集合覆盖

问题提出

例：设集合S={a,b,c,d,e,f},P={A1,A2,A3,A4},A1={a,b,c,d},A2={d,e,f},A3={a,e,f}

请找出一个Ai的集合C，使C覆盖S中的所有元素，如C={A1,A2}

可以使用贪心算法首先找出能覆盖最多S元素的Ai，然后将覆盖的元素移除S，P移除Ai，最后将Ai插入C，依次...直至S元素全部被覆盖，或Ai不足以覆盖S

#include <stdlib.h>
#include "cover.h"
#include "list.h"
#include "set.h"

int cover(Set *members, Set *subsets, Set *covering) {
    Set intersection;
    KSet *subset;
    ListElmt *member,
             *max_member;
    void *data;
    int max_size;
    
    set_init(covering, subsets->match, NULL);
    
    while(set_size(members) > 0 && set_size(subsets) > 0) {
        max_size = 0;
        for (member = list_head(subsets); member != NULL; member = list_next(member)) {
            if (set_intersection(&intersection, &(KSet *)list_data(member))->set, members) != 0) {
                return -1;
            }
            if (set_size(&intersection) > max_size) {
                max_member = member;
                max_size = set_size(&intersection);
            }
            set_destroy(&intersection);
        }
        if (max_size == 0)
            return 1;
        subset = (KSet *)list_data(max_member);
        if (set_insert(covering, subset) != 0)
            return -1;
        for (member = list_head(&((KSet *)list_data(max_member))->set); member != NULL; member = list_next(member)) {
            data = list_data(member);
            if (set_remove(member, (void**)&data) == 0 && member->destroy != NULL) {
                members->destroy(data);
            }
            if (set_remove(subsets, (void**)&subset) != 0)
                return -1;
        }
    }
    
    if (set_size(members) > 0)
        return -1;
    return 0;
}