PAT1019:General Palindromic Number

1019. General Palindromic Number (20)

时间限制
400 ms
内存限制
65536 kB
代码长度限制
16000 B
判题程序
Standard
作者
CHEN, Yue

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 the sum of (aibi) for i from 0 to k. 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 non-negative 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 non-negative 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

思路

进制转换题,检验一个十进制数字用b进制数表示的时候是否是一个回文数。用一个数组保存b进制每一位的数字,然后检查是否对称就行。

代码

#include<iostream>
#include<vector>
using namespace std;
vector<int> digits(30);
int main()
{
int N,b;
while(cin >> N >> b)
{
int index = 0;
while( N != 0)
{
digits[index++] = N % b;
N = N/b;
}
bool isPal = true;
for(int i = 0;i < index/2;i++)
{
if(digits[i] != digits[index - i - 1])
{
isPal = false;
break;
}
}
if(isPal)
cout << "Yes" <<endl;
else
cout << "No" << endl;
for(int i = index - 1;i >= 0;i--)
{
cout << digits[i];
if( i != 0)
cout << " ";
}
if(index == 0 )
cout << 0;
cout << endl;
}
}

  

上一篇:Eclipse 中 Maven 项目默认JDK版本为1.5 的解决方法


下一篇:关于Linux学习中的问题和体会