HDU 5742 It's All In The Mind

It's All In The Mind

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 409    Accepted Submission(s): 189

Problem Description

Professor Zhang has a number sequence a₁,a₂,...,a_n.
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≤a_i≤100.
2. The sequence is non-increasing, i.e. a₁≥a₂≥...≥a_n.
3. The sum of all elements in the sequence is not zero.

Professor Zhang wants to know the maximum value of (a1+a2)/∑ⁿ_i=1 a_i 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 x_i and y_i (1≤x_i≤n,0≤y_i≤100,x_i<x_i+1,y_i≥y_i+1)  indicating that a_xi = y_i.

 

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

 

Author

zimpha

 

Source

2016 Multi-University Training Contest 2

 

 

 

解析：

 

 

 

 

 

#include <bits/stdc++.h>
 
int a[105];
 
int gcd(int a, int b)
{
    return b == 0 ? a : gcd(b, a%b);
}
 
int main()
{
    int T, n, m;
    scanf("%d", &T);
    while(T--){
        scanf("%d%d", &n, &m);
        memset(a, -1, sizeof(a));
        int x, y;
        while(m--){
            scanf("%d%d", &x, &y);
            a[x] = y;
        }
        if(a[1] == -1)
            a[1] = 100;
        if(a[2] == -1)
            a[2] = a[1];
        int p = a[1]+a[2], q = p;
        a[n+1] = 0;
        for(int i = n; i >= 3; --i){
            if(a[i] == -1)
                a[i] = a[i+1];
            q += a[i];
        }
        int g = gcd(p, q);
        printf("%d/%d\n", p/g, q/g);
    }
    return 0;
}