#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;
}
习题8-14(uva-1616)
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Origin blog.csdn.net/seanbill/article/details/117232161
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