代码随想录算法训练营第五十七天

代码随想录算法训练营第五十七天 | 图论part07

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53. 寻宝 prim算法

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minDestisInTree[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;
}