图论07&08

53. 寻宝（第七期模拟笔试）

1. prim

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

using namespace std;

int main() {

    int v, e;
    cin >> v >> e;
    int v1, v2 , val;
    vector<vector<int>> grid(v + 1, vector<int>(v + 1, 10001));
    for (int i = 1; i <= e; i++) {
        cin >> v1 >> v2 >> val;
        grid[v1][v2] = val;
        grid[v2][v1] = val; //无向图
    }
    vector<int> visit(v + 1, 0);
    vector<int> minDist(v + 1, 10001);
    for (int i = 1; i < v; i++) {
        int cur = -1;
        int minD = INT_MAX;
        for (int j = 1; j <= v; j++) {
            if (!visit[j] && minDist[j] < minD) {
                minD = minDist[j];
                cur = j;
            }
        }
        visit[cur] = 1;
        for (int j = 1; j <= v; j++) {
            if (!visit[j] && grid[cur][j] < minDist[j] ) {
                minDist[j] = grid[cur][j];
            }
        }
    }
    int result = 0;
    for (int i = 2; i <= v; i++) { // 不计第一个顶点，因为统计的是边的权值，v个节点有 v-1条边
        result += minDist[i];
    }
    cout << result;
    return 0;
}

2.kruscal

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

using namespace std;
struct Edge {
    int v1, v2;
    int val;
};
vector<int> father(10001, 0);
void init() {
    for (int i = 0; i < father.size(); i++)
    father[i] = i;
}

int find(int x) {
    if (x == father[x]) return father[x];
    return find(father[x]);
}

void join(int x, int y) {
    int fx = find(x);
    int fy = find(y);
    if (fx == fy) return;
    else {
        father[fx] = fy;
        return;
    }
}

bool isSame(int x, int y) {
    int fx = find(x);
    int fy = find(y);
    if (fx == fy) return true;
    else {
        return false;
    }
}

int main() {

    int v, e;
    cin >> v >> e;
    int v1, v2 , val;
    vector<Edge> edges(e + 1);
    for (int i = 1; i <= e; i++) {
        cin >> v1 >> v2 >> val;
        edges[i].v1 = v1;
        edges[i].v2 = v2;
        edges[i].val = val;
    }
    sort(edges.begin(), edges.end(), [&](Edge e1, Edge e2){
        return e1.val < e2.val;
    });
    init();
    int result = 0;
    for (Edge &edge: edges) {
        if (!isSame(edge.v1, edge.v2)) {
            join(edge.v1, edge.v2);
            result += edge.val;
        }
    }
    cout << result;
    return 0;
}

117. 软件构建

#include <iostream>
#include <unordered_map>
#include <vector>
#include <queue>

using namespace std;

int main() {
    int n, m;
    cin >> n >> m;
    unordered_map<int, vector<int>> mp;
    vector<int> indegree(n, 0);
    int s, t;
    for (int i = 0; i < m; i++) {
        cin >> s >> t;
        mp[s].push_back(t);
        indegree[t]++;
    }
 
    vector<int> result;
    queue<int> que;
    for (int i = 0; i < n; i++) {
        if (indegree[i] == 0)
        {
            que.push(i);
            result.push_back(i);
        }
    }
    while(!que.empty()) {
        int cur = que.front(); que.pop();;
        vector<int>& curv = mp[cur];
        for (int i = 0; i < curv.size(); i++) {
            indegree[curv[i]]--;
            if (indegree[curv[i]] == 0) {
                que.push(curv[i]);
                result.push_back(curv[i]);
            }
        }
    }
    if (result.size() != n){
        cout << -1;
    } 
    else {
        for (int i = 0; i < n - 1; i++) cout << result[i] << " ";
        cout << result[n - 1];
    }
    return 0;
}

47. 参加科学大会（第六期模拟笔试）

Dijkstra

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

using namespace std;

int main() {

    int n, m;
    cin >> n >> m;
    int s, e, v;
    vector<vector<int>> grid(n + 1, vector<int>(n + 1, INT_MAX));
    for (int i = 0; i < m; i++) {
        cin >> s >> e >> v;
        grid[s][e] = v;

    }
    int start = 1, end = n;
    vector<int> visited(n + 1, 0);
    vector<int> minDist(n + 1, INT_MAX);
    minDist[start] = 0;
    for (int i = 1; i <= n; i++) {
        int cur = 1;
        int Dist = INT_MAX;
        for (int j = 1; j <= n; j++) {
            if (!visited[j] && minDist[j] < Dist) {
                Dist = minDist[j];
                cur  = j;
            }
        }
        visited[cur] = 1;

        for (int j = 1; j <= n; j++) {
            if (!visited[j] && grid[cur][j] != INT_MAX && minDist[j] > grid[cur][j] + minDist[cur])  //grid[cur][j] != INT_MAX  反溢出
                minDist[j] = grid[cur][j] + minDist[cur];

        }
    }
    if (minDist[end] == INT_MAX) cout << -1;
    else {
        cout << minDist[end];
    } 
    return 0;
}