1136 A Delayed Palindrome

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 C becomes 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.

题意：

　　寻找回文数字（关于中心对称）

思路：

　　大数加法模拟。

Code：

#include <bits/stdc++.h>

using namespace std;

string addFunction(string num1, string num2) {
    int carry = 0, n1, n2, temp;
    int len = num1.length();
    reverse(num2.begin(), num2.end());
    string ans = "";
    while (len >= 1) {
        len--;
        n1 = num1[len] - '0';
        n2 = num2[len] - '0';
        temp = n1 + n2 + carry;
        carry = temp / 10;
        ans = to_string(temp % 10) + ans;
    }
    if (carry == 1) ans = to_string(carry) + ans;
    return ans;
}

bool isPalindrome(string str) {
    int i = 0, j = str.length() - 1;
    while (i < j) {
        if (str[i++] != str[j--]) return false;
    }
    return true;
}

int main() {
    string str, sum, temp;
    cin >> str;
    for (int i = 0; i < 10; ++i) {
        if (isPalindrome(str)) {
            cout << str << " is a palindromic number." << endl;
            break;
        }
        temp = str;
        sum = addFunction(str, str);
        reverse(temp.begin(), temp.end());
        cout << str << " + " << temp << " = " << sum << endl;
        if (i == 9) cout << "Not found in 10 iterations." << endl;
        str = sum;
    }

    return 0;
}

　　刚开始因为求进位的时候不小心算错了，结果最后一组数据没有通过。