zoj 2406 Specialized FourDigit Numbers

Specialized Four-Digit Numbers

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Time Limit: 2 Seconds      Memory Limit: 65536 KB

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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 189312, 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

分析：

（1）题意很简单，就是求各种进制下数字之和相等的四位数。16进制和12进制求解过程就是分解成因子的形式计算，先求出能组成这些数字的因子的所有情况，然后组合求出每个因子的系数返回相加之和即可。

#include <stdio.h>

int i;
int base_duo[4] = {1,12,144,1728};
int base_hex[4] = {1,16,256,4096};

//得到12进制的数字之和
int get_sum_duo(int num)
{
    int ex[4]={0},sum=0;
    for(i=3;i>=0;i--)
    {

        if(num>=base_duo[i])
        {
            num -= base_duo[i];
            ex[i]++;
            i++;
        }
    }
    for(i=0;i<4;i++)
    sum+=ex[i];
    return sum;
}

//得到16进制的数字之和
int get_sum_hex(int num)
{
    int ex[4]={0},sum=0;
    for(i=3;i>=0;i--)
    {
        if(num>=base_hex[i])
        {
            num -= base_hex[i];
            ex[i]++;
            i++;
        }
    }
    for(i=0;i<4;i++)
    sum+=ex[i];
    return sum;
}
//得到10进制之和
int get_sum(int num)
{
    int sum=0;
    while(num>0)
    {
        sum += num%10;
        num /=10;
    }
    return sum;
}

int main()
{
    int j,tem;
    for(j=2992;j<10000;j++)
    {
        tem = get_sum(j);
        if(get_sum_duo(j)==tem&&get_sum_hex(j)==tem)
        printf("%d\n",j);
    }
    return 0;
}