hdu 1800 Flying to the Mars

　　　　　　　　Flying to the Mars

　　　　　　　　　　Time Limit: 5000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
　　　　　　　　　　　　　　　　Total Submission(s): 4318    Accepted Submission(s): 1393

Problem Description

In the year 8888, the Earth is ruled by the PPF Empire . As the population growing , PPF needs to find more land for the newborns . Finally , PPF decides to attack Kscinow who ruling the Mars . Here the problem comes! How can the soldiers reach the Mars ? PPF convokes his soldiers and asks for their suggestions . “Rush … ” one soldier answers. “Shut up ! Do I have to remind you that there isn’t any road to the Mars from here!” PPF replies. “Fly !” another answers. PPF smiles :“Clever guy ! Although we haven’t got wings , I can buy some magic broomsticks from HARRY POTTER to help you .” Now , it’s time to learn to fly on a broomstick ! we assume that one soldier has one level number indicating his degree. The soldier who has a higher level could teach the lower , that is to say the former’s level > the latter’s . But the lower can’t teach the higher. One soldier can have only one teacher at most , certainly , having no teacher is also legal. Similarly one soldier can have only one student at most while having no student is also possible. Teacher can teach his student on the same broomstick .Certainly , all the soldier must have practiced on the broomstick before they fly to the Mars! Magic broomstick is expensive !So , can you help PPF to calculate the minimum number of the broomstick needed .
For example :
There are 5 soldiers (A B C D E)with level numbers : 2 4 5 6 4;
One method :
C could teach B; B could teach A; So , A B C are eligible to study on the same broomstick.
D could teach E;So D E are eligible to study on the same broomstick;
Using this method , we need 2 broomsticks.
Another method:
D could teach A; So A D are eligible to study on the same broomstick.
C could teach B; So B C are eligible to study on the same broomstick.
E with no teacher or student are eligible to study on one broomstick.
Using the method ,we need 3 broomsticks.
……

After checking up all possible method, we found that 2 is the minimum number of broomsticks needed.

 

Input

Input file contains multiple test cases.
In a test case,the first line contains a single positive number N indicating the number of soldiers.(0<=N<=3000)
Next N lines :There is only one nonnegative integer on each line , indicating the level number for each soldier.( less than 30 digits);

 

Output

For each case, output the minimum number of broomsticks on a single line.

 

Sample Input

4

10

20

30

04

5

2

3

4

3

4

 

Sample Output

1

2

根据题意可知：意思是有若干个飞行员，需要在扫帚上练习飞行，每个飞行员具有不同的等级，且等级高的飞行员可以当等级低的飞行员的老师，且每个飞行员至多有且只有一个老师和学生。具有老师和学生关系的飞行员可以在同一把扫帚上练习，并且这个性质具有传递性。即比如有A，B，C，D，E五个飞行员，且等级是A>B>C>D>E，那么可以使A当B的老师，B当C的老师，E当D的老师，那么A，B，C可以在同一扫帚上练习，D，E在同一把扫帚上练习，这样需要2把扫帚，而如果是A当B的老师，B当C的老师，C当D的老师，D当E的老师，那么只需要一把扫帚。题目所求即所需最少的扫帚数目。

假设有若干个飞行员，{{A1,A2,A3...AK},{B1,B2,B3,...Bm}......{F1,F2,F3.....Fn}}。其已经按照等级由低到高排好序，在同一个集合里的飞行员等级相同。若需要最少数目的扫帚，则只能是{A1,B1.....F1},{A2,B2....F2}..这样进行组合，扫帚数目最少。因此决定所需最少扫帚数目的集合是含有飞行员最多的集合，即同一等级数目最多的飞行员集合。因此可以采用STL中的map直接实现。

实现代码:

/*hdu 1800 最大分配 2011.10.12*/ 
#include <iostream>
#include<map>
using namespace std;

int main(int argc, char *argv[])
{
    int n;
    while(scanf("%d",&n)==1)
    {
        int i;
        map<int,int> mp;
        int max=INT_MIN;
        for(i=0;i<n;i++)
        {
            int level;
            scanf("%d",&level);
            mp[level]++;
            if(mp[level]>max)
            {
                max=mp[level];                     
            }
        }
        printf("%d\n",max);
    }
    return 0;
}