POJ 1759

1759.cpp

#include <cstdio>
#include <cmath>
#include <algorithm>
using namespace std;

#define EPS 10e-3

int N;
double A;
double high;
double low;
double ans;

double check(double t) {
    double a = A;
    double b = t;

    for (int i=3; i<=N; i++) {
        double x = 2*b - a + 2;
        if (x < 0) return -1.0;
        a = b;
        b = x;
    }

    return b;
}

int main() {
    scanf("%d", &N);
    scanf("%lf", &A);

    high = 1000000.00;
    ans = high;
    low = 0.00;
    for (int i=0; i<10000; i++) {
        double mid = (high+low)/2;
        double ret = check(mid);

        if (ret > -1.0) {
            high = mid;
            ans = min(ans, ret);
        }
        else low = mid;
    }

    printf("%.2f\n", ans);
}