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149 lines
3.7 KiB
149 lines
3.7 KiB
package class21;
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import java.util.HashMap;
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import java.util.Map.Entry;
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public class Code04_CoinsWaySameValueSamePapper {
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public static class Info {
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public int[] coins;
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public int[] zhangs;
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public Info(int[] c, int[] z) {
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coins = c;
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zhangs = z;
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}
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}
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public static Info getInfo(int[] arr) {
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HashMap<Integer, Integer> counts = new HashMap<>();
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for (int value : arr) {
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if (!counts.containsKey(value)) {
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counts.put(value, 1);
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} else {
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counts.put(value, counts.get(value) + 1);
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}
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}
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int N = counts.size();
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int[] coins = new int[N];
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int[] zhangs = new int[N];
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int index = 0;
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for (Entry<Integer, Integer> entry : counts.entrySet()) {
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coins[index] = entry.getKey();
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zhangs[index++] = entry.getValue();
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}
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return new Info(coins, zhangs);
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}
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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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Info info = getInfo(arr);
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return process(info.coins, info.zhangs, 0, aim);
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}
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// coins 面值数组,正数且去重
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// zhangs 每种面值对应的张数
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public static int process(int[] coins, int[] zhangs, int index, int rest) {
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if (index == coins.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 * coins[index] <= rest && zhang <= zhangs[index]; zhang++) {
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ways += process(coins, zhangs, index + 1, rest - (zhang * coins[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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Info info = getInfo(arr);
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int[] coins = info.coins;
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int[] zhangs = info.zhangs;
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int N = coins.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 * coins[index] <= rest && zhang <= zhangs[index]; zhang++) {
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ways += dp[index + 1][rest - (zhang * coins[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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Info info = getInfo(arr);
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int[] coins = info.coins;
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int[] zhangs = info.zhangs;
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int N = coins.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 - coins[index] >= 0) {
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dp[index][rest] += dp[index][rest - coins[index]];
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}
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if (rest - coins[index] * (zhangs[index] + 1) >= 0) {
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dp[index][rest] -= dp[index + 1][rest - coins[index] * (zhangs[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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for (int i = 0; i < N; i++) {
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arr[i] = (int) (Math.random() * maxValue) + 1;
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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 = 20;
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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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