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package class21;
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public class Code03_CoinsWayNoLimit {
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public static int coinsWay(int[] arr, int aim) {
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if (arr == null || arr.length == 0 || aim < 0) {
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return 0;
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}
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return process(arr, 0, aim);
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}
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// arr[index....] 所有的面值，每一个面值都可以任意选择张数，组成正好rest这么多钱，方法数多少？
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public static int process(int[] arr, int index, int rest) {
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if (index == arr.length) { // 没钱了
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return rest == 0 ? 1 : 0;
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}
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int ways = 0;
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for (int zhang = 0; zhang * arr[index] <= rest; zhang++) {
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ways += process(arr, index + 1, rest - (zhang * arr[index]));
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}
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return ways;
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}
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public static int dp1(int[] arr, int aim) {
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if (arr == null || arr.length == 0 || 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] = 1;
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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 ways = 0;
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for (int zhang = 0; zhang * arr[index] <= rest; zhang++) {
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ways += dp[index + 1][rest - (zhang * arr[index])];
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}
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dp[index][rest] = ways;
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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 (arr == null || arr.length == 0 || 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] = 1;
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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] += dp[index][rest - arr[index]];
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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 = 10;
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int maxValue = 30;
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int testTime = 1000000;
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System.out.println("测试开始");
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for (int i = 0; i < testTime; i++) {
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int[] arr = randomArray(maxLen, maxValue);
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int aim = (int) (Math.random() * maxValue);
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int ans1 = coinsWay(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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System.out.println(ans3);
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break;
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}
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}
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System.out.println("测试结束");
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}
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}
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