백준 25996 (C++) Equalising Audio

최초 업로드: 2025-09-21 06:27:50

최근 수정 시간: 2025-09-21 06:27:50

게시자: rlatjwls3333

카테고리: 백준

# [Silver III] Equalising Audio

[문제 링크](https://www.acmicpc.net/problem/25996)

## 문제 설명

As a radio engineer at the Balanced Audio Podcast \copyright{} your job is to deliver an equal listening experience at all times. You did a poll among the listeners and they are especially concerned about fluctuations in loudness. To resolve this you bought a transformer to equalise the audio, but alas, its software got corrupted during transport.

Your job is to rewrite the equalising software. As input the transformer gets $n$ amplitudes $a_1, \ldots, a_n$, with an average perceived loudness of $\frac{1}{n}\sum_{i=1}^n a_i^2$. The output should contain the same amplitudes, but renormalised by some constant positive factor, such that the average perceived loudness is $x$. There is one exception: total silence should always be preserved.

## 입력

The input consists of:

<ul>
	<li>One line with a two integers $n$ and $x$ ($1\leq n\leq 10^5$, $0 \leq x \leq 10^6)$, the number of amplitudes and the average perceived loudness to achieve.</li>
	<li>One line with $n$ integers $a_1, \ldots, a_n$ ($\left| a_i \right| \leq 10^6$), the amplitudes.</li>
</ul>

## 출력

Output one line containing $n$ numbers, the renormalised amplitudes with an average perceived loudness of $x$.

Your answers should have an absolute or relative error of at most $10^{-6}$.

## 풀이
평균이 0인 경우 전부 0으로 출력하는 케이스를 고려해야 한다. 나머지 경우는 x를 평균으로 나누고 제곱근 씌워서 모든 수에 곱해주면 된다.

``` c++
#include<bits/stdc++.h>
using namespace std;

typedef long double ld;

int main() {
    ios::sync_with_stdio(0); cin.tie(0);
    ld n, x; cin >> n >> x;

ld average=0;
 vector<ld> a(n);
 for(int i=0;i<n;i++) {
 cin >> a[i];
 average += a[i]*a[i];
 }
 average /= n;

if(average==0) {
 for(int i=0;i<n;i++) cout << "0 ";
 return 0;
 }

ld w = sqrtl(x/average);
 for(int i=0;i<n;i++) cout << fixed << setprecision(6) << a[i]*w << ' ';
}
```