Codeforces 185B（玄学）

男娘i 2022-06-03 10:56 266阅读 0赞

B. Mushroom Scientists

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

As you very well know, the whole Universe traditionally uses three-dimensional Cartesian system of coordinates. In this system each point corresponds to three real coordinates (*x*, *y*, *z*). In this coordinate system, the distance between the center of the Universe and the point is calculated by the following formula: ![e4685dd705b47f2fa253d6749205486b43fa05c8.png][]. Mushroom scientists that work for the Great Mushroom King think that the Universe isn't exactly right and the distance from the center of the Universe to a point equals *x**a*·*y**b*·*z**c*.

To test the metric of mushroom scientists, the usual scientists offered them a task: find such *x*, *y*, *z* (0 ≤ *x*, *y*, *z*; *x* + *y* + *z* ≤ *S*), that the distance between the center of the Universe and the point (*x*, *y*, *z*) is maximum possible in the metric of mushroom scientists. The mushroom scientists aren't good at maths, so they commissioned you to do the task.

Note that in this problem, it is considered that 00 = 1.

Input

The first line contains a single integer *S* (1 ≤ *S* ≤ 103) — the maximum sum of coordinates of the sought point.

The second line contains three space-separated integers *a*, *b*, *c* (0 ≤ *a*, *b*, *c* ≤ 103) — the numbers that describe the metric of mushroom scientists.

Output

Print three real numbers — the coordinates of the point that reaches maximum value in the metrics of mushroom scientists. If there are multiple answers, print any of them that meets the limitations.

A natural logarithm of distance from the center of the Universe to the given point in the metric of mushroom scientists shouldn't differ from the natural logarithm of the maximum distance by more than 10 - 6. We think that *ln*(0) =  - ∞.

Examples

input

3
    1 1 1

output

1.0 1.0 1.0

input

3
    2 0 0

output

3.0 0.0 0.0

题解：

这题题目意思看了好久，应该是给s代表三维坐标(x,y,z)里x+y+z=s，然后给a，b，c，让你求它给出的第二个式子的最大值是多少

先讨论特殊情况当a，b，c都是0的时候，那么这个时候x，y，z应该是随便填结果都是一样的，所以满足x+y+z=s等式就行了

其他情况我是按照a,b,c的比重分配的。。猜了一发就a了，莫名其妙，貌似可以用数学公式证明

代码：

#include<stdio.h>
    #include<string.h>
    #include<stdlib.h>
    #include<queue>
    #include<stack>
    #include<math.h>
    #include<vector>
    #include<map>
    #include<set>
    #include<stdlib.h>
    #include<cmath>
    #include<string>
    #include<algorithm>
    #include<iostream>
    #include<stdio.h>
    using namespace std;
    #define ll long long
    
    int main()
    {
        double s,a,b,c,x,y,z;
        scanf("%lf%lf%lf%lf",&s,&a,&b,&c);
        if(a+b+c==0)
        {
            printf("%.18lf 0 0",s);
            return 0;
        }
        x=a*s/(a+b+c);
        y=b*s/(a+b+c);
        z=c*s/(a+b+c);
        printf("%.18lf %.18lf %.18lf",x,y,z);
        return 0;
    }

[e4685dd705b47f2fa253d6749205486b43fa05c8.png]: /images/20220603/89f50cbebe1f41daa3f70f165e1c9a5d.png