algorithm-class/体系学习班/class46/Code04_MaxSumLengthNoMore.java

package class46;

import java.util.LinkedList;

// 给定一个数组arr，和一个正数M
// 返回在子数组长度不大于M的情况下，最大的子数组累加和
public class Code04_MaxSumLengthNoMore {

	// O(N^2)的解法，暴力解，用作对数器
	public static int test(int[] arr, int M) {
		if (arr == null || arr.length == 0 || M < 1) {
			return 0;
		}
		int N = arr.length;
		int max = Integer.MIN_VALUE;
		for (int L = 0; L < N; L++) {
			int sum = 0;
			for (int R = L; R < N; R++) {
				if (R - L + 1 > M) {
					break;
				}
				sum += arr[R];
				max = Math.max(max, sum);
			}
		}
		return max;
	}

	// O(N)的解法，最优解
	public static int maxSum(int[] arr, int M) {
		if (arr == null || arr.length == 0 || M < 1) {
			return 0;
		}
		int N = arr.length;
		int[] sum = new int[N];
		sum[0] = arr[0];
		for (int i = 1; i < N; i++) {
			sum[i] = sum[i - 1] + arr[i];
		}
		LinkedList<Integer> qmax = new LinkedList<>();
		int i = 0;
		int end = Math.min(N, M);
		for (; i < end; i++) {
			while (!qmax.isEmpty() && sum[qmax.peekLast()] <= sum[i]) {
				qmax.pollLast();
			}
			qmax.add(i);
		}
		int max = sum[qmax.peekFirst()];
		int L = 0;
		for (; i < N; L++, i++) {
			if (qmax.peekFirst() == L) {
				qmax.pollFirst();
			}
			while (!qmax.isEmpty() && sum[qmax.peekLast()] <= sum[i]) {
				qmax.pollLast();
			}
			qmax.add(i);
			max = Math.max(max, sum[qmax.peekFirst()] - sum[L]);
		}
		for (; L < N - 1; L++) {
			if (qmax.peekFirst() == L) {
				qmax.pollFirst();
			}
			max = Math.max(max, sum[qmax.peekFirst()] - sum[L]);
		}
		return max;
	}

	// 用作测试
	public static int[] randomArray(int len, int max) {
		int[] arr = new int[len];
		for (int i = 0; i < len; i++) {
			arr[i] = (int) (Math.random() * max) - (int) (Math.random() * max);
		}
		return arr;
	}

	// 用作测试
	public static void main(String[] args) {
		int maxN = 50;
		int maxValue = 100;
		int testTime = 1000000;
		System.out.println("测试开始");
		for (int i = 0; i < testTime; i++) {
			int N = (int) (Math.random() * maxN);
			int M = (int) (Math.random() * maxN);
			int[] arr = randomArray(N, maxValue);
			int ans1 = test(arr, M);
			int ans2 = maxSum(arr, M);
			if (ans1 != ans2) {
				System.out.println(ans1);
				System.out.println(ans2);
				System.out.println("Oops!");
			}
		}
		System.out.println("测试结束");
	}

}