69 lines
1.9 KiB
Dart
69 lines
1.9 KiB
Dart
/**
|
|
* File: coin_change.dart
|
|
* Created Time: 2023-08-11
|
|
* Author: liuyuxin (gvenusleo@gmail.com)
|
|
*/
|
|
|
|
import 'dart:math';
|
|
|
|
/* Coin change: Dynamic programming */
|
|
int coinChangeDP(List<int> coins, int amt) {
|
|
int n = coins.length;
|
|
int MAX = amt + 1;
|
|
// Initialize dp table
|
|
List<List<int>> dp = List.generate(n + 1, (index) => List.filled(amt + 1, 0));
|
|
// State transition: first row and first column
|
|
for (int a = 1; a <= amt; a++) {
|
|
dp[0][a] = MAX;
|
|
}
|
|
// State transition: the rest of the rows and columns
|
|
for (int i = 1; i <= n; i++) {
|
|
for (int a = 1; a <= amt; a++) {
|
|
if (coins[i - 1] > a) {
|
|
// If exceeding the target amount, do not choose coin i
|
|
dp[i][a] = dp[i - 1][a];
|
|
} else {
|
|
// The smaller value between not choosing and choosing coin i
|
|
dp[i][a] = min(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1);
|
|
}
|
|
}
|
|
}
|
|
return dp[n][amt] != MAX ? dp[n][amt] : -1;
|
|
}
|
|
|
|
/* Coin change: Space-optimized dynamic programming */
|
|
int coinChangeDPComp(List<int> coins, int amt) {
|
|
int n = coins.length;
|
|
int MAX = amt + 1;
|
|
// Initialize dp table
|
|
List<int> dp = List.filled(amt + 1, MAX);
|
|
dp[0] = 0;
|
|
// State transition
|
|
for (int i = 1; i <= n; i++) {
|
|
for (int a = 1; a <= amt; a++) {
|
|
if (coins[i - 1] > a) {
|
|
// If exceeding the target amount, do not choose coin i
|
|
dp[a] = dp[a];
|
|
} else {
|
|
// The smaller value between not choosing and choosing coin i
|
|
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;
|
|
|
|
// Dynamic programming
|
|
int res = coinChangeDP(coins, amt);
|
|
print("Minimum number of coins required to make up the target amount = $res");
|
|
|
|
// Space-optimized dynamic programming
|
|
res = coinChangeDPComp(coins, amt);
|
|
print("Minimum number of coins required to make up the target amount = $res");
|
|
}
|