History Grading

History Grading

Time Limit: 3000MS

Memory Limit: Unknown

64bit IO Format: %lld & %llu

SubmitStatus

Description

Background

Many problems in Computer Science involve maximizing some measure according to constraints.

Consider a history exam in which students are asked to put several historical events into chronological order. Students who order all the events correctly will receive full credit, but how should partial credit be awarded to students who incorrectly rank one or more of the historical events?

Some possibilities for partial credit include:

1. 1 point for each event whose rank matches its correct rank
2. 1 point for each event in the longest (not necessarily contiguous) sequence of events which are in the correct order relative to each other.

For example, if four events are correctly ordered 1 2 3 4 then the order 1 3 2 4 would receive a score of 2 using the first method (events 1 and 4 are correctly ranked) and a score of 3 using the second method (event sequences 1 2 4 and 1 3 4 are both in the correct order relative to each other).

In this problem you are asked to write a program to score such questions using the second method.

The Problem

Given the correct chronological order of n events as where denotes the ranking of eventi in the correct chronological order and a sequence of student responses where denotes the chronological rank given by the student to eventi; determine the length of the longest (not necessarily contiguous) sequence of events in the student responses that are in the correct chronological order relative to each other.

The Input

The first line of the input will consist of one integer n indicating the number of events with . The second line will containn integers, indicating the correct chronological order of n events. The remaining lines will each consist ofn integers with each line representing a student's chronological ordering of the n events. All lines will containn numbers in the range , with each number appearing exactly once per line, and with each number separated from other numbers on the same line by one or more spaces.

The Output

For each student ranking of events your program should print the score for that ranking. There should be one line of output for each student ranking.

Sample Input 1

4
4 2 3 1
1 3 2 4
3 2 1 4
2 3 4 1

Sample Output 1

1
2
3

Sample Input 2

10
3 1 2 4 9 5 10 6 8 7
1 2 3 4 5 6 7 8 9 10
4 7 2 3 10 6 9 1 5 8
3 1 2 4 9 5 10 6 8 7
2 10 1 3 8 4 9 5 7 6

Sample Output 2

6
5
10
9

题目描述：

     最长公共子序列:给出发生的历史事件的个数，第一行为正确的历史顺序，例4 2 3 1，1发生在4的位置，2发生在2的位置，...,转换过来为4 2 3 1。下面是学生的答案，要求输出学生所得的分数。

#include<stdio.h>
#include<iostream>
#include<string.h>
using namespace std;
#define N 30
int a[N];
int b[N];
int dp[N][N];
int main()
{
    int n,t;
    scanf("%d",&n);
    for(int i=1;i<=n;i++)
    {
        scanf("%d",&t);
        a[t]=i;
    }
    while(scanf("%d",&t)!=EOF)
    {
        b[t]=1;
        for(int i=2;i<=n;i++)
        {
            scanf("%d",&t);
            b[t]=i;
        }
		memset(dp,0,sizeof(dp));
        for(int i=1;i<=n;i++)
        {
            for(int j=1;j<=n;j++)
            {
                if(a[i]==b[j])           //最长公共子序列公式 
                	dp[i][j]=dp[i-1][j-1]+1;
                else
                	dp[i][j]=max(dp[i-1][j],dp[i][j-1]);
            }
        }
        printf("%d\n",dp[n][n]);
    }
    return 0;
}