我本来希望C++ Standard Library
中包含这样一个有用的数据结构,但我似乎找不到它。
它不是,但有一个提升: http : //www.boost.org/doc/libs/1_64_0/libs/disjoint_sets/disjoint_sets.html ,所以如果你想要一个现成的实现,我建议这个。
No. I written a simple implementation. It's very extensible.
struct DisjointSet {
vector<int> parent;
vector<int> size;
DisjointSet(int maxSize) {
parent.resize(maxSize);
size.resize(maxSize);
for (int i = 0; i < maxSize; i++) {
parent[i] = i;
size[i] = 1;
}
}
int find_set(int v) {
if (v == parent[v])
return v;
return parent[v] = find_set(parent[v]);
}
void union_set(int a, int b) {
a = find_set(a);
b = find_set(b);
if (a != b) {
if (size[a] < size[b])
swap(a, b);
parent[b] = a;
size[a] += size[b];
}
}
};
And the usage as follows.
void solve() {
int n;
cin >> n;
DisjointSet S(n); // Initializing with maximum Size
S.union_set(1, 2);
S.union_set(3, 7);
int parent = S.find_set(1); // root of 1
}
The implementation of disjoint set using tree. There are two operations:
Tree representation is efficient than linked list representation with two heuristics: -- "union by rank" and "path compression" --
union by rank: assign rank to each node. Rank is height of the node (number of edges in the longest simple path between the node and a descendant leaf)
path compression: during "find_set" operation, make parent of node as root
(Ref: Introduction to Algorithms, 3rd Edition by CLRS)
The STL implementation is given below:
#include<bits/stdc++.h>
using namespace std;
struct disjointSet{
vector<int> parent, rank;
disjointSet(int n){
rank.assign(n, 0);
for (int i = 0; i < n; i++)
parent.push_back(i);
}
int find_set(int v){
if(parent[v]!=v)
parent[v] = find_set(parent[v]);
return parent[v];
}
void union_set(int x,int y){
x = find_set(x);
y = find_set(y);
if (rank[x] > rank[y])
parent[y] = x;
else{
parent[x] = y;
if(rank[x]==rank[y])
rank[y]++;
}
}
};
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