一、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 different 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 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
二、题目大意
给一个长度不超过20位的整数,问这个整数的两倍后的数位是不是原整数数位的一个排列。
三、考点
大数乘法
四、解题思路
1、使用string保存数字;
2、使用一维数组保存每位上的数字;
3、大数乘法;
4、新数字每一位对一维数组求减;
5、判断最终一维数组meiy每一位是否恰好消除。
五、代码
#include<iostream>
#include<string>
#include<algorithm>
using namespace std;
int main() {
//read
string s, t="";
cin >> s ;
//solve the original number
int a[10] = {0};
for (int i = 0; i < s.length(); ++i)
a[s[i] - '0'] ++ ;
//double the number
reverse(s.begin(), s.end());
int jin = 0;
for (int i = 0; i < s.length(); ++i) {
int b = jin + 2*(s[i] - '0');
t += (char)(b % 10 + '0');
jin = b / 10;
}
if (jin != 0)
t += (char)(jin + '0');
reverse(t.begin(), t.end());
//solve the second number
for (int i = 0; i < t.length(); ++i)
a[t[i] - '0']--;
//result
bool flag = true;
for (int i = 0; i < 10; ++i) {
if (a[i] != 0) {
flag = false;
break;
}
}
if (flag == true)
cout << "Yes" << endl;
else
cout << "No" << endl;
cout << t << endl;
system("pause");
return 0;
}