CF794B.Cutting Carrot
普及-
通过率:0%
时间限制:2.00s
内存限制:256MB
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题目描述
Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area.
Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?
Illustration to the first example.
分析员伊戈尔收养了 n 只小兔子。众所周知,兔子喜欢吃胡萝卜。因此,伊戈尔买了一根胡萝卜,准备分给他的兔子们。伊戈尔希望公平地对待所有兔子,于是他打算将这根胡萝卜切成 n 块面积相等的部分。
形式化地说,这根胡萝卜可视为一个底边长度为 1、高为 h 的等腰三角形。伊戈尔计划作 n−1 次平行于底边的切割,将胡萝卜分成 n 块,并确保每一块的面积都相等。你能帮伊戈尔确定切割位置,使得每一块面积都相等吗?
第一个样例的示意图。
输入格式
The first and only line of input contains two space-separated integers, n and h (2 ≤ n ≤ 1000, 1 ≤ h ≤ 105).
输入仅有一行,包含两个以空格分隔的整数 n 和 h(2 ≤ n ≤ 1000,1 ≤ h ≤ 105)。
输出格式
The output should contain n - 1 real numbers _x_1, _x_2, ..., x__n - 1. The number x__i denotes that the i-th cut must be made x__i units away from the apex of the carrot. In addition, 0 < _x_1 < _x_2 < ... < x__n - 1 < h must hold.
Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.
Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if
.
输出应包含 n−1 个实数 x1,x2,…,xn−1。其中,数 xi 表示第 i 次切割必须在距胡萝卜顶点 xi 个单位处进行。此外,还需满足 0<x1<x2<⋯<xn−1<h。
若输出中每个数的绝对误差或相对误差均不超过 10−6,则你的输出将被视为正确。
形式化地,设你的答案为 a,评测机的答案为 b。当满足
时,你的答案即被视为正确。
输入输出样例
输入#1
3 2
输出#1
1.154700538379 1.632993161855
输入#2
2 100000
输出#2
70710.678118654752
说明/提示
Definition of isosceles triangle: https://en.wikipedia.org/wiki/Isosceles_triangle.
输入解题思路,AI测评打分。不知道怎么写?