如何让输出的左陪集的陪集头按照优先权值升序再对应十进制数升序

Question

我用chatgpt生成的代码可以输出左陪集但顺序和要求（见图一）不同如图二，代码如下

#include <stdio.h>#include <stdlib.h>#include <string.h>#include <math.h>#define MAX_N 7#define MAX_M 7#define MAX_CODEWORDS (1 << MAX_N)// 二进制数组转十进制数int binary_to_decimal(int *bin, int size) { int num = 0; for (int i = 0; i < size; i++) { num = (num << 1) | bin[i]; } return num;}// 计算汉明权值int hamming_weight(int *bin, int size) { int weight = 0; for (int i = 0; i < size; i++) { weight += bin[i]; } return weight;}// 生成所有长度为m的二进制向量void generate_binary_vectors(int m, int vectors[][MAX_M]) { for (int i = 0; i < (1 << m); i++) { for (int j = 0; j < m; j++) { vectors[i][j] = (i >> (m - j - 1)) & 1; } }}// 计算群码void calculate_codewords(int m, int n, int r, int H[MAX_M][MAX_N], int codewords[][MAX_N]) { int input_vectors[1 << MAX_M][MAX_M]; generate_binary_vectors(m, input_vectors); int code_count = 0; for (int i = 0; i < (1 << m); i++) { int codeword[MAX_N] = {0}; // 复制前m位 for (int j = 0; j < m; j++) { codeword[j] = input_vectors[i][j]; } // 根据H计算后r位 for (int j = 0; j < r; j++) { for (int k = 0; k < m; k++) { codeword[m + j] ^= input_vectors[i][k] & H[k][j]; } } // 保存码字 for (int j = 0; j < n; j++) { codewords[code_count][j] = codeword[j]; } code_count++; }}
// 构造左陪集表void construct_coset_table(int m, int n, int r, int H[MAX_M][MAX_N]) { int codewords[1 << MAX_M][MAX_N]; calculate_codewords(m, n, r, H, codewords); int visited[MAX_CODEWORDS] = {0}; // 遍历所有可能的码字 for (int i = 0; i < (1 << n); i++) { if (visited[i]) continue; int coset[MAX_CODEWORDS][MAX_N]; int coset_size = 0; // 当前码字作为陪集头 int coset_head[MAX_N]; for (int j = 0; j < n; j++) { coset_head[j] = (i >> (n - j - 1)) & 1; } // 遍历群码的所有元素，计算陪集 for (int j = 0; j < (1 << m); j++) { int coset_element[MAX_N]; for (int k = 0; k < n; k++) { coset_element[k] = coset_head[k] ^ codewords[j][k]; } int index = binary_to_decimal(coset_element, n); if (!visited[index]) { for (int k = 0; k < n; k++) { coset[coset_size][k] = coset_element[k]; } coset_size++; visited[index] = 1; } } // 按列顺序排序 for (int j = 0; j < coset_size - 1; j++) { for (int k = j + 1; k < coset_size; k++) { if (binary_to_decimal(coset[j], n) > binary_to_decimal(coset[k], n)) { int temp[MAX_N]; memcpy(temp, coset[j], sizeof(temp)); memcpy(coset[j], coset[k], sizeof(temp)); memcpy(coset[k], temp, sizeof(temp)); } } } // 输出结果 for (int j = 0; j < coset_size; j++) { for (int k = 0; k < n; k++) { printf("%d", coset[j][k]); } printf(" "); } printf("\n"); }}
int main() { int m, n; scanf("%d %d", &m, &n); int r = n - m; int H[MAX_M][MAX_N] = {0}; for (int i = 0; i < m; i++) { for (int j = 0; j < r; j++) { scanf("%d", &H[i][j]); } } construct_coset_table(m, n, r, H); return 0;}