HDU 1197 Specialized Four-Digit Numbers

Posted 2020-09-30 十年换你一句好久不见

Specialized Four-Digit Numbers

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 7358    Accepted Submission(s): 5415

Problem Description

Find and list all four-digit numbers in decimal notation that have the property that the sum of its four digits equals the sum of its digits when represented in hexadecimal (base 16) notation and also equals the sum of its digits when represented in duodecimal (base 12) notation.

For example, the number 2991 has the sum of (decimal) digits 2+9+9+1 = 21. Since 2991 = 1*1728 + 8*144 + 9*12 + 3, its duodecimal representation is 1893(12), and these digits also sum up to 21. But in hexadecimal 2991 is BAF16, and 11+10+15 = 36, so 2991 should be rejected by your program.

The next number (2992), however, has digits that sum to 22 in all three representations (including BB016), so 2992 should be on the listed output. (We don‘t want decimal numbers with fewer than four digits - excluding leading zeroes - so that 2992 is the first correct answer.)

 

 

Input

There is no input for this problem.

 

 

Output

Your output is to be 2992 and all larger four-digit numbers that satisfy the requirements (in strictly increasing order), each on a separate line with no leading or trailing blanks, ending with a new-line character. There are to be no blank lines in the output. The first few lines of the output are shown below.

 

 

Sample Input

There is no input for this problem.

 

 

Sample Output

2992 2993 2994 2995 2996 2997 2998 2999

水题，问一个四位数的十进制和十二进制和十六进制个各位数之和是否相等

#include <iostream>
#include <algorithm>
#include <cstring>
#include <cstdio>
#include <vector>
#include <queue>
#include <cstdlib>
#include <iomanip>
#include <cmath>
#include <ctime>
#include <map>
#include <set>
using namespace std;
#define lowbit(x) (x&(-x))
#define max(x,y) (x>y?x:y)
#define min(x,y) (x<y?x:y)
#define MAX 100000000000000000
#define MOD 1000000007
#define pi acos(-1.0)
#define ei exp(1)
#define PI 3.141592653589793238462
#define INF 0x3f3f3f3f3f
#define mem(a) (memset(a,0,sizeof(a)))
typedef long long ll;
int main()
{
    for(int i=2992;i<=9999;i++)
    {
        int n=i;
        int k=i;
        int m=i;
        int ans=0,pos=0,cnt=0;
        while(n)
        {
            ans+=n%10;
            n/=10;
        }
        while(m>=12)
        {
            cnt+=m%12;
            m/=12;
        }
        cnt+=m;
        while(k>=16)
        {
            pos+=k%16;
            k/=16;
        }
        pos+=k;
        if(pos==ans && ans==cnt) printf("%d\n",i);
    }
    return 0;
}