PAT Advanced 1023 Have Fun with Numbers (20) [⼤整数运算]

题目

Notice that the number 123456789 is a 9-digit number consisting exactly the numbers from 1 to 9, with no duplication. Double it we will obtain 246913578, which happens to be another 9-digit number consisting exactly the numbers from 1 to 9, only in a diferent permutation. Check to see the result if we double it

again!

Now you are suppose to check if there are more numbers with this property. That is, double a given number with k digits, you are to tell if the resulting number consists of only a permutation of the digits in the original number.

Input Specification:

Each input file contains one test case. Each case contains one positive integer with no more than 20 digits.

Output Specification:

For each test case, first print in a line “Yes” if doubling the input number gives a number that consists of only a permutation of the digits in the original number, or “No” if not. Then in the next line, print the doubled number.

Sample Input:

1234567899

Sample Output:

Yes

2469135798

题目分析

已知一个最多20位的数字N，判断N乘2后的数字M是否只是组成N的各位数字的重新排列

解题思路

1. 用一个数组记录N中各位数字出现的次数，乘2后的数字M中出现相同数字则出现次数减一（该判断隐含M和N的长度不相等的情况，长度不相等则出现次数一定不相等，数组中出现次数不相等时元素值不为0）
2. 大整数相乘算法

易错点

1. 字符和数字的转换（字符-'0'=数字）

知识点

1. 字符串转换

#include <algorithm>
reverse(ds.begin(),ds.end());

Code

Code 01

#include <iostream>
#include <algorithm>
using namespace std;
int main(int argc,char * argv[]) {
	string s,ds;
	cin>>s;
	int sf[10]= {0},carry=0;
	for(int i=s.length()-1; i>=0; i--) {
		sf[s[i]-'0']++;
		int temp=(s[i]-'0')*2+carry;
		ds.push_back(temp%10+'0');
		carry=temp/10;
		sf[temp%10]--;
	}
	while(carry!=0) {
		ds.push_back(carry%10+'0');
		sf[carry%10]--;
		carry/=10;
	}

	bool flag = true;

//	strrev(s.c_str());
//	if(ds.length()!=s.length())flag=false;
//	else {}
	for(int i=0; i<10; i++) {
		if(sf[i]!=0) {
			flag = false;
			break;
		}
	}
	printf("%s", flag? "Yes\n" : "No\n");
	reverse(ds.begin(),ds.end());
	printf("%s",ds.c_str());
	return 0;
}

Code 02

#include <cstdio>
#include <string.h>
using namespace std;
int book[10];
int main() {
	char num[22];
	scanf("%s", num);
	int flag = 0, len = strlen(num);
	for(int i = len - 1; i >= 0; i--) {
		int temp = num[i] - '0';
		book[temp]++;
		temp = temp * 2 + flag;
		flag = 0;
		if(temp >= 10) {
			temp = temp - 10;
			flag = 1;
		}
		num[i] = (temp + '0');
		book[temp]--;
	}
	int flag1 = 0;
	for(int i = 0; i < 10; i++) {
		if(book[i] != 0)
			flag1 = 1;
	}
	printf("%s", (flag == 1 || flag1 == 1) ? "No\n" : "Yes\n");
	if(flag == 1) printf("1");
	printf("%s", num);
	return 0;
}