17年秋季第一题 PAT甲级 1136 A Delayed Palindrome (20分)

1136 A Delayed Palindrome (20分)

Consider a positive integer N written in standard notation with k+1 digits a​i​​ as a​k​​⋯a​1​​a​0​​ with 0≤a​i​​<10 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.

#include<iostream>
#include<vector>
#include<set>
#include<map>
#include<algorithm>
#include<cmath>
using namespace std;
int main(){
    string s,r,k,t;
    long long p;
    cin>>s;
    r=s;
    reverse(r.begin(), r.end());
    if(r==s){
        cout<<s<<" is a palindromic number.";
        return 0;
    }
    bool f=false;
    for(int i=0;i<10;i++){
        k="";
        int carry=0,x;
        for(int i=0;i<s.size();i++){
            x=(s[i]-'0')+(r[i]-'0');
            k+=to_string((x%10+carry)%10);
            carry=x/10+(x%10+carry)/10;
        }
        if(carry!=0)k+=to_string(carry);
        cout<<s<<" + "<<r<<" = ";
        r=k;
        s=r;
        reverse(s.begin(), s.end());
        cout<<s<<endl;
        if(s==r){
            cout<<k<<" is a palindromic number.";
            f=true;
            break;
        }
    }
    if(!f){
        cout<<"Not found in 10 iterations.";
    }
    return 0;
}