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package class12;
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public class Code09_CoinsWay {
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// arr中都是正数且无重复值，返回组成aim的方法数
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public static int ways(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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// 如果自由使用arr[index...]的面值，组成rest这么多钱，返回方法数 （1 , 6）
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public static int process(int[] arr, int index, int rest) {
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if (index == arr.length) { // 无面值的时候
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return rest == 0 ? 1 : 0;
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}
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// 有面值的时候
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int ways = 0;
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// arr[index] 当钱面值
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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 waysdp(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 i = N - 1; i >= 0; i--) { // 大顺序 从下往上
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for (int rest = 0; rest <= aim; rest++) {
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dp[i][rest] = dp[i + 1][rest];
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if (rest - arr[i] >= 0) {
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dp[i][rest] += dp[i][rest - arr[i]];
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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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public static void main(String[] args) {
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int[] arr = { 5, 2, 3, 1 };
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int sum = 350;
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System.out.println(ways(arr, sum));
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System.out.println(waysdp(arr, sum));
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}
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}
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