Consider a positive integer N written in standard notation with k+1 digits ai as ak⋯a1a0 with 0 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.
#include<iostream>
#include<algorithm>
using namespace std; bool isPalindromic(string &str){
int len = str.size();
for(int i = ; i < len/; i++){
if(str[i] != str[len - i - ])
return false;
}
return true;
} string add(const string &A,const string &B){
string C;
int len = A.size();
int carry = ;
for(int i = len - ; i >= ; i--){
int temp = A[i] - '' + B[i] - '' + carry;
C += temp % +'';
carry = temp / ;
}
if(carry != ) C += carry + '';
reverse(C.begin(),C.end());
return C;
} int main(){
string A,B,C;
cin >> A;
int cnt = ;
if(isPalindromic(A)){
cout << A << " is a palindromic number.";
return ;
}
while(cnt--){
B = A;
reverse(A.begin(),A.end());
C = add(A,B);
cout << B << " + " << A << " = " << C << endl;
if(isPalindromic(C)){
cout << C << " is a palindromic number.";
return ;
}
A = C;
}
cout <<"Not found in 10 iterations.";
return ;
}