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.
Given the correct
chronological order of n events 
as 
where 
denotes the ranking of event i in the correct chronological order and a sequence of student
responses 
where 
denotes the chronological rank given by the
student to event i; 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.
as where denotes the ranking of event i in the correct chronological order and a sequence of student
responses where denotes the chronological rank given by the
student to event i; 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 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 of n integers with each line representing a student's chronological
ordering of the n events. All lines will contain n 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 second line will containn integers, indicating the correct chronological
order of n events. The remaining lines will each consist of n integers with each line representing a student's chronological
ordering of the n events. All lines will contain n 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.
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.
4
4 2 3 1
1 3 2 4
3 2 1 4
2 3 4 1
1
2
3
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
6
5
10
9
Solution:
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <string>
#include <cctype>
#include <stack>
#include <queue>
#include <vector>
#include <map>
#include <sstream>
#include <set>
#include <math.h>
using namespace std;
#define MAXN 22
int Orginal[MAXN],Rank[MAXN],Store[MAXN];
int N, X[MAXN];
void ReadOrginal()
{
int i;
scanf("%d",&N);
for(i = 0; i<N; i++)
scanf("%d",&Orginal[i]);
}
void LIS()
{
int i, j, max;
int largest = 0;
for(i = 1; i<= N; i ++)
{
max = 0;
for(j = i-1; j >= 0; j --)
{
if(Store[i]>Store[j])
if(X[j] > max)
max = X[j];
}
X[i] = max+1;
if(max>largest)
largest = max;
}
printf("%d\n",largest+1 );
}
int main()
{
int temp, i ;
ReadOrginal();
while(scanf("%d",&temp) == 1)
{
Store[temp] = Orginal[0];
for(i = 1; i<N; i++)
{
scanf("%d",&temp);
Store[temp] = Orginal[i];
}
LIS();
}
return 0;
}
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