UVa 1616 Caravan Robbers (二分）

题目链接：https://vjudge.net/problem/UVA-1616

大意：输入n个区间，把它们分成等长的、互不相交的子区间，求子区间的最大长度。

思路：二分答案，再小数化分数即可。

#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
#include<vector>
#include<iostream>
using namespace std;
const int maxn = 1e6 + 10;
const double eps = 1e-9;
int n;
struct Node {
   int l, r;
   bool operator < (const Node& rhs) const {
      return l < rhs.l || l == rhs.l && r < rhs.r;
   }
}C[maxn];

bool judge(double mid) {
   double cur = 0;
   for(int i = 0; i < n; i++) {
   	  double r = max(cur, (double)C[i].l) + mid;
   	  if(r > C[i].r) return false;
   	  cur = r;
   }
   return true;
}

int main()
{
	while(scanf("%d",&n) == 1) {
	   for(int i = 0; i < n; i++)
	     scanf("%d%d",&C[i].l, &C[i].r);
	   sort(C, C+n);
	   double l = 0.0, r = 1000000.0;
	   while(r - l > eps) {
	   	  double mid = (l + r) / 2.0;
	   	  if(judge(mid)) l = mid;
	   	  else r = mid;
	   }
	   double ans = l;
	   int rp = 0, rq = 1;
	   for(int p, q = 1; q <= n; q++) {
	   	  p = round(ans * q);
	   	  if(fabs((double)p/q - ans) < fabs((double)rp/rq - ans)) {
	   	     rp = p; rq = q; 	
		  } 
	   }
	   printf("%d/%d\n", rp, rq);
	}
	return 0;
}