uva 1555 Garland

题意：有n个灯笼。第一个的高度是A，最后一个是B。灯笼的关系给出。并要求每一个灯笼的高度是非负数的。求最低的B

思路：推出公式：H[i]=2*H[i-1]+2-H[i-2],然后枚举H[2],在知道H[1]的情况下就能求出全部的高度，然后推断是否都是非负数

#include <iostream>
#include <cstring>
#include <algorithm>
#include <cstdio>
using namespace std;
const int MAXN = 1500;

int n;
double A, B, H[MAXN];

int check(double cnt) {
	H[1] = cnt;
	for (int i = 2; i < n; i++) {
		H[i] = 2*H[i-1] + 2 - H[i-2];
		if (H[i] < 0)
			return 0;
	}
	B = H[n-1];
	return true;
}

int main() {
	while (scanf("%d%lf", &n, &A) != EOF) {
		H[0] = A;
		double l = -1, r = MAXN;
		while (r-l > 1e-6) {
			double mid = (l+r)/2;
			if (check(mid))
				r = mid;
			else l = mid;
		}
		printf("%.2lf\n", B);
	}
	return 0;
}