最长单调递增子序列问题

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最长单调递增子序列问题

题目：设计一个 O（ n ^ 2 ）复杂度的算法，找出由 n 个数组成的序列的最长单调递增子序列。

import java.util.Scanner;public class Main {public static void main(String[] args) {Scanner scanner = new Scanner(System.in);while (scanner.hasNext()) {int n = scanner.nextInt();int[] nums = new int[n + 1];// 数列数据int[] sub_len = new int[n + 1];// sub_len[i]表示从i到n的最长递增序列的长度int[] sub_index = new int[n + 1];// sub_index[i]表示第i个数据的后面一个数据的下标for (int i = 1; i <= n; i++) {nums[i] = scanner.nextInt();sub_len[i] = 1;sub_index[i] = 0;}for (int i = n - 1; i >= 1; i--) {int max = 0, p = 0;// 临时变量for (int j = i + 1; j <= n; j++) {if (nums[i] < nums[j] && sub_len[j] > max) {max = sub_len[j];p = j;}if (p != 0) {sub_len[i] = sub_len[p] + 1;sub_index[i] = p;}}}int max = 0, p = 0;for (int i = 1; i <= n; i++) {if (sub_len[i] > max) {max = sub_len[i];p = i;}}System.out.println("最长长度：" + max);System.out.print("最长递增序列：");while (p != 0) {System.out.print(nums[p] + " ");p = sub_index[p];}System.out.println();}scanner.close();}}

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