PAT甲级——A1104 Sum of Number Segments【20】

Consider a positive integer N written in standard notation with k+1 digits a​i​​ as a​k​​⋯a​1​​a​0​​ with 0 for all i and a​k​​>0. Then N is palindromic if and only if a​i​​=a​k−i​​ for all i. Zero is written 0 and is also palindromic by definition.

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. Such number is called a delayed palindrome. (Quoted from https://en.wikipedia.org/wiki/Palindromic_number )

Given any positive integer, you are supposed to find its paired palindromic number.

Input Specification:

Each input file contains one test case which gives a positive integer no more than 1000 digits.

Output Specification:

For each test case, print line by line the process of finding the palindromic number. The format of each line is the following:

A + B = C

where A is the original number, B is the reversed A, and C is their sum. A starts being the input number, and this process ends until Cbecomes a palindromic number -- in this case we print in the last line C is a palindromic number.; or if a palindromic number cannot be found in 10 iterations, print Not found in 10 iterations. instead.

Sample Input 1:

97152

Sample Output 1:

97152 + 25179 = 122331
122331 + 133221 = 255552
255552 is a palindromic number.

Sample Input 2:

196

Sample Output 2:

196 + 691 = 887
887 + 788 = 1675
1675 + 5761 = 7436
7436 + 6347 = 13783
13783 + 38731 = 52514
52514 + 41525 = 94039
94039 + 93049 = 187088
187088 + 880781 = 1067869
1067869 + 9687601 = 10755470
10755470 + 07455701 = 18211171
Not found in 10 iterations.

 #include <iostream>
 #include <string>
 #include <algorithm>
 using namespace std;
 int main()
 {
     int k = ;
     string str1, str2, str;
     cin >> str;
     while (k < )
     {
         int c = ;
         str1 = str2 = str;
         reverse(str2.begin(), str2.end());
         if (str1 == str2)
             break;
         cout << str1 << " + " << str2 << " = ";
         for (int i = str1.length()-; i>=; --i)
         {
             str[i] = (str1[i] - '' + str2[i] - '' + c) %  + '';
             c = (str1[i] - '' + str2[i] - '' + c) / ;
         }
         if (c > )
             str.insert(str.begin(), , c + '');
         cout << str << endl;
         k++;
     }
     if (k == )
         cout << "Not found in 10 iterations." << endl;
     else
         cout << str1 << " is a palindromic number." << endl;
     return ;
 }