关键路径

数据结构课程-关键路径

拓扑排序 判环 + bfs(栈实现)

#include <bits/stdc++.h>
using namespace std;
inline void _A_A_();
signed main() {_A_A_();return 0;}
 
const int maxn = 1e3 + 10;
 
struct edge {
    int to, nxt, w;
}e[maxn * 4];
 
int idx,h[maxn];
void add(int u,int v, int w) {
    e[idx].to = v;
    e[idx].w = w;
    e[idx].nxt = h[u];
    h[u] = idx++;
}
 
int n, m;

vector<int> topo; // 拓扑序
vector<int> ve(maxn, 0), vl(maxn,0), in(maxn, 0), vis(maxn, 0); // 不建议
int ve[5000], vl[5000], in[5000], vis[5000];    // 建议

bool TopoSort() {
    stack<int> stk;
    for (int i = 0;i < n;i++) {
        if (in[i] == 0) {
            vis[i] = 1;
            stk.push(i);
        }
    }
    while (!stk.empty()) {
        int u = stk.top();
        stk.pop();
        topo.push_back(u);
        for (int i = h[u];~i;i=e[i].nxt) {
            in[e[i].to]--;
            if (in[e[i].to] == 0) {
                vis[e[i].to] = 1;
                stk.push(e[i].to);
            }
        }
    }
    for (int i = 0;i < n;i++) {
        if (!vis[i]) {
            return 0;
        }
    }
    return 1;
}

拓扑排序 判环 + dfs

注意：dfs得到的topo是拓扑逆序

#include <bits/stdc++.h>
using namespace std;
inline void _A_A_();
signed main() {_A_A_();return 0;}
struct edge {
    int from, to, nxt, w;
}e[5000];

int idx,h[5000];
void add(int u,int v, int w) {
    e[idx].to = v;
    e[idx].w = w;
    e[idx].nxt = h[u];
    h[u] = idx++;
}

int n, m;
vector<int> topo; // 拓扑序
int ve[5000], vl[5000], in[5000], vis[5000];

bool dfs(int u) {
    vis[u] = 1;
    for (int i = h[u];i != -1;i=e[i].nxt) {
        if (vis[e[i].to] == 1) return 1;
        if (vis[e[i].to] == 0 && dfs(e[i].to)) return 1;
    }
    vis[u] = -1;
    topo.push_back(u);
    return 0;
}
bool TopoSort() {
    for (int i = 0;i < n;i++) {
        if (vis[i] == 0 && dfs(i) ) {
            return 0;
        }
    }
    return 1;
}

关键路径

包含：

• ve与vl
• ee与el
• 关键路径

#include <bits/stdc++.h>
using namespace std;
inline void _A_A_();
signed main() {_A_A_();return 0;}
struct edge {
    int from, to, nxt, w;
}e[5000];
 
int idx,h[5000];
void add(int u,int v, int w) {
    e[idx].from = u;
    e[idx].to = v;
    e[idx].w = w;
    e[idx].nxt = h[u];
    h[u] = idx++;
}
 
int n, m;
vector<int> topo; // 拓扑序
int ve[5000], vl[5000], in[5000], vis[5000];
 
bool dfs(int u) {
    vis[u] = 1;
    for (int i = h[u];i != -1;i=e[i].nxt) {
        if (vis[e[i].to] == 1) return 1;
        if (vis[e[i].to] == 0 && dfs(e[i].to)) return 1;
    }
    vis[u] = -1;
    topo.push_back(u);
    return 0;
}
 
bool TopoSort() {
    for (int i = 0;i < n;i++) {
        if (vis[i] == 0 && dfs(i) ) {
            return 0;
        }
    }
    return 1;
}
 
void GJLJ() {
    assert(TopoSort());
    // 按拓扑序 求ve
    for (int i = n - 1;i >= 0;i -- ) {
        int u = topo[i];
        for (int j= h[u];j != -1;j=e[j].nxt) {
            ve[e[j].to] = max(ve[e[j].to], ve[u] + e[j].w);
        }
    }
    // 按逆拓扑序 求vl
    for (int i = 0;i < n;i++) vl[i] = ve[topo[0]];
    for (int i = 0;i < n;i++) {
        int u = topo[i];
        for (int j = h[u];~j;j=e[j].nxt) {
            vl[u] = min(vl[u], vl[e[j].to] - e[j].w);
        }
    }
    // 易知ee[i]就是边e[i].from的ve
    for (int i = 0;i < idx;i++) {
        cout << ve[e[i].from] << "\n";
    }
    // 易知el[i]就是边e[i].to的vl 再减掉e[i].w
    for (int i = 0;i < idx;i++) {
        cout << vl[e[i].to] - e[i].w << "\n";
    }        
    // 关键路径 ee[i] == el[i]
    for (int i = 0;i < idx;i++) {
        if (ve[e[i].from] == (vl[e[i].to] - e[i].w))
            cout << e[i].from << "-->" << e[i].to << ":" << ve[e[i].from] << "\n";
    }
}

inline void _A_A_() {
    memset(h,-1,sizeof h);
    cin >> n >> m;
    for (int i = 0;i < m;i++) {
        int aa, bb, cc;
        cin >> aa >> bb >> cc;
        add(aa,bb,cc);
        in[bb]++;
    }
    GJLJ();
}