【代碼超詳解】POJ 2421 Constructing Roads（Kruskal 算法）

一、題目描述

二、算法分析說明與代碼編寫指導

在 Kruskal 之前，先將已經修過的路連的點都併入並查集。

三、AC 代碼

#include<cstdio>
#include<algorithm>
#include<bitset>
#pragma warning(disable:4996)
using namespace std;
template<size_t n> class union_find {
private:
	unsigned root[n]; int rank[n];
public:
	union_find<n>() { init(); }
	union_find<n>(const bool& WannaInit) { if (WannaInit == true)init(); }
	void init() {
		fill(rank, rank + n, 1); for (unsigned i = 0; i < n; ++i)root[i] = i;
	}
	void init(const size_t& _n) {
		fill(rank, rank + _n, 1); for (unsigned i = 0; i < _n; ++i)root[i] = i;
	}
	unsigned find_root(const unsigned& v) {
		unsigned r = v, t = v, u;
		if (t == root[v])return v;
		while (r != root[r]) { r = root[r]; }
		while (t != r) { u = root[t]; root[t] = r; t = u; }
		return r;
	}
	void path_compress() const { for (unsigned i = 0; i < n; ++i)find_root(i); }
	void merge(unsigned u, unsigned v) {
		unsigned fu = find_root(u), fv = find_root(v); int d = rank[fu] - rank[fv];
		if (d < 0) { swap(fu, fv); swap(u, v); }
		else if (d == 0)++rank[fu];
		root[fv] = fu;
	}
	void merge_no_path_compression(const unsigned& u, const unsigned& v) {
		root[v] = u; if (rank[u] == rank[v])++rank[u];
	}
	void merge_directly(const unsigned& u, const unsigned& v) { root[v] = u; }
	unsigned _rank(const unsigned& v) const { return rank[find_root(v)]; }
	size_t size() const { return n; }
};
struct edge { unsigned u, v, w; };
inline bool cmp(const edge& e, const edge& f) { return e.w < f.w; }
unsigned a, N, n, q, x, y; union_find<101> u; edge e[4950], * E = e;
int main() {
	scanf("%u", &n);
	for (unsigned i = 1; i <= n; ++i) {
		for (unsigned j = 1; j <= i; ++j)scanf("%u", &E->w);
		for (unsigned j = i + 1; j <= n; ++j) { scanf("%u", &E->w); E->u = i, E->v = j; ++E; }
	}
	scanf("%u", &q); ++q; E = e; sort(e, e + n * (n - 1) / 2, cmp); --n;
	while (--q) { scanf("%u%u", &x, &y); if (u.find_root(x) != u.find_root(y)) { u.merge(x, y); ++N; } }
	while (N < n) {
		if (u.find_root(E->u) != u.find_root(E->v)) { u.merge(E->u, E->v); ++N; a += E->w; }
		++E;
	}
	printf("%u\n", a);
}