回溯与分支限界算法实现最大团问题c语言代码
时间: 2023-10-21 14:05:40 浏览: 89
回溯算法实现最大团问题的C语言代码如下:
```c
#include <stdio.h>
#include <stdbool.h>
#define N 5
int graph[N][N] = {
{0, 1, 1, 0, 1},
{1, 0, 1, 1, 0},
{1, 1, 0, 1, 0},
{0, 1, 1, 0, 1},
{1, 0, 0, 1, 0}
};
int maxclique[N];
int ans = 0;
bool is_clique(int clique[], int size) {
for (int i = 0; i < size; i++) {
for (int j = i + 1; j < size; j++) {
if (graph[clique[i]][clique[j]] == 0) {
return false;
}
}
}
return true;
}
void backtrack(int clique[], int size, int start) {
if (size > ans) {
ans = size;
for (int i = 0; i < size; i++) {
maxclique[i] = clique[i];
}
}
for (int i = start; i < N; i++) {
int new_clique[N];
for (int j = 0; j < size; j++) {
new_clique[j] = clique[j];
}
new_clique[size] = i;
if (is_clique(new_clique, size + 1)) {
backtrack(new_clique, size + 1, i + 1);
}
}
}
int main() {
int clique[N];
backtrack(clique, 0, 0);
printf("Maximum clique size: %d\n", ans);
printf("Maximum clique: ");
for (int i = 0; i < ans; i++) {
printf("%d ", maxclique[i]);
}
printf("\n");
return 0;
}
```
分支限界算法实现最大团问题的C语言代码如下:
```c
#include <stdio.h>
#include <stdbool.h>
#include <stdlib.h>
#define N 5
int graph[N][N] = {
{0, 1, 1, 0, 1},
{1, 0, 1, 1, 0},
{1, 1, 0, 1, 0},
{0, 1, 1, 0, 1},
{1, 0, 0, 1, 0}
};
int maxclique[N];
int ans = 0;
typedef struct Node {
int clique[N];
int size;
int start;
int lb;
} Node;
int calc_lb(int clique[], int size, int start) {
int cnt = 0;
for (int i = start; i < N; i++) {
bool flag = true;
for (int j = 0; j < size; j++) {
if (graph[clique[j]][i] == 0) {
flag = false;
break;
}
}
if (flag) {
cnt++;
}
}
return cnt;
}
bool is_clique(int clique[], int size) {
for (int i = 0; i < size; i++) {
for (int j = i + 1; j < size; j++) {
if (graph[clique[i]][clique[j]] == 0) {
return false;
}
}
}
return true;
}
void branch_bound() {
Node queue[N * N];
int front = 0, rear = 0;
Node root = {{}, 0, 0, 0};
queue[rear++] = root;
while (front < rear) {
Node node = queue[front++];
if (node.lb + node.size <= ans) {
continue;
}
if (node.size > ans) {
ans = node.size;
for (int i = 0; i < node.size; i++) {
maxclique[i] = node.clique[i];
}
}
for (int i = node.start; i < N; i++) {
if (graph[node.clique[node.size - 1]][i] == 0) {
continue;
}
int new_clique[N];
for (int j = 0; j < node.size; j++) {
new_clique[j] = node.clique[j];
}
new_clique[node.size] = i;
int lb = calc_lb(new_clique, node.size + 1, i + 1);
Node new_node = {new_clique, node.size + 1, i + 1, lb};
if (is_clique(new_clique, node.size + 1)) {
queue[rear++] = new_node;
}
}
}
}
int main() {
branch_bound();
printf("Maximum clique size: %d\n", ans);
printf("Maximum clique: ");
for (int i = 0; i < ans; i++) {
printf("%d ", maxclique[i]);
}
printf("\n");
return 0;
}
```