算法训练营|图论第6天 108.冗余连接 109.冗余连接2

题目：108.冗余连接

题目链接：

108. 冗余连接 (kamacoder.com)

代码：

#include
#include
#include
using namespace std;
vectorfather;
int find(int u) {
	if (father[u] == u) {
		return u;
	}
	else {
		return father[u] = find(father[u]);
	}
}
void join(int u, int v) {
	u = find(u);
	v = find(v);
	if (u == v) return;
	father[v] = u;
}
bool isSame(int u, int v) {
	u = find(u);
	v = find(v);
	return u == v;
}
int main() {
	int n;
	cin >> n;
	father = vector(n + 1);
	for (int i = 0; i <= n; i++) father[i] = i;
	for (int i = 0; i < n; i++) {
		int s, t;
		cin >> s >> t;
		if (isSame(s, t)) {
			cout << s << ' ' << t << endl;
		}
		else {
			join(s, t);
		}
	}

}

题目：109.冗余连接2

题目链接：

109. 冗余连接II (kamacoder.com)

代码：

#include
#include
#include
using namespace std;
int n;
vectorfather;
void init() {
	for (int i = 0; i <= n; i++) {
		father[i] = i;
	}
}
int find(int u) {
	if (u == father[u]) return u;
	else {
		return father[u] = find(father[u]);
	}
}
void join(int u, int v) {
	u = find(u);
	v = find(v);
	if (u == v) return;
	father[v] = u;
}
bool isSame(int u, int v) {
	u = find(u);
	v = find(v);
	return u == v;
}
bool isTree(const vector>& edges, int deleteEdge) {
	init(); // 初始化并查集
	for (int i = 0; i < n; i++) {
		if (i == deleteEdge) continue;
		if (isSame(edges[i][0], edges[i][1])) { // 构成有向环了，一定不是树
			return false;
		}
		join(edges[i][0], edges[i][1]);
	}
	return true;
}
void getRemoveEdge(vector>& edges) {
	init();
	for (int i = 0; i < n; i++) {
		if (isSame(edges[i][0], edges[i][1])) {
			cout << edges[i][0] << " " << edges[i][1] << endl;
		}
		else {
			join(edges[i][0], edges[i][1]);
		}
	}
}

int main() {
	cin >> n;
	father = vector(n + 1, 0);
	int s, t;
	vector>edges;
	vectorinDegree(n + 1, 0);//记录入度
	for (int i = 0; i < n; i++) {
		cin >> s >> t;
		edges.push_back({ s,t });
		inDegree[t]++;
	}
	vectorvec;//记录入度为2的边
	for (int i = n - 1; i >= 0; i--) {
		if (inDegree[edges[i][1]] == 2) {
			vec.push_back(i);
		}
	}
	if (vec.size() > 0) {
		//非环形
		if (isTree(edges, vec[0])) {
			cout << edges[vec[0]][0] << " " << edges[vec[0]][1];
			return 0;
		}
		else {
			cout << edges[vec[1]][0] << " " << edges[vec[1]][1];
			return 0;
		}
	}
	getRemoveEdge(edges);
}