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package class46;
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import java.util.LinkedList;
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// 给定一个数组arr，和一个正数M
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// 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
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public class Code04_MaxSumLengthNoMore {
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// O(N^2)的解法，暴力解，用作对数器
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public static int test(int[] arr, int M) {
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if (arr == null || arr.length == 0 || M < 1) {
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return 0;
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}
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int N = arr.length;
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int max = Integer.MIN_VALUE;
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for (int L = 0; L < N; L++) {
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int sum = 0;
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for (int R = L; R < N; R++) {
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if (R - L + 1 > M) {
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break;
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}
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sum += arr[R];
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max = Math.max(max, sum);
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}
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}
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return max;
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}
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// O(N)的解法，最优解
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public static int maxSum(int[] arr, int M) {
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if (arr == null || arr.length == 0 || M < 1) {
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return 0;
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}
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int N = arr.length;
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int[] sum = new int[N];
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sum[0] = arr[0];
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for (int i = 1; i < N; i++) {
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sum[i] = sum[i - 1] + arr[i];
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}
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LinkedList<Integer> qmax = new LinkedList<>();
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int i = 0;
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int end = Math.min(N, M);
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for (; i < end; i++) {
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while (!qmax.isEmpty() && sum[qmax.peekLast()] <= sum[i]) {
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qmax.pollLast();
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}
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qmax.add(i);
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}
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int max = sum[qmax.peekFirst()];
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int L = 0;
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for (; i < N; L++, i++) {
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if (qmax.peekFirst() == L) {
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qmax.pollFirst();
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}
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while (!qmax.isEmpty() && sum[qmax.peekLast()] <= sum[i]) {
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qmax.pollLast();
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}
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qmax.add(i);
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max = Math.max(max, sum[qmax.peekFirst()] - sum[L]);
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}
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for (; L < N - 1; L++) {
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if (qmax.peekFirst() == L) {
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qmax.pollFirst();
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}
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max = Math.max(max, sum[qmax.peekFirst()] - sum[L]);
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}
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return max;
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}
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// 用作测试
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public static int[] randomArray(int len, int max) {
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int[] arr = new int[len];
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for (int i = 0; i < len; i++) {
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arr[i] = (int) (Math.random() * max) - (int) (Math.random() * max);
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}
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return arr;
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}
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// 用作测试
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public static void main(String[] args) {
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int maxN = 50;
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int maxValue = 100;
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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 N = (int) (Math.random() * maxN);
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int M = (int) (Math.random() * maxN);
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int[] arr = randomArray(N, maxValue);
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int ans1 = test(arr, M);
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int ans2 = maxSum(arr, M);
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if (ans1 != ans2) {
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System.out.println(ans1);
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System.out.println(ans2);
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System.out.println("Oops!");
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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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