## PAT (Advanced Level)-1024. Palindromic Number (25)

PAT (Advanced Level)-1024. Palindromic Number (25)

### 1024. Palindromic Number (25)

400 ms

65536 kB

16000 B

Standard

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.

Non-palindromic numbers can be paired with palindromic ones via a series of operations. First, the non-palindromic number is reversed and the result is added to the original number. If the result is not a palindromic number, this is repeated until it gives a palindromic number. For example, if we start from 67, we can obtain a palindromic number in 2 steps: 67 + 76 = 143, and 143 + 341 = 484.

Given any positive integer N, you are supposed to find its paired palindromic number and the number of steps taken to find it.

Input Specification:

Each input file contains one test case. Each case consists of two positive numbers N and K, where N (<= 1010) is the initial numer and K (<= 100) is the maximum number of steps. The numbers are separated by a space.

Output Specification:

For each test case, output two numbers, one in each line. The first number is the paired palindromic number of N, and the second number is the number of steps taken to find the palindromic number. If the palindromic number is not found after K steps, just output the number obtained at the Kth step and K instead.

Sample Input 1:

``67 3``

Sample Output 1:

``````484
2``````

Sample Input 2:

``69 3``

Sample Output 2:

``````1353
3``````

### 完整代码

``````#include<iostream>
#include<cstring>
#include<string>

using namespace std;

string add(string str1, string str2)
{
if (str2.length() > str1.length())
{
string buf;
for (int i = 0; i < (str2.length() - str1.length()); i++)
{
buf += "0";
}
buf += str1;
str1 = buf;
}
else
{
string buf;
for (int i = 0; i < (str1.length() - str2.length()); i++)
{
buf += "0";
}
buf += str2;
str2 = buf;
}

string result;
bool addition = false;
for (int i = str1.length() - 1; i >= 0; i--)
{
int val = (str1[i] - '0') + (str2[i] - '0') + addition;
if (val >= 10)
{
result += (val - 10 + '0');
}
else
{
result += (val + '0');
}
}
{
result += '1';
}

string RealResult;
for (int i = 0; i < result.length(); i++)
{
RealResult += result[result.length() - 1 - i];
}

return RealResult;
}

string inverted_sequence(string N)// 翻转数字
{
string rN;

for (int i = 0; i < N.length(); i++)
{
rN += N[N.length() - 1 - i];
}

return rN;
}

bool J_Palindromic(string Palindromic)//判断回文
{
int L = Palindromic.length();
int signBOOL=0;
for (int i = L-1; i > ((L-1) / 2); i--)
{
if (Palindromic[i] != Palindromic[L - 1 - i])
signBOOL = 1;
}
if (signBOOL == 1)
return false;
else
return true;

}

int main()
{
string N;
int K;
cin >> N >> K;

if (J_Palindromic(N))//判断输入的数字是否为回文，是则输出。
{
cout << N << '\n' << 0;
}
else
{
string rN;
bool signBOOL;//回文标记。

for (int i = 1; i <= K; i++)
{
rN = inverted_sequence(N);
N = add(N, rN);
if (signBOOL = J_Palindromic(N))
{
cout << N << '\n' << i;
break;
}
if (i == K)
{
cout << N << '\n' << K;
}
}

}

return 0;
}``````