习题8-14(uva-1616)

#include <iostream>
#include <istream>
#include <sstream>
#include <vector>
#include <stack>
#include <list>
#include <map>
#include <set>
#include <deque>
#include <queue>
#include <cstring>
#include <unordered_map>
#include <unordered_set>
#include <algorithm>
#include <numeric>
#include <chrono>
#include <ctime>
#include <cmath>
#include <cctype>
#include <string>
#include <cstdio>
#include <iomanip>


#include <thread>
#include <mutex>
#include <condition_variable>
#include <functional>
#include <iterator>
using namespace std;
const int maxn = 1e5 + 7;
const long double eps = 1e-11;
struct Node
{
    
    
	int head,tail;
	bool operator<(const Node& input) {
    
    
		if (head == input.head) return tail < input.tail;
		return head < input.head;
	}
}nodes[maxn];
int n;

bool IsOk(long double l) {
    
    
	long double cur = 0;
	for (int i = 0; i < n; i++) {
    
    
		cur = max(cur, (long double)nodes[i].head);
		cur += l;
		if (cur - nodes[i].tail > eps) return false;
	}
	return true;
}
int main()
{
    
    
	while (cin >> n && n) {
    
    
		for (int i = 0; i < n; i++) {
    
    
			cin >> nodes[i].head >> nodes[i].tail;
		}
		sort(nodes, nodes + n);

		long double l = 0, r = nodes[n-1].tail,ans = 0;
		while ((r - l) > eps) {
    
    
			long double mid = (r + l) / 2;
			if (IsOk(mid)) ans = l = mid;
			else r = mid;
		}

		int rp = 0, rq = 1;
		//分母总是1-n中的一个 现在知道结果 逐个尝试分母 选择最贴近的
		for (int p, q = 1; q <= n; q++) {
    
    
			p = round(ans * q);
			if (fabs(1.0 * p / q - ans) < fabs(1.0 * rp / rq - ans)) {
    
    
				rp = p, rq = q;
			}
		}
		cout << rp << "/" << rq << endl;
	}
	return 0;
}