Given a K + . 1-bit positive integer N, written as A K ⋯ A . 1 A 0 form, wherein of all there is I 0 and A K > 0. N is called a palindrome, if and only if for all have I A I = A K - I . Zero is also defined as a palindrome.
The number of non-palindromic series of operations can also change the palindrome. The first digital reversed, and then added to the number of reversal number, and if not a palindrome Repeat this operation to reverse again added until a palindrome appears. If a non-palindromic number can change a palindrome, and called the number palindrome delay. (Translated from the definition https://en.wikipedia.org/wiki/Palindromic_number )
Given any positive integer, this question asks you to find out the number of variants of the palindrome.
Input formats:
Input gives a positive integer of not more than 1,000 in a row.
Output formats:
For a given integer, line by line and outputs the number of variants of a process palindrome. Each line has the form
A + B = C
Which A
is the original number, B
is A
the number of reversal C
is their sum. A
Starting integer input. Repeat until C
becomes palindrome within 10 steps, in this case the output line C is a palindromic number.
; the step 10, or if failed to get palindrome, the final outputs in a row Not found in 10 iterations.
.
Sample Input 1:
97152
Output Sample 1:
97152 + 25179 = 122331
122331 + 133221 = 255552
255552 is a palindromic number.
Sample Input 2:
196
Output Sample 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 plus_str(string s1,string s2){ reverse(s1.begin(),s1.end()); reverse(s2.begin(),s2.end()); string res="";int i;bool jinwei=false; for(i=0;i<s2.size();i++){ if(jinwei) { res+=((s1[i]-'0'+s2[i]+1-'0')%10+'0'); jinwei=false; if((s1[i]-'0'+s2[i]-'0'+1)/10>0) jinwei=true; } else { res+=((s1[i]-'0'+s2[i]-'0')%10+'0'); if((s1[i]-'0'+s2[i]-'0')/10>0) jinwei=true; } } if(jinwei) res+='1'; reverse(res.begin(),res.end()); return res; } int main() { string str,rev,add;int n=10; cin>>str; while(n--){ rev=str; reverse(rev.begin(),rev.end()); if(str==rev) { printf("%s is a palindromic number.",str.data()); system("pause"); return 0; } add=plus_str(str,rev); printf("%s + %s = %s\n",str.data(),rev.data(),add.data()); str=add; } printf("Not found in 10 iterations."); system("pause"); return 0; }