Codeforces Round #569 (Div. 2)A. Alex and a Rhombus

左手的ㄟ右手 2022-01-07 15:35 207阅读 0赞

# A. Alex and a Rhombus #

题目链接：[http://codeforces.com/contest/1180/problem/A][http_codeforces.com_contest_1180_problem_A]

# 题目： #

While playing with geometric figures Alex has accidentally invented a concept of an-th order rhombusin a cell grid.A1-st order rhombusis just a square1×1(i.e just a cell).An-th order rhombusfor alln≥2one obtains from an−1-th order rhombusadding all cells which have a common side with it to it (look at the picture to understand it better).  
  
Alex asks you to compute the number of cells in a n-th order rhombus.  
InputThe first and only input line contains integern(1≤n≤100) — order of a rhombus whose numbers of cells should be computed.  
OutputPrint exactly one integer — the number of cells in a n-th order rhombus.

![1705372-20190629160529011-1498659285.png][]

**Examples**

Input  
1  
Output  
1  
Input  
2  
Output  
5  
Input  
3  
Output  
13  
NoteImages of rhombus corresponding to the examples are given in the statement.

**题意：求第N个图形的小方格个数**

**思路：**

**找规律题：**

**1+3+5+7+..+5+3+1**

#include<bits/stdc++.h>
    typedef long long ll;
    using namespace std;
    const int maxn=2e5+7;
    ll ji[maxn];
    int main()
    {
            int n;
            while(cin>>n) {
                ll ji[maxn];
                ji[0]=1;
                for(int i=1;i<205;i++)
                {
                    ji[i]=ji[i-1]+2;
                }
                if (n == 1)
                    cout << 1 << endl;
                else if (n == 2)
                    cout << 5 << endl;
                else {
                    ll sum = 0;
                    for (int i = 0; i <= n - 2; i++)
                    {
                        sum += ji[i];
                    }
                    cout << 2 * sum + ji[n - 1] << endl;
                }
            }
        return 0;
    }

转载于:https://www.cnblogs.com/Vampire6/p/11106869.html

[http_codeforces.com_contest_1180_problem_A]: http://codeforces.com/contest/1180/problem/A
[1705372-20190629160529011-1498659285.png]: /images/20211220/e04f8f500e4e4a14a16b0780f6e38094.png