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package class22;
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public class Code02_MinCoinsNoLimit {
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public static int minCoins(int[] arr, int aim) {
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return process(arr, 0, aim);
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}
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// arr[index...]面值，每种面值张数自由选择，
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// 搞出rest正好这么多钱，返回最小张数
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// 拿Integer.MAX_VALUE标记怎么都搞定不了
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public static int process(int[] arr, int index, int rest) {
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if (index == arr.length) {
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return rest == 0 ? 0 : Integer.MAX_VALUE;
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} else {
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int ans = Integer.MAX_VALUE;
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for (int zhang = 0; zhang * arr[index] <= rest; zhang++) {
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int next = process(arr, index + 1, rest - zhang * arr[index]);
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if (next != Integer.MAX_VALUE) {
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ans = Math.min(ans, zhang + next);
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}
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}
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return ans;
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}
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}
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public static int dp1(int[] arr, int aim) {
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if (aim == 0) {
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return 0;
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}
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int N = arr.length;
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int[][] dp = new int[N + 1][aim + 1];
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dp[N][0] = 0;
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for (int j = 1; j <= aim; j++) {
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dp[N][j] = Integer.MAX_VALUE;
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}
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for (int index = N - 1; index >= 0; index--) {
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for (int rest = 0; rest <= aim; rest++) {
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int ans = Integer.MAX_VALUE;
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for (int zhang = 0; zhang * arr[index] <= rest; zhang++) {
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int next = dp[index + 1][rest - zhang * arr[index]];
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if (next != Integer.MAX_VALUE) {
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ans = Math.min(ans, zhang + next);
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}
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}
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dp[index][rest] = ans;
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}
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}
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return dp[0][aim];
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}
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public static int dp2(int[] arr, int aim) {
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if (aim == 0) {
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return 0;
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}
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int N = arr.length;
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int[][] dp = new int[N + 1][aim + 1];
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dp[N][0] = 0;
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for (int j = 1; j <= aim; j++) {
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dp[N][j] = Integer.MAX_VALUE;
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}
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for (int index = N - 1; index >= 0; index--) {
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for (int rest = 0; rest <= aim; rest++) {
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dp[index][rest] = dp[index + 1][rest];
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if (rest - arr[index] >= 0
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&& dp[index][rest - arr[index]] != Integer.MAX_VALUE) {
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dp[index][rest] = Math.min(dp[index][rest], dp[index][rest - arr[index]] + 1);
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}
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}
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}
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return dp[0][aim];
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}
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// 为了测试
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public static int[] randomArray(int maxLen, int maxValue) {
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int N = (int) (Math.random() * maxLen);
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int[] arr = new int[N];
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boolean[] has = new boolean[maxValue + 1];
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for (int i = 0; i < N; i++) {
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do {
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arr[i] = (int) (Math.random() * maxValue) + 1;
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} while (has[arr[i]]);
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has[arr[i]] = true;
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}
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return arr;
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}
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// 为了测试
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public static void printArray(int[] arr) {
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for (int i = 0; i < arr.length; i++) {
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System.out.print(arr[i] + " ");
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}
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System.out.println();
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}
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// 为了测试
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public static void main(String[] args) {
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int maxLen = 20;
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int maxValue = 30;
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int testTime = 300000;
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System.out.println("功能测试开始");
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for (int i = 0; i < testTime; i++) {
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int N = (int) (Math.random() * maxLen);
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int[] arr = randomArray(N, maxValue);
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int aim = (int) (Math.random() * maxValue);
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int ans1 = minCoins(arr, aim);
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int ans2 = dp1(arr, aim);
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int ans3 = dp2(arr, aim);
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if (ans1 != ans2 || ans1 != ans3) {
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System.out.println("Oops!");
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printArray(arr);
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System.out.println(aim);
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System.out.println(ans1);
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System.out.println(ans2);
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break;
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}
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}
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System.out.println("功能测试结束");
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}
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}
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