백준 9130 (C++) Herbert

최초 업로드: 2025-07-07 21:24:12

최근 수정 시간: 2025-07-25 08:45:57

게시자: rlatjwls3333

카테고리: 백준

# [Silver I] Herbert

[문제 링크](https://www.acmicpc.net/problem/9130)

## 문제 설명

Herbert is a game in which you control a robot on an infinite two-dimensional grid. There are three commands available to you:

<ul>
	<li>s: Go one square forward in the current direction. </li>
	<li>l: Turn ninety degrees counterclockwise.</li>
	<li>r: Turn ninety degrees clockwise.</li>
</ul>

After playing this game for a while, you wonder how many squares you can reach within a certain number of moves. Write a program to calculate the answer to this question.

## 입력

On the first line an integer t (1 ≤ t ≤ 100): the number of test cases. Then for each test case:

<ul>
	<li>One line with an integer n (0 ≤ n ≤ 1 000 000 000): the maximum number of moves.</li>
</ul>

## 출력

For each test case:

<ul>
	<li>One line with the number of reachable squares.</li>
</ul>

## 풀이
#### 규칙을 찾아, 등차수열의 합 공식을 이용하여 풀 수 있다.

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

int main() {
 ios::sync_with_stdio(0); cin.tie(0);
 int t; cin >> t;
 while(t--) {
 long long n; cin >> n;
 
 long long sum = n+1; // 앞
 if(n>=1) sum += (n-1)*2 // 중앙 위 아래
 + (n-2)*(n-1); // 앞쪽 위 아래
 if(n>=2) sum += max(n-2, 0LL) // 뒤
 + (n-3)*(n-2); // 뒤쪽 위 아래
 
 cout << sum << '
';
 }
}
```