PAT A1019 General Palindromic Number

1019 General Palindromic Number

分数 20

作者 CHEN, Yue

单位 浙江大学

A number that will be the same when it is written forwards or backwards is known as a Palindromic Number. For example, 1234321 is a palindromic number. All single digit numbers are palindromic numbers.

Although palindromic numbers are most often considered in the decimal system, the concept of palindromicity can be applied to the natural numbers in any numeral system. Consider a number N>0 in base b≥2, where it is written in standard notation with k+1 digits ai​ as ∑i=0k​(ai​bi). Here, as usual, 0≤ai​<b for all i and ak​ is non-zero. Then N is palindromic if and only if ai​=ak−i​ for all i. Zero is written 0 in any base and is also palindromic by definition.

Given any positive decimal integer N and a base b, you are supposed to tell if N is a palindromic number in base b.

Input Specification:

Each input file contains one test case. Each case consists of two positive numbers N and b, where 0<N≤109 is the decimal number and 2≤b≤109 is the base. The numbers are separated by a space.

Output Specification:

For each test case, first print in one line Yes if N is a palindromic number in base b, or No if not. Then in the next line, print N as the number in base b in the form "ak​ ak−1​ ... a0​". Notice that there must be no extra space at the end of output.

Sample Input 1:

27 2

Sample Output 1:

Yes
1 1 0 1 1

Sample Input 2:

121 5

Sample Output 2:

No
4 4 1

给定一个十进制数n，和一个进制d，将n转换为d进制，判断转换后的d进制串是否是一个回文串。

/**
 * 给定一个十进制数n，和一个进制d，将n转换为d进制，判断转换后的d进制串是否是一个回文串。
*/

#include <iostream>
#include <algorithm>
#include <vector>

using namespace std;

vector<int> int_str(int n, int d)
{
    vector<int> vec;
    while(n)
    {
        int mod = n % d;
        n /= d;
        vec.push_back(mod);
    }
    
    reverse(vec.begin(), vec.end());
    
    return vec;
}

bool is_level(vector<int> vec)
{
    int len = vec.size();
    for(int i=0; i<len/2; ++i)
        if(vec[i] != vec[len-1-i])
            return false;
    return true;
}

int main()
{
    int n, d;
    cin >> n >> d;
    vector<int> vec = int_str(n, d);
    
    if(is_level(vec))
        puts("Yes");
    else
        puts("No");
    
    bool flag = true;
    for(auto ele : vec)
    {
        if(flag)    flag = false;
        else cout << ' ';
        cout << ele;
    }
    
    puts("");
    
    return 0;
}