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package class12;
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import java.util.HashMap;
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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 ways1(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 process1(arr, 0, aim);
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}
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public static int process1(int[] arr, int index, int rest) {
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if(index == arr.length) {
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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 += process1(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 ways2(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[][] dp = new int[arr.length+1][aim+1];
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// 一开始所有的过程，都没有计算呢
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// dp[..][..] = -1
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for(int i = 0 ; i < dp.length; i++) {
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for(int j = 0 ; j < dp[0].length; j++) {
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dp[i][j] = -1;
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}
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}
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return process2(arr, 0, aim , dp);
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}
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// 如果index和rest的参数组合，是没算过的，dp[index][rest] == -1
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// 如果index和rest的参数组合，是算过的，dp[index][rest] > - 1
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public static int process2(int[] arr,
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int index, int rest,
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int[][] dp) {
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if(dp[index][rest] != -1) {
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return dp[index][rest];
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}
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if(index == arr.length) {
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dp[index][rest] = rest == 0 ? 1 :0;
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return dp[index][rest];
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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 += process2(arr, index + 1, rest - (zhang * arr[index]) , dp );
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}
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dp[index][rest] = ways;
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return ways;
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}
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public static int ways3(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;// dp[N][1...aim] = 0;
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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 ways4(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;// dp[N][1...aim] = 0;
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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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public static void main(String[] args) {
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int[] arr = { 5, 10,50,100 };
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int sum = 1000;
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System.out.println(ways1(arr, sum));
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System.out.println(ways2(arr, sum));
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System.out.println(ways3(arr, sum));
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System.out.println(ways4(arr, sum));
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}
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}
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