Basic Level 1079 Delayed palindrome (20 points)

topic

Given a k+1k+1k+1-bit positive integer NNN, write it as ak...a1a0a_k \cdots a_1 a_0a​k​​...a​1​​a​0​​, where 0≤ai for all iii <100 \le a_i <100≤a​i​​<10 and ak>0a_k> 0a​k​​>0. NN is called a palindrome number , if and only if ai=ak−ia_i = a_{ki}a​i​​=a​k−i​​ for all iii. Zero is also defined as a palindrome number.

The number of non-palindromes can also be transformed into the number of palindromes through a series of operations. First reverse the number, and then add the reversal number to the number. If the sum is not a palindrome number, repeat the reversal and then add operation until a palindrome number appears. If a non-palindromic number can be transformed into a palindromic number, this number is called the delayed palindrome number . (The definition is translated from https://en.wikipedia.org/wiki/Palindromic_number )

Given any positive integer, this question requires you to find the palindrome number that it changes.

Input format:

Enter a positive integer with no more than 1000 digits in one line.

Output format:

For a given integer, output the process of changing the number of palindrome line by line. The format of each line is as follows

A + B = C

Which Ais the original number, Bis Athe number of reversal Cis their sum. AStart with the integer entered. Repeat until Cbecomes palindrome within 10 steps, in this case the output line C is a palindromic number.; the step 10, or if failed to get palindrome, the final outputs in a row Not found in 10 iterations..

Input example 1:

 97152

Output sample 1:

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

Input example 2:

196

Output sample 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.

Thinking analysis:

Note that the return value of reverse is void, so you have to write a new function. Pay attention to carry when adding.

Code:

#include <iostream>
#include <algorithm>
#include <string>

using namespace std;

string rev(string s){
    
    
	reverse(s.begin(), s.end());
	return s;
}

string add(string s1, string s2){
    
    
    string s = s1;
    int cnt = 0;
    for(int i = s.size() - 1; i >= 0; i--){
    
    
        s[i] = (s1[i] + s2[i] - 96 + cnt) % 10 + 48;
        cnt = (s1[i] + s2[i] - 96 + cnt) / 10;
    }
    if(cnt > 0) s = "1" + s;
    return s;
}

int main(){
    
    
    string s;
    cin >> s;
    string sum = s;
    for(int i = 0; i < 10; i++){
    
    
        if(sum == rev(sum)){
    
    
            cout << sum << " is a palindromic number." << endl;
            return 0;
        }
        s = sum;
        sum = add(s, rev(sum));
        cout << s << " + " << rev(s) << " = " << sum << endl;
    }
    cout << "Not found in 10 iterations." << endl;
    return 0;
}

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PAT_BasicLevel