【二分答案】逮虾户

题意

已知ti，vi，si，t
求解方程
t1*(d+v1)=s1
t2*(d+v2)=s2
t3*(d+v3)=s3
…
t1+t2+t3+…+tn=t

思路

可以发现$\sum si/(d+vi)=t$，且结果是随着d的增减而增减的，满足单调性，故二分答案即可。

代码

#include <cmath>
#include <cstdio>

int n;
double t;
double s[1001], v[1001];

int check(double d) {
	double res = 0;
	for (int i = 1; i <= n; i++) {
		if (d + v[i] <= 0) return 1;
		res += s[i] / (d + v[i]);
	}
	return res > t;
}

int main() {
	scanf("%d %lf", &n, &t);
	for (int i = 1; i <= n; i++)
		scanf("%lf %lf", &s[i], &v[i]);
	double l = -1e9, r = 1e9, mid;
	for (int i = 0; i < 100; i++) {
		mid = (l + r) / 2.0;
		if (check(mid)) l = mid;
		else r = mid;
	}
	if(fabs(l) < 1e-14) l = 0;
	printf("%.12lf", l);
}