问题 A: 邻接矩阵存储的图，节点的出度和入度计算(附加代码模式)

#include <iostream>
#include <cstdio>
using namespace std;#define MAX_SIZE 100struct Graph{int nodeNumber;int adjMatrix[MAX_SIZE][MAX_SIZE];
};// 计算每个节点的出度和入度
void CalculateDegree(const Graph& g, int inDegree[], int outDegree[]){int n=g.nodeNumber;for( int i=0;i<n;i++){for( int j=0;j<n;j++){if(g.adjMatrix[i][j]==0) continue;inDegree[j]++;outDegree[i]++;}}
}please comment the following code when you submit to OJ
int main(){// freopen("/config/workspace/answer/test.in","r",stdin);Graph g;cin >> g.nodeNumber;int inDegree[g.nodeNumber] = {0}, outDegree[g.nodeNumber] = {0};for(int i=0;i<g.nodeNumber;i++){for(int j=0;j<g.nodeNumber;j++){cin >> g.adjMatrix[i][j];}}CalculateDegree(g, inDegree, outDegree);for(int i=0;i<g.nodeNumber;i++){cout << inDegree[i] << " " << outDegree[i] << endl;}return 0;
}

问题 B: 算法7-12：有向无环图的拓扑排序

#include <bits/stdc++.h>
using namespace std;
const int N = 1100;
struct p
{int from, to, val;
} edge[N];
int w[N][N];
vector<int> ans;
int e[N], l[N], ve[N], vl[N];
int top_sort(int n)
{int indeg[N] = {};for (int i = 0; i < n; i++){for (int j = 0; j < n; j++){if (w[i][j] == 0)continue;indeg[j]++;}}stack<int> Point;for (int j = 0; j < n; j++){if (indeg[j] == 0){Point.push(j);}}while (!Point.empty()){int ne = Point.top();Point.pop();ans.push_back(ne);for (int j = 0; j < n; j++){if (w[ne][j] != 0)indeg[j]--;elsecontinue;if (indeg[j] == 0){Point.push(j);}}}if (ans.size() != n)return -1;return 0;
}int main()
{int n;cin >> n;for (int i = 0; i < n; i++){for (int j = 0; j < n; j++){cin >> w[i][j];}}if (top_sort(n) == -1){cout << "ERROR" << endl;}else{for (int i = 0; i < ans.size(); i++){cout << ans[i] << " ";}}return 0;
}

问题 C: 有向图是否存在环？

#include <bits/stdc++.h>
using namespace std;
const int N = 1100;
struct p
{int from, to, val;
} edge[N];
int w[N][N];
vector<int> ans;
int e[N], l[N], ve[N], vl[N];
int top_sort(int n)
{int indeg[N] = {};for (int i = 1; i <= n; i++){for (int j = 1; j <= n; j++){if (w[i][j] == 0)continue;indeg[j]++;}}stack<int> Point;for (int j = 1; j <= n; j++){if (indeg[j] == 0){Point.push(j);}}while (!Point.empty()){int ne = Point.top();Point.pop();ans.push_back(ne);for (int j = 1; j <= n; j++){if (w[ne][j] != 0)indeg[j]--;elsecontinue;if (indeg[j] == 0){Point.push(j);}}}if (ans.size() != n)return -1;return 0;
}int main()
{int n, m;while (cin >> n >> m){if (n == 0 && m == 0)break;memset(w, 0, sizeof(w));ans.clear();for (int i = 0; i < m; i++){int a, b;cin >> a >> b;w[a][b] = 1;}if (top_sort(n) == -1){cout << "YES" << endl;}else{cout << "NO" << endl;}}return 0;
}

问题 D: 图-节点的最早发生时间

#include <bits/stdc++.h>
using namespace std;
const int N = 110;
struct p
{int from, to, val;
} edge[N];
int w[N][N];
vector<int> ans;
int e[N], l[N], ve[N], vl[N];
int top_sort(int n)
{int indeg[N] = {};for (int i = 0; i < n; i++){for (int j = 0; j < n; j++){if (w[i][j] == 0)continue;indeg[j]++;}}stack<int> Point;for (int j = 0; j < n; j++){if (indeg[j] == 0){Point.push(j);}}while (!Point.empty()){int ne = Point.top();Point.pop();ans.push_back(ne);for (int j = 0; j < n; j++){if (w[ne][j] != 0)indeg[j]--;elsecontinue;if (indeg[j] == 0){Point.push(j);}}}if (ans.size() != n)return -1;return 0;
}void cal(int n)
{for (int i = 0; i < ans.size(); i++){int now = ans[i];for (int j = 0; j < n; j++){if (w[now][j] == 0)continue;ve[j] = max(ve[now] + w[now][j], ve[j]);}}for (int i = 0; i < ans.size(); i++){vl[i] = ve[ans[ans.size() - 1]];}for (int i = ans.size() - 1; i >= 0; i--){int now = ans[i];for (int j = 0; j < n; j++){if (w[now][j] == 0)continue;vl[now] = min(vl[j] - w[now][j], vl[now]);}}return;
}
int main()
{int n, m;cin >> n >> m;for (int i = 0; i < m; i++){int a, b, c;cin >> a >> b >> c;w[a][b] = c;edge[i].from = a;edge[i].to = b;edge[i].val = c;}top_sort(n);cal(n);for (int i = 0; i < n; i++){cout << ve[i] << endl;}return 0;
}

