PAT甲级2017秋季1136 A Delayed Palindrome (20分)

太过爱你忘了你带给我的痛 2023-02-22 10:42 18阅读 0赞

[1136 A Delayed Palindrome (20分)][1136 A Delayed Palindrome _20]  
![在这里插入图片描述][20200702221619126.png]

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;
    string rev(string s) { 
        reverse(s.begin(), s.end());
        return s;
    }
    string add(string s1, string s2) { 
        string s = s1;
        int carry = 0;
        for (int i = s1.size() - 1; i >= 0; i--) { 
            s[i] = (s1[i] - '0' + s2[i] - '0' + carry) % 10 + '0';
            carry = (s1[i] - '0' + s2[i] - '0' + carry) / 10;
        }
        if (carry > 0) s = "1" + s;
        return s;
    }
    int main() { 
        string s, sum;
        int n = 10;
        cin >> s;
        if (s == rev(s)) { 
            cout << s << " is a palindromic number.\n";
            return 0;
        }
        while (n--) { 
            sum = add(s, rev(s));
            cout << s << " + " << rev(s) << " = " << sum << endl;
            if (sum == rev(sum)) { 
                cout << sum << " is a palindromic number.\n";
                return 0;
            }
            s = sum;
        }
        cout << "Not found in 10 iterations.\n";
        return 0;
    }

#include <bits/stdc++.h>
    using namespace std;
    bool ifPalin(string a){ 
    	for(int i=0;i<a.length()/2;i++){ 
    		if(a[i]!=a[a.length()-i-1])return false;
    	}
    	return true;
    }
    string add(string a, string b) { 
        string c = a;
        int carry = 0;
        for (int i = a.size() - 1; i >= 0; i--) { 
            c[i] = (a[i] - '0' + b[i] - '0' + carry) % 10 + '0';
            carry = (a[i] - '0' + b[i] - '0' + carry) / 10;
        }
        if (carry > 0) c = "1" + c;
        return c;
    }
    int main(){ 
      string a;
      int k=0;
      cin>>a;
      while(!ifPalin(a)) { 
      	string b("");
      	for(int i=0;i<a.length();i++){ 
      		b.push_back(a[a.length()-1-i]);
    	  }
    	 // printf("%s + %s = %s\n",a.c_str(),b.c_str(),add(a,b).c_str());
    	  cout<<a<<" + "<<b<<" = "<<add(a,b)<<endl;
    	  a=add(a,b);
    	  k++;
    	  if(k==10)break;
      }
      if(k<=10 && ifPalin(a)) cout<<a<<" is a palindromic number.";
      else cout<<"Not found in 10 iterations.";
      return 0;
    }

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzIxNDgwNjA3_size_16_color_FFFFFF_t_70]

[1136 A Delayed Palindrome _20]: https://pintia.cn/problem-sets/994805342720868352/problems/994805345732378624
[20200702221619126.png]: https://img-blog.csdnimg.cn/20200702221619126.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzIxNDgwNjA3_size_16_color_FFFFFF_t_70]: https://img-blog.csdnimg.cn/20200702221422187.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzIxNDgwNjA3,size_16,color_FFFFFF,t_70