用C++通过aoe网和关键路径，求出每个事件的最早开始时间及最迟开始时间。 再求出每个事件的最早发生时间及最迟发生时间及时间余量。由此确认关键活动及关键路径。给出代码

以下是通过C++实现求解AOE网和关键路径的代码，其中假设AOE网中所有活动的时间都是确定的，不考虑随机因素：

#include <iostream>
#include <vector>
#include <queue>
using namespace std;

const int MAXN = 10000;

int n, m;   // n表示节点数，m表示边数
int earliest[MAXN], latest[MAXN], slack[MAXN]; // 记录每个节点的最早开始时间、最迟开始时间和时间余量
int head[MAXN], nxt[MAXN], to[MAXN], weight[MAXN], cnt;  // 存储图的信息
int inDegree[MAXN]; // 记录每个节点的入度
vector<int> criticalPath; // 存储关键路径上的节点

void addEdge(int u, int v, int w) {
    to[++cnt] = v;
    weight[cnt] = w;
    nxt[cnt] = head[u];
    head[u] = cnt;
    inDegree[v]++;
}

void topologicalSort() {
    queue<int> q;
    for (int i = 1; i <= n; i++) {
        if (inDegree[i] == 0) {
            q.push(i);
            earliest[i] = 0;
        }
    }
    while (!q.empty()) {
        int u = q.front();
        q.pop();
        for (int i = head[u]; i; i = nxt[i]) {
            int v = to[i];
            earliest[v] = max(earliest[v], earliest[u] + weight[i]);
            if (--inDegree[v] == 0) {
                q.push(v);
            }
        }
    }
}

void calcLatest() {
    queue<int> q;
    for (int i = 1; i <= n; i++) {
        if (inDegree[i] == 0) {
            q.push(i);
            latest[i] = earliest[n];
        }
    }
    while (!q.empty()) {
        int u = q.front();
        q.pop();
        for (int i = head[u]; i; i = nxt[i]) {
            int v = to[i];
            latest[u] = min(latest[u], latest[v] - weight[i]);
            if (--inDegree[v] == 0) {
                q.push(v);
            }
        }
    }
}

void calcSlack() {
    for (int u = 1; u <= n; u++) {
        for (int i = head[u]; i; i = nxt[i]) {
            int v = to[i];
            slack[i] = latest[v] - earliest[u] - weight[i];
        }
    }
}

void findCriticalPath() {
    for (int i = 1; i <= m; i++) {
        if (slack[i] == 0) {
            criticalPath.push_back(to[i]);
        }
    }
}

int main() {
    cin >> n >> m;
    cnt = 0;
    memset(head, 0, sizeof(head));
    memset(inDegree, 0, sizeof(inDegree));
    memset(earliest, 0, sizeof(earliest));
    memset(latest, 0x7f, sizeof(latest));
    memset(slack, 0, sizeof(slack));
    for (int i = 1; i <= m; i++) {
        int u, v, w;
        cin >> u >> v >> w;
        addEdge(u, v, w);
    }
    topologicalSort();
    calcLatest();
    calcSlack();
    findCriticalPath();
    cout << "节点的最早开始时间为：" << endl;
    for (int i = 1; i <= n; i++) {
        cout << i << ": " << earliest[i] << endl;
    }
    cout << "节点的最迟开始时间为：" << endl;
    for (int i = 1; i <= n; i++) {
        cout << i << ": " << latest[i] << endl;
    }
    cout << "节点的时间余量为：" << endl;
    for (int i = 1; i <= m; i++) {
        cout << i << ": " << slack[i] << endl;
    }
    cout << "关键路径上的节点为：" << endl;
    for (int i = 0; i < criticalPath.size(); i++) {
        cout << criticalPath[i] << " ";
    }
    cout << endl;
    return 0;
}

这段代码实现了AOE网的拓扑排序、求解最早开始时间、最迟开始时间和时间余量，并且找出了关键路径上的节点。