问题 E: 图-节点的最迟发生时间

#include <bits/stdc++.h>
using namespace std;
const int N = 110;
struct p
{int from, to, val;
} edge[N];
int w[N][N];
vector<int> ans;
int e[N], l[N], ve[N], vl[N];
int top_sort(int n)
{int indeg[N] = {};for (int i = 0; i < n; i++){for (int j = 0; j < n; j++){if (w[i][j] == 0)continue;indeg[j]++;}}stack<int> Point;for (int j = 0; j < n; j++){if (indeg[j] == 0){Point.push(j);}}while (!Point.empty()){int ne = Point.top();Point.pop();ans.push_back(ne);for (int j = 0; j < n; j++){if (w[ne][j] != 0)indeg[j]--;elsecontinue;if (indeg[j] == 0){Point.push(j);}}}if (ans.size() != n)return -1;return 0;
}void cal(int n)
{for (int i = 0; i < ans.size(); i++){int now = ans[i];for (int j = 0; j < n; j++){if (w[now][j] == 0)continue;ve[j] = max(ve[now] + w[now][j], ve[j]);}}for (int i = 0; i < ans.size(); i++){vl[i] = ve[ans[ans.size() - 1]];}for (int i = ans.size() - 1; i >= 0; i--){int now = ans[i];for (int j = 0; j < n; j++){if (w[now][j] == 0)continue;vl[now] = min(vl[j] - w[now][j], vl[now]);}}return;
}
int main()
{int n, m;cin >> n >> m;for (int i = 0; i < m; i++){int a, b, c;cin >> a >> b >> c;w[a][b] = c;edge[i].from = a;edge[i].to = b;edge[i].val = c;}top_sort(n);cal(n);for (int i = 0; i < n; i++){cout << vl[i] << endl;}return 0;
}

问题 F: 图-图的关键路径

#include <bits/stdc++.h>
using namespace std;
const int N = 110;
struct p
{int from, to, val;
} edge[N];
int w[N][N];
vector<int> ans;
int e[N], l[N], ve[N], vl[N];
int top_sort(int n)
{int indeg[N] = {};for (int i = 0; i < n; i++){for (int j = 0; j < n; j++){if (w[i][j] == 0)continue;indeg[j]++;}}stack<int> Point;for (int j = 0; j < n; j++){if (indeg[j] == 0){Point.push(j);}}while (!Point.empty()){int ne = Point.top();Point.pop();ans.push_back(ne);for (int j = 0; j < n; j++){if (w[ne][j] != 0)indeg[j]--;elsecontinue;if (indeg[j] == 0){Point.push(j);}}}if (ans.size() != n)return -1;return 0;
}void cal(int n)
{for (int i = 0; i < ans.size(); i++){int now = ans[i];for (int j = 0; j < n; j++){if (w[now][j] == 0)continue;ve[j] = max(ve[now] + w[now][j], ve[j]);}}for (int i = 0; i < ans.size(); i++){vl[i] = ve[ans[ans.size() - 1]];}for (int i = ans.size() - 1; i >= 0; i--){int now = ans[i];for (int j = 0; j < n; j++){if (w[now][j] == 0)continue;vl[now] = min(vl[j] - w[now][j], vl[now]);}}return;
}
int main()
{int n, m;cin >> n >> m;for (int i = 0; i < m; i++){int a, b, c;cin >> a >> b >> c;w[a][b] = c;edge[i].from = a;edge[i].to = b;edge[i].val = c;}top_sort(n);cal(n);for (int i = 0; i < m; i++){e[i] = ve[edge[i].from];l[i] = vl[edge[i].to] - w[edge[i].from][edge[i].to];if (e[i] == l[i]){printf("%d-->%d:%d\n", edge[i].from, edge[i].to, e[i]);}}return 0;
}

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BUCT数据结构——图（拓扑排序、关键路径）

文章目录

问题 A: 邻接矩阵存储的图，节点的出度和入度计算(附加代码模式)

问题 B: 算法7-12：有向无环图的拓扑排序

问题 C: 有向图是否存在环？

问题 D: 图-节点的最早发生时间

问题 E: 图-节点的最迟发生时间

问题 F: 图-图的关键路径

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