PAT A1136 A Delayed Palindrome (20point(s))

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Consider a positive integer N written in standard notation with k+1 digits ai as ak⋯a1 a0 with 0≤a​i<10 for all i and ak>0. Then N is palindromic if and only if ai=ak−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.

解答

#include<iostream>
#include<string>

using namespace std;

void output(string str, int depth)
{
	bool flag = true;
	int slength = str.length(), c = 0, tmp;
	string res(slength, '\0'), strReverse(slength, '\0');
	for (int i = slength-1; i >=0; i--) {
		if (str[i] != str[slength - i - 1]) flag = false;
		tmp = str[i] + str[slength - i - 1] - 2 * '0' + c;
		if (tmp >= 10) {
			c = 1;
			tmp %= 10;
		}
		else c = 0;
		res[i] = tmp + '0';
		strReverse[slength - i - 1] = str[i];
	}
	if (flag == true) {
		printf("%s is a palindromic number.\n", str.c_str());
		return;
	}
	if (c == 1) res = string(1, '1') + res;
	printf("%s + %s = %s\n", str.c_str(), strReverse.c_str(), res.c_str());
	if (depth == 10) printf("Not found in 10 iterations.");
	else output(res, depth + 1);
}
int main()
{
	string num;
	cin >> num;
	output(num, 1);
	return 0;
}