POJ1759

    同样是二分搜索，这道题也挺好的，值得做做。首先你需要对公式Hi = (Hi-1 + Hi+1)/2 - 1做一个变换，改成Hi+1 = 2*Hi - Hi-1 + 2。使用这样的递推公式，那么只要知道H2就可以把剩下的都求出来，那么如何这道题就明朗多了。首先枚举H2的值，然后递推出剩余的H值，然后判断是否满足Hi >= 0, for all 1 <= i <= N的要求。当我们用H1和H2来表示Hi时，我们可以发现一个规律，就是Hi = (i-2) * H2 - (i-1) * H1 + (i-1)*(i-2)，也就意味着H2和Hn成正相关，求最小的Hn也就变成了求最小的H2。
    顺便说一下，有浮点数的时候精度有可能是一个要注意的问题，如果你觉得方法已经对了，那你就想想如何处理精度问题，倒不一定是越精确越好，因为要AC重要的是要和标答一致，所以有时就有点坑了。

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代码（G++）：

#include <iostream>#include <iomanip>#include <cmath>#define MAXN 1003using namespace std;int n;double h[MAXN], ans;bool is_ok(double h2){    if(h2 < 0) return false;    h[2] = h2;    for(int i=3; i<=n; i++)    {        h[i] = h[i-1]*2 - h[i-2] + 2;        if(h[i] < 0) return false;    }    ans = h[n];    return true;}int main(){    double lb, ub, mid;    while(cin>>n>>h[1])    {        lb = -1;        ub = h[1];        for(int i=0; i<100; i++)        {            mid = (lb + ub) / 2;            if(is_ok(mid)) ub = mid;            else lb = mid;        }        //ans = abs((n-1)*ub - (n-2)*h[1] + (n-1)*(n-2));        //ans = floor(ans * 100) / 100;        cout<<setiosflags(ios::fixed)<<setprecision(2)<<ans<<endl;    }    return 0;}

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题目（注意：题干中的图没有贴过来）：
Garland
Time Limit: 1000MS Memory Limit: 10000K

DescriptionThe New Year garland consists of N lamps attached to a common wire that hangs down on the ends to which outermost lamps are affixed. The wire sags under the weight of lamp in a particular way: each lamp is hanging at the height that is 1 millimeter lower than the average height of the two adjacent lamps. The leftmost lamp in hanging at the height of A millimeters above the ground. You have to determine the lowest height B of the rightmost lamp so that no lamp in the garland lies on the ground though some of them may touch the ground. You shall neglect the lamp's size in this problem. By numbering the lamps with integers from 1 to N and denoting the ith lamp height in millimeters as Hi we derive the following equations: H1 = A Hi = (Hi-1 + Hi+1)/2 - 1, for all 1 < i < N HN = B Hi >= 0, for all 1 <= i <= N The sample garland with 8 lamps that is shown on the picture has A = 15 and B = 9.75. InputThe input file consists of a single line with two numbers N and A separated by a space. N (3 <= N <= 1000) is an integer representing the number of lamps in the garland, A (10 <= A <= 1000) is a real number representing the height of the leftmost lamp above the ground in millimeters.OutputWrite to the output file the single real number B accurate to two digits to the right of the decimal point representing the lowest possible height of the rightmost lamp.Sample Input692 532.81Sample Output446113.34