1019 General Palindromic Number

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本文探讨了回文数的概念及其在不同进制下的性质，通过实例解释了如何判断一个十进制正整数在特定进制下是否为回文数，并提供了详细的算法实现。

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(aibi). 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

Analyze:

It's just a easy problem to change radix. Nothing to explain.

#include<iostream>

using namespace std;

int main(){
	int N, b, flag = 1;
	int a[1000] = {0};
	cin >> N >> b;
	if(N == 0){
		cout << "Yes" << endl << '0';
		return 0;
	}
	int i;
	for(i = 0; N > 0; i++){
		a[i] = N % b;
		N /= b;
	}
	for(int j = i - 1; j != (i - 1) / 2; j--){
		if(a[j] != a[i - 1 - j]){
			flag = 0;
			break;
		}
	}
	cout << (flag == 1 ? "Yes" : "No") << endl;
	for(int j = i - 1; j >= 0; j--){
		if(j == i - 1) cout << a[j];
		else cout << ' ' << a[j];
	}
	return 0;
}