java最长单调递增子序列_最长单调递增子序列问题

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();

}

}

原文：/u011506951/article/details/37074901