PAT 1136. A Delayed Palindrome (20)-PAT甲级真题

Consider a positive integer N written in standard notation with k+1 digits ai as ak…a1a0 with 0 <= ai < 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.

分析：1 将字符串倒置与原字符串比较看是否相等可知s是否为回文串
2 字符串s和它的倒置t相加，只需从头到尾相加然后再倒置（记得要处理最后一个进位carry，如果有进位要在末尾+’1’）
3 倒置可采用algorithm头文件里面的函数reverse(s.begin(), s.end())直接对s进行倒置

#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 <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;

}

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