POJ1759-Garland
来源:互联网 发布:安装java linux 编辑:程序博客网 时间:2024/05/16 14:47
Garland
Time Limit: 1000MS Memory Limit: 10000KTotal Submissions: 2168 Accepted: 932
Description
The 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.
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.
Input
The 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.
Output
Write 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 Input
692 532.81
Sample Output
446113.34
Source
Northeastern Europe 2000
题意:n个灯泡离地H_i,满足H1 = A ,Hi = (Hi-1 + Hi+1)/2 – 1,HN = B ,求最小B
解题思路:二分第二个灯泡的高度
#include <iostream>#include <cstdio>#include <cstring>#include <string>#include <algorithm>#include <queue>#include <cmath>#include <map>#include <bitset>#include <set>#include <vector>#include <functional>using namespace std;#define LL long longconst int INF = 0x3f3f3f3f;double a,b,x[1005],ans;int n;bool check(double k){ x[1]=a,x[2]=k; for(int i=3;i<=n;i++) { x[i]=(x[i-1]+1)*2-x[i-2]; if(x[i]<0) return 0; } ans=x[n]; return 1;}int main(){while(~scanf("%d%lf",&n,&a)) { double l=0,r=a; while(fabs(r-l)>=1e-8) { double mid=(l+r)/2; if(check(mid)) {b=mid;r=mid;} else l=mid; } printf("%.2f\n",ans); }return 0;}
阅读全文
0 0
- POJ1759--Garland
- poj1759 Garland
- POJ1759-Garland
- POJ1759-Garland
- poj1759 Garland二分
- poj1759
- poj1759
- POJ1759
- Garland
- Garland
- Garland
- poj1759 二分
- 推公式+二分--poj1759
- poj1759 数学+二分
- 【数学】Garland
- 【二分】Garland
- CF:Garland
- B. Garland
- 爬楼梯-斐波那契
- [2016陕西省赛B] Rui and her functions
- display取值的用法
- mysql主从复制
- JVM初窥: 类文件结构
- POJ1759-Garland
- NBU 1763
- 【wireless】Channel State Information
- 折半查找算法(二分查找算法)
- c运算符优先级
- javascript将json字符串转换为json对象
- ssm
- 星期几
- NYOJ-32组合数(递归实现)