2016 Multi-University Training Contest 2 It's All In The Mind

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Problem Description

Professor Zhang has a number sequence  a1,a2,...,an. However, the sequence is not complete and some elements are missing. Fortunately, Professor Zhang remembers some properties of the sequence:

1. For every  i∈{1,2,...,n},  0≤ai≤100.
2. The sequence is non-increasing, i.e.  a1≥a2≥...≥an.
3. The sum of all elements in the sequence is not zero.

Professor Zhang wants to know the maximum value of  a1+a2∑ni=1ai among all the possible sequences.

 

Input

There are multiple test cases. The first line of input contains an integer  T, indicating the number of test cases. For each test case:

The first contains two integers  n and  m  (2≤n≤100,0≤m≤n) -- the length of the sequence and the number of known elements.

In the next  m lines, each contains two integers  xi and  yi  (1≤xi≤n,0≤yi≤100,xi<xi+1,yi≥yi+1), indicating that  axi=yi.

 

Output

For each test case, output the answer as an irreducible fraction " p/ q", where  p,  q are integers,  q>0.

 

Sample Input

2 2 0 3 1 3 1

 

Sample Output

1/1 200/201

坑点：当啊a1有数的时候，a2=a1;

#include<iostream>
#include<cstring>
using namespace std;
int gcd(int a,int b)
{
    return b==0?a:gcd(b,a%b);
}
int x,y,a[200];
int main()
{
    int t,n,m;
    cin>>t;
    while(t--)
    {
        int s1=0,s2=0;
        memset(a,-1,sizeof a);
        cin>>n>>m;
        for(int i=1;i<=m;i++)
        {
            cin>>x>>y;
            a[x]=y;
        }
        if(a[1]!=-1)
        {
            s1+=a[1];
            s2+=a[1];
        }
        else
        {
            s1+=100;
            s2+=100;
            a[1]=100;
        }
        if(a[2]!=-1)
        {
            s1+=a[2];
            s2+=a[2];
        }
        else
        {
            s1+=min(a[1],100);
            s2+=min(a[1],100);
        }
        int ma=0;
        for(int i=n;i>=3;i--)
        {
            //cout<<a[i]<<endl;
            if(a[i]!=-1)
            ma=max(a[i],ma);
            s2+=ma;    
        }
        int aa=gcd(s1,s2);
        cout<<s1/aa<<"/"<<s2/aa<<endl;
    }
    
 }