
|
|
* Author: liuyuxin (gvenusleo@gmail.com)
|
|
*/
|
|
|
|
import 'dart:math';
|
|
|
|
/* 零钱兑换：动态规划 */
|
|
int coinChangeDP(List<int> coins, int amt) {
|
|
int n = coins.length;
|
|
int MAX = amt + 1;
|
|
// 初始化 dp 表
|
|
List<List<int>> dp = List.generate(n + 1, (index) => List.filled(amt + 1, 0));
|
|
// 状态转移：首行首列
|
|
for (int a = 1; a <= amt; a++) {
|
|
dp[0][a] = MAX;
|
|
}
|
|
// 状态转移：其余行和列
|
|
for (int i = 1; i <= n; i++) {
|
|
for (int 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] = 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 */
|
|
int coinChangeDPComp(List<int> coins, int amt) {
|
|
int n = coins.length;
|
|
int MAX = amt + 1;
|
|
// 初始化 dp 表
|
|
List<int> dp = List.filled(amt + 1, MAX);
|
|
dp[0] = 0;
|
|
// 状态转移
|
|
for (int i = 1; i <= n; i++) {
|
|
for (int 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] = min(dp[a], dp[a - coins[i - 1]] + 1);
|
|
}
|
|
}
|
|
}
|
|
return dp[amt] != MAX ? dp[amt] : -1;
|
|
}
|
|
|
|
/* Driver Code */
|
|
void main() {
|
|
List<int> coins = [1, 2, 5];
|
|
int amt = 4;
|
|
|
|
// 动态规划
|
|
int res = coinChangeDP(coins, 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, amt);
|
|
print("凑到目标金额所需的最少硬币数量为 $res");
|
|
}
|