1024. Palindromic Number (25)

最新推荐文章于 2022-02-03 12:50:03 发布

weixin_30488313

最新推荐文章于 2022-02-03 12:50:03 发布

阅读量53

点赞数

CC 4.0 BY-SA版权

原文链接：http://www.cnblogs.com/gcczhongduan/p/4876908.html

本文介绍了一种算法，用于找到任意正整数的配对回文数及其所需步骤。通过不断将数字反转并加上自身，直至得到回文数。同时提供了一个C++实现示例。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

主题链接：http://www.patest.cn/contests/pat-a-practise/1024

题目：

1024. Palindromic Number (25)

时间限制

400 ms

内存限制

65536 kB

代码长度限制

16000 B

判题程序

Standard

作者

CHEN, Yue

A number that will be the same when it is written forwards or backwards is known as a Palindromic Number. For example, 1234321 is a palindromic number. All single digit numbers are palindromic numbers.

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. For example, if we start from 67, we can obtain a palindromic number in 2 steps: 67 + 76 = 143, and 143 + 341 = 484.

Given any positive integer N, you are supposed to find its paired palindromic number and the number of steps taken to find it.

Input Specification:

Each input file contains one test case. Each case consists of two positive numbers N and K, where N (<= 10¹⁰) is the initial numer and K (<= 100) is the maximum number of steps. The numbers are separated by a space.

Output Specification:

For each test case, output two numbers, one in each line. The first number is the paired palindromic number of N, and the second number is the number of steps taken to find the palindromic number. If the palindromic number is not found after K steps, just output the number obtained at the Kth step and K instead.

Sample Input 1:

67 3

Sample Output 1:

484
2

Sample Input 2:

69 3

Sample Output 2:

1353
3

分析：

题目基于一个事实，不论什么一个数，假设本身不是回文数字，那么把自己反转再加上自己。经过有限步后。会变成一个回文数。

那么主要是写两个函数：

1）推断是否是回文

2）反转自加的函数

AC代码：

#include<stdio.h>
#include<string.h>
using namespace std;
char str1[50];
char str3[50];
bool isPalin(char* str){//推断是否是回文
 int i;
 for (i = 0; str[i] != 0; i++);
 for (int j = 0; j <= i; j++){
  if (str[--i] != str[j])return false;
 }
 return true;
}
void add(char* str_a,char* str_sum){//反转自加
 int i;
 for (i = 0; str_a[i] != 0; i++);
 int a, b, sum, jin = 0;
 int j;
 for (j = 0; j < i; j++){
  a = str_a[j] - '0';
  b = str_a[i - 1 - j] - '0';
  sum = a + b + jin;
  jin = sum / 10;
  str_sum[j] = sum % 10 + '0';
 }
 if (jin != 0)
  str_sum[j++] = jin + '0';
 j--;
 for (int w = 0; w <= j / 2; w++){
  char temp = str_sum[w];
  str_sum[w] = str_sum[j - w];
  str_sum[j - w] = temp;
 }
 return ;
}
int main(void){
 int k;
 while (scanf("%s%d", str1, &k) != EOF){
  int count = 0;
  strcpy(str3, str1);
  for (; count < k; count++){
   if (isPalin(str3) == true){
    break;
   }
   else{
    add(str1,str3);
    strcpy(str1, str3);
   }
  }
  puts(str3);
  printf("%d\n", count);
 }
 return 0;
}

截图：