PAT 1019. General Palindromic Number (20)

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

这道题由于N和b的范围都在10^9内，所以用int 就可以解决，较为简单。

代码如下：

#include <iostream>
#include <algorithm>
#include <map>
#include <vector>
using namespace std;

int main(int argc, char** argv) {
vector<int> number;
int N,b;
cin>>N>>b;
if(N<b)
{
cout<<"Yes"<<endl;
cout<<N<<endl;
return 0;
}
int quotient,rem;
quotient=N;
while(quotient>0)
{
rem=quotient%b;
number.push_back(rem);
quotient/=b;
}
int size=number.size();
int i;
for(i=0;i<=size/2;i++)
{
if(number[i]!=number[size-i-1])
break;
}
if(i<=size/2)
cout<<"No"<<endl;
else
cout<<"Yes"<<endl;
for(int k=size-1;k>0;k--)
cout<<number[k]<<" ";
cout<<number[0];
return 0;
}