代码随想录算法训练营第五十七天 | 图论part07

53. 寻宝 prim算法

#include <iostream>
#include <vector>
#include <fstream>
#include <climits>

using namespace std;

int main() {
	int v, e;
	int v1, v2, val;
	ifstream infile("input.txt");
	cin >> v >> e;
	vector<vector<int>> graph(v + 1, vector<int>(v + 1, INT_MAX));
	while (e--) {
		cin >> v1 >> v2 >> val;
		graph[v1][v2] = val;
		graph[v2][v1] = val;
	}
	
	/*for (int i = 0; i < v + 1; ++i) {
		for (int j = 0; j < v + 1; ++j) {
			cout << "v1: " << i << " v2: " << j << " val: " << graph[i][j] << endl;
		}
	}*/

	vector<bool> isInTree(v + 1, false);
	vector<int> minDest(v + 1, INT_MAX);

	// 找到第一个顶点
	// 将它放入树中
	// 更新minDest
	isInTree[1] = true;
	for (int j = 1; j < v + 1; ++j) {
		if (!isInTree[j] && graph[1][j] < minDest[j])
			minDest[j] = graph[1][j];
	}

	for (int i = 2; i < v; ++i) { // 只需要循环v-1次
		int curMin = 0;
		int minVal = INT_MAX;
		for (int j = 1; j < v + 1; ++j) {
			if (!isInTree[j] && minDest[j] < minVal) {
				minVal = minDest[j];
				curMin = j;
			}
		}

		isInTree[curMin] = true;

		for (int j = 1; j < v + 1; ++j) {
			if (!isInTree[j] && graph[curMin][j] < minDest[j])
				minDest[j] = graph[curMin][j];
		}
	}
	int result = 0;
	for (int i = 2; i <= v; ++i) {
		result += minDest[i];
	}
	cout << result << endl;
	return 0;
}

kruskal算法

算法思路是按边的val进行从小到大的排序，在不出现环的情况下，将这个边作为最小完全树的一部分。

#include <iostream>
#include <vector>
#include <fstream>
#include <algorithm>

using namespace std;

struct Edge {
	int v1, v2, val;
};

void init(vector<int>& father) {
	for (int i = 0; i < father.size(); ++i) {
		father[i] = i;
	}
}

int find(vector<int>& father, int u) {
	if (father[u] == u) return u;
	return father[u] = find(father, father[u]);
}

bool same(vector<int>& father, int u, int v) {
	u = find(father, u);
	v = find(father, v);
	if (u == v) return true;
	else return false;
}

void join(vector<int>& father, int u, int v) {
	u = find(father, u);
	v = find(father, v);
	if (u == v) return;
	else father[v] = u;
}

int main() {
	int v, e;
	int v1, v2, val;
	ifstream infile("input.txt");
	cin >> v >> e;
	vector<Edge> edges;
	while (e--) {
		cin >> v1 >> v2 >> val;
		edges.emplace_back(Edge{v1, v2, val});
	}
	
	/*for (int i = 0; i < v + 1; ++i) {
		for (int j = 0; j < v + 1; ++j) {
			cout << "v1: " << i << " v2: " << j << " val: " << graph[i][j] << endl;
		}
	}*/
	vector<int> father(v + 1, 0);
	sort(edges.begin(), edges.end(), [](const Edge &a, const Edge &b) {
		return a.val < b.val;
		});

	init(father);

	int result = 0;

	for (Edge edge : edges) {
		if (!same(father, edge.v1, edge.v2)) {
			join(father, edge.v1, edge.v2);
			result += edge.val;
		}
	}
	cout << result << endl;
	return 0;
}