PAT (Advanced Level) Practise 1045 Favorite Color Stripe (30)-优快云博客

本文链接：https://blog.youkuaiyun.com/a664607530/article/details/75331985

本文介绍了一个类似最长公共子序列的问题，但允许元素重复。通过动态规划解决如何从一个颜色序列中提取最大长度的子序列，使得该子序列与给定的偏好序列保持相同的元素顺序。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

1045. Favorite Color Stripe (30)

时间限制

200 ms

内存限制

65536 kB

代码长度限制

16000 B

判题程序

Standard

作者

CHEN, Yue

Eva is trying to make her own color stripe out of a given one. She would like to keep only her favorite colors in her favorite order by cutting off those unwanted pieces and sewing the remaining parts together to form her favorite color stripe.

It is said that a normal human eye can distinguish about less than 200 different colors, so Eva's favorite colors are limited. However the original stripe could be very long, and Eva would like to have the remaining favorite stripe with the maximum length. So she needs your help to find her the best result.

Note that the solution might not be unique, but you only have to tell her the maximum length. For example, given a stripe of colors {2 2 4 1 5 5 6 3 1 1 5 6}. If Eva's favorite colors are given in her favorite order as {2 3 1 5 6}, then she has 4 possible best solutions {2 2 1 1 1 5 6}, {2 2 1 5 5 5 6}, {2 2 1 5 5 6 6}, and {2 2 3 1 1 5 6}.

Input Specification:

Each input file contains one test case. For each case, the first line contains a positive integer N (<=200) which is the total number of colors involved (and hence the colors are numbered from 1 to N). Then the next line starts with a positive integer M (<=200) followed by M Eva's favorite color numbers given in her favorite order. Finally the third line starts with a positive integer L (<=10000) which is the length of the given stripe, followed by L colors on the stripe. All the numbers in a line are separated by a space.

Output Specification:

For each test case, simply print in a line the maximum length of Eva's favorite stripe.

Sample Input:

6
5 2 3 1 5 6
12 2 2 4 1 5 5 6 3 1 1 5 6

Sample Output:

题意：给出一个有若干个数的偏好序列，同时给出另一个任意的数组，并且参照前面序列中元素出现的相对顺序（某些元素可以丢弃）依次从前往后选择数组中的元素组成一个新的数组，求这个数组的最大长度

解题思路：这个和最长公共子序列问题相类似（LCS），不同的地方是允许元素重复，如｛a｝和｛aaa｝，匹配出来的是3，a可以重复3次，那么也是可以用dp来推的，并且根据题目意思，第一个串中应该不会出现重复数字

#include <iostream>
#include <cstdio>
#include <cstring>
#include <string>
#include <algorithm>
#include <cmath>
#include <map>
#include <set>
#include <stack>
#include <queue>
#include <vector>
#include <bitset>
#include <functional>

using namespace std;

#define LL long long
const int INF = 0x3f3f3f3f;

int k,n,m;
int a[10009],b[10009];
int dp[205][10009];

int main()
{
    while(~scanf("%d",&k))
    {
        memset(dp,0,sizeof dp);
        scanf("%d",&n);
        for(int i=1;i<=n;i++) scanf("%d",&a[i]);
        scanf("%d",&m);
        for(int i=1;i<=m;i++) scanf("%d",&b[i]);
        for(int i=1;i<=n;i++)
        {
            for(int j=1;j<=m;j++)
            {
                dp[i][j]=max(dp[i-1][j],dp[i][j-1]);
                if(a[i]==b[j]) dp[i][j]++;
            }
        }
        printf("%d\n",dp[n][m]);
    }
    return 0;
}