algorithm-class/MCA算法突击课/第01期/mca_test/Code03_CoinsWayNoLimit.java

package 第01期.mca_test;

public class Code03_CoinsWayNoLimit {

	public static int coinsWay(int[] arr, int aim) {
		if (arr == null || arr.length == 0 || aim < 0) {
			return 0;
		}
		return process(arr, 0, aim);
	}

	// 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？
	public static int process(int[] arr, int index, int rest) {
		if (index == arr.length) { // 没钱了
			return rest == 0 ? 1 : 0;
		}
		int ways = 0;
		for (int zhang = 0; zhang * arr[index] <= rest; zhang++) {
			ways += process(arr, index + 1, rest - (zhang * arr[index]));
		}
		return ways;
	}

	public static int dp1(int[] arr, int aim) {
		if (arr == null || arr.length == 0 || aim < 0) {
			return 0;
		}
		int N = arr.length;
		int[][] dp = new int[N + 1][aim + 1];
		dp[N][0] = 1;
		for (int index = N - 1; index >= 0; index--) {
			for (int rest = 0; rest <= aim; rest++) {
				int ways = 0;
				for (int zhang = 0; zhang * arr[index] <= rest; zhang++) {
					ways += dp[index + 1][rest - (zhang * arr[index])];
				}
				dp[index][rest] = ways;
			}
		}
		return dp[0][aim];
	}

	public static int dp2(int[] arr, int aim) {
		if (arr == null || arr.length == 0 || aim < 0) {
			return 0;
		}
		int N = arr.length;
		int[][] dp = new int[N + 1][aim + 1];
		dp[N][0] = 1;
		for (int index = N - 1; index >= 0; index--) {
			for (int rest = 0; rest <= aim; rest++) {
				dp[index][rest] = dp[index + 1][rest];
				if (rest - arr[index] >= 0) {
					dp[index][rest] += dp[index][rest - arr[index]];
				}
			}
		}
		return dp[0][aim];
	}

	// 为了测试
	public static int[] randomArray(int maxLen, int maxValue) {
		int N = (int) (Math.random() * maxLen);
		int[] arr = new int[N];
		boolean[] has = new boolean[maxValue + 1];
		for (int i = 0; i < N; i++) {
			do {
				arr[i] = (int) (Math.random() * maxValue) + 1;
			} while (has[arr[i]]);
			has[arr[i]] = true;
		}
		return arr;
	}

	// 为了测试
	public static void printArray(int[] arr) {
		for (int i = 0; i < arr.length; i++) {
			System.out.print(arr[i] + " ");
		}
		System.out.println();
	}

	// 为了测试
	public static void main(String[] args) {
		int maxLen = 10;
		int maxValue = 30;
		int testTime = 1000000;
		System.out.println("测试开始");
		for (int i = 0; i < testTime; i++) {
			int[] arr = randomArray(maxLen, maxValue);
			int aim = (int) (Math.random() * maxValue);
			int ans1 = coinsWay(arr, aim);
			int ans2 = dp1(arr, aim);
			int ans3 = dp2(arr, aim);
			if (ans1 != ans2 || ans1 != ans3) {
				System.out.println("Oops!");
				printArray(arr);
				System.out.println(aim);
				System.out.println(ans1);
				System.out.println(ans2);
				System.out.println(ans3);
				break;
			}
		}
		System.out.println("测试结束");
	}

}