1024 Palindromic Number

1024 Palindromic Number （25 分）

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 (≤10​10​​) 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

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题型分类：字符串处理

题目大意：将给定的一个数字串，反转再加到原来的数字串上，直到到达最大步数或者变成回文串。

解题思路：模拟大整数的加法。

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#include 
#include 
#include 
#include 

using namespace std;

typedef struct bign{
	int d[1000]; //数组要开的足够大，不然存不下数据，数据最大约为2^100 ×10^11 
	int len;
	bign(){
		memset(d, 0, sizeof(d));
		len = 0;
	}
}bign;

bign convert(string str);
bign reverseAndAdd(bign a);
bool isPalin(bign a);
void printBign(bign a);

int main(int argc, char** argv) {
	string str;
	int K, step;
	cin >> str >> K;
	bign a = convert(str); //将字符串转换成"大数"的结构类型 
	for(step = 0; step < K; step++){
		if(isPalin(a)){
			break;
		}
		a = reverseAndAdd(a);
	}
	printBign(a);
	printf("%d\n", step);
	return 0;
}

bign convert(string str){
	bign a;
	for(int i = str.length() - 1; i >= 0; i--){ //将低位存在数组的开头部分 
		a.d[a.len++] = str[i] - '0';
	}
	return a;
}

bign reverseAndAdd(bign a){
	bign result;
	int carry = 0; //相加时的进位 
	for(int i = 0; i < a.len; i++){
		int temp = carry + a.d[a.len - i - 1] + a.d[i];
		result.d[result.len++] = temp % 10;
		carry = temp / 10;
	}
	if(carry != 0){ //最高位有进位 
		result.d[result.len++] = carry;
	}
	return result;
}

bool isPalin(bign a){
	for(int i = 0; i < a.len / 2; i++){
		if(a.d[i] != a.d[a.len - i - 1]) return false;
	}
	return true;
}

void printBign(bign a){
	for(int i = a.len - 1; i >= 0; i--){
		printf("%d", a.d[i]);
	}
	printf("\n");
}