贝壳：月光宝盒的密码（二分查找,暴力破解,动态规划）

1. 题目描述

图片来源：https://www.nowcoder.com/discuss/220718?type=0&order=0&pos=5&page=1

2. 代码

方法1（动态规划）81%超时　　

import java.util.Scanner;

public class Main{
     private static int N;//序列长度
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        N = sc.nextInt();
        int [] val = new int[N];//正整数
        for (int i = 0; i < N; i++) {
            val[i] =  sc.nextInt();
        }
       int max = 0;
       int [] dp = new int[N];
       for (int i = 0; i < N; i++) {
           for (int j = 0; j < i; j++) {
             if(val[j]<val[i]){
                 dp[i] = Math.max(dp[i],dp[j]+1);
                 max = Math.max(max, dp[i]);
             }
           }
       }
        System.out.print(max+1);
    }        
}

方法二，AC 100　

import java.util.Scanner;

public class Main {
    private static int N;//序列长度
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        N = sc.nextInt();
        int [] val = new int[N];//正整数
        for (int i = 0; i < N; i++) {
            val[i] =  sc.nextInt();
        }
        int max = 0;
        int [] dp = new int[N];
        for(int num: val){
           //二分找位置
           int j = Arrays.binarySearch(dp, 0,max,num);
           //找不到新增
           j = j<0? -(j+1) : j;
           dp[j] = num;
           max = j== max?(++max):max;
        }
        System.out.println(max);
    }   
}

方法三，自己写二分查找

import java.util.Scanner;
public class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int[] number = new int[n];
        for (int i = 0; i < n; i++) {
            number[i] = scanner.nextInt();
        }
        System.out.println(lengthOfLIS(number));
    }
    public static int lengthOfLIS(int[] nums) {
        int[] top = new int[nums.length];
        int piles = 0;
        for (int i = 0; i < nums.length; i++) {
            int poker = nums[i];
 
            /***** 搜索左侧边界的二分查找 *****/
            int left = 0, right = piles;
            while (left < right) {
                int mid = (left + right) / 2;
                if (top[mid] > poker) {
                    right = mid;
                } else if (top[mid] < poker) {
                    left = mid + 1;
                } else {
                    right = mid;
                }
            }
            if (left == piles) piles++;
            top[left] = poker;
        }
        return piles;
    }
}

方法四

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
public class Main{
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.valueOf(br.readLine().trim());
        long[] nums = new long[n];
        long[] dp = new long[n];
        for(int i = 1; i <= n; i++) {
            long temp = Long.valueOf(br.readLine().trim());
            nums[i] = temp;
        }
     
        for(int i = 0; i < n; i++) {
            long max = 1;
            for(int j = 0; j < i; j++) {
                max = Math.max(max, dp[j]+1);
            }
            dp[i] = max;
        }
        System.out.println(Arrays.stream(dp).max().orElse(0));
    }
}

网址：

1. https://www.nowcoder.com/discuss/220718?type=0&order=0&pos=5&page=1
2. https://www.nowcoder.com/discuss/220715?type=0&order=0&pos=2&page=1