USACO Training 2.1 Hamming Codes

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解决一个特定的编码问题，寻找N个长度为B比特的码字，确保它们之间的最小哈明距离至少为D。该程序使用递归算法来找出所有可能的组合，并选择符合要求的最小数值解。

Given N, B, and D: Find a set of N codewords (1 <= N <= 64), each of length B bits (1 <= B <= 8), such that each of the codewords is at least Hamming distance of D (1 <= D <= 7) away from each of the other codewords.

The Hamming distance between a pair of codewords is the number of binary bits that differ in their binary notation. Consider the two codewords 0x554 and 0x234 and their differences (0x554 means the hexadecimal number with hex digits 5, 5, and 4)(a hex digit requires four bits):

           0x554 = 0101 0101 0100
           0x234 = 0010 0011 0100
Bit differences:   -XXX -XX- ----

Since five bits were different, the Hamming distance is 5.

PROGRAM NAME: hamming

INPUT FORMAT

N, B, D on a single line

SAMPLE INPUT (file hamming.in)

16 7 3

OUTPUT FORMAT

N codewords, sorted, in decimal, ten per line. In the case of multiple solutions, your program should output the solution which, if interpreted as a base 2^B integer, would have the least value.

SAMPLE OUTPUT (file hamming.out)

0 7 25 30 42 45 51 52 75 76
82 85 97 102 120 127

#include <stdio.h>
#include <stdlib.h>
#include <iostream.h>
#define MAX (1 << 8 + 1)
#define NMAX 65
#define BMAX 10
#define DMAX 10

int nums[NMAX], dist[MAX][MAX];
int N, B, D, maxval;
FILE *in, *out;

void findgroups(int cur, int start) {
    int a, b, canuse;
    char ch;
    if (cur == N) {
        for (a = 0; a < cur; a++) {
            if (a % 10)
                fprintf(out, " ");
            fprintf(out, "%d", nums[a]);
            if (a % 10 == 9 || a == cur-1)
                fprintf(out, "\n");
        }
        exit(0);
    }
    for (a = start; a < maxval; a++) {
        canuse = 1;
        for (b = 0; b < cur; b++)
            if (dist[nums[b]][a] < D) {
                canuse = 0;
                break;
            }
        if (canuse) {
            nums[cur] = a;
            findgroups(cur+1, a+1);
        }
    }
}

int main() {
    in = fopen("hamming.in", "r");
    out = fopen("hamming.out", "w");
    int a, b, c;
    fscanf(in, "%d%d%d", &N, &B, &D);
    maxval = (1 << B);
    for (a = 0; a < maxval; a++)
        for (b = 0; b < maxval; b++) {
            dist[a][b] = 0;
            for (c = 0; c < B; c++) 
                if (((1 << c) & a) != ((1 << c) & b))
                    dist[a][b]++;
        }
    nums[0] = 0;
    findgroups(1, 1);
    return 0;
}