hdu 1232, disjoint set, linked list vs. rooted tree, a minor but substantial optimization for path c

three version are provided.

disjoint set, linked list version with weighted-union heuristic, rooted tree version with rank by union and path compression, and a minor but substantial optimization for path compression version FindSet to avoid redundancy so to be more efficient. (31 ms to 15 ms)

reference:

1. Thomas H. Cormen, Introduction to Algorithms

2. Disjoint-set Data Structures By vlad_D– TopCoder Member https://www.topcoder.com/community/data-science/data-science-tutorials/disjoint-set-data-structures/

in linked list version with weighted-union heuristic, with a extra tail member in struct myNode to speedup union, find is O(1), simply the p->head, so I remove find() and just used p->head as the find function.

(one main point) every time a list become no longer list, change its head’s num from 1 to 0, thus facilitate the afterwards count process – all node’s num is simply 0 except the ones as the head of linked lists. – similar process in the rooted tree version.

// linked list version with weighted-union heuristic, 15 ms

#include <cstdio>
#include <cstring>
#include <algorithm>

#define MAXSIZE 1005
struct myNode {
    int num;
    myNode *head;
    myNode *next;
    myNode *tail;
};

void MergeSet(myNode *p1, myNode *p2) {
    p1=p1->head, p2=p2->head;
    if(p1->num<p2->num) { std::swap(p1,p2); }
    p1->num+=p2->num, p2->num=0;
    p1->tail->next=p2, p1->tail=p2->tail;
    for(;p2;p2=p2->next) { p2->head=p1; }
}

int main() {
#ifndef ONLINE_JUDGE
    freopen("in.txt","r",stdin);
#endif
    int T, n,m,u,v,i,cnt;
    myNode cities[MAXSIZE], *p,*pend, *q;
    while(scanf("%d%d",&n,&m)==2 && n>0) {
        for(p=&cities[1],pend=p+n;p!=pend;++p) { p->num=1; p->head=p; p->next=0; p->tail=p; }
        for(i=0;i<m;++i) {
            scanf("%d%d",&u,&v);
            if(cities[u].head!=cities[v].head) { MergeSet(&cities[u],&cities[v]); }
        }
        for(cnt=-1, p=&cities[1],pend=p+n;p!=pend;++p) {
            if(p->num>0) ++cnt;
        }
        printf("%d\n",cnt);
    }
    return 0;
}

// rooted tree version, with rank by union and path compression, 31 ms

#include <cstdio>
#include <cstring>
#include <algorithm>

#define MAXSIZE 1005
struct myNode {
    int rank;
    myNode *parent;
};

myNode* FindSet(myNode *p1) {
    if(p1->parent==p1) return p1;
    return p1->parent=FindSet(p1->parent);
}

void Link(myNode *p1, myNode *p2) {
    if(p1->rank<p2->rank) std::swap(p1,p2);
    p2->parent=p1;
    p2->rank=0;
    if(p1->rank==p2->rank) ++p1->rank;
}

void MergeSet(myNode *p1, myNode *p2) {
    Link(FindSet(p1),FindSet(p2));
}

int main() {
#ifndef ONLINE_JUDGE
    freopen("in.txt","r",stdin);
#endif
    int T, n,m,u,v,i,cnt;
    myNode cities[MAXSIZE], *p,*pend, *q;
    while(scanf("%d%d",&n,&m)==2 && n>0) {
        for(p=&cities[1],pend=p+n;p!=pend;++p) { p->rank=1; p->parent=p; }
        for(i=0;i<m;++i) {
            scanf("%d%d",&u,&v);
            if(FindSet(&cities[u])!=FindSet(&cities[v]))
                MergeSet(&cities[u],&cities[v]);
        }
        for(cnt=-1, p=&cities[1],pend=p+n;p!=pend;++p) {
            if(p->rank>0) ++cnt;
        }
        printf("%d\n",cnt);
    }
    return 0;
}

note that in version 2, the path compression FindSet is a two pass recursive function, first pass up to find parent and then pass down return it to update p->parent, thus achieve path compression.

(another main point) But, note that, even when p->parent is the representative, there is no need to update p->parent, FindSet still obliviously call FindSet(p->parent) and assign it to p->parent, which does nothing useful. We can remove this redundancy by a simple modification, in FindSet, replace

if(p1->parent==p1) return p1;

with

if(p1->parent==p1->parent->parent) return p1->parent;

// almost same with version 2, with the optimization just mentioned, 15 ms

#include <cstdio>
#include <cstring>
#include <algorithm>

#define MAXSIZE 1005
struct myNode {
    int rank;
    myNode *parent;
};

myNode* FindSet(myNode *p1) {
    if(p1->parent==p1->parent->parent) return p1->parent;
    return p1->parent=FindSet(p1->parent);
}

void Link(myNode *p1, myNode *p2) {
    if(p1->rank<p2->rank) std::swap(p1,p2);
    p2->parent=p1;
    p2->rank=0;
    if(p1->rank==p2->rank) ++p1->rank;
}

void MergeSet(myNode *p1, myNode *p2) {
    Link(FindSet(p1),FindSet(p2));
}

int main() {
#ifndef ONLINE_JUDGE
    freopen("in.txt","r",stdin);
#endif
    int T, n,m,u,v,i,cnt;
    myNode cities[MAXSIZE], *p,*pend, *q;
    while(scanf("%d%d",&n,&m)==2 && n>0) {
        for(p=&cities[1],pend=p+n;p!=pend;++p) { p->rank=1; p->parent=p; }
        for(i=0;i<m;++i) {
            scanf("%d%d",&u,&v);
            if(FindSet(&cities[u])!=FindSet(&cities[v]))
                MergeSet(&cities[u],&cities[v]);
        }
        for(cnt=-1, p=&cities[1],pend=p+n;p!=pend;++p) {
            if(p->rank>0) ++cnt;
        }
        printf("%d\n",cnt);
    }
    return 0;
}

版权声明：本文为博主原创文章，未经博主允许不得转载。