HDU3549 ISAP板子题_hdu 3549 isap-优快云博客

本文介绍了一种改进的最大流算法——ISAP算法的具体实现。该算法通过预处理距离标号来加速增广过程，使用间隙数组记录节点的距离标号出现次数，减少不必要的搜索路径，提高算法效率。

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#include <bits/stdc++.h>
using namespace std;
const int inf = 0x3fffffff;
template <int N, int M>
struct Isap
{
    int top;
    int d[N], pre[N], cur[N], gap[N];
    struct Vertex {
        int head;
    } V[N];
    struct Edge {
        int v, next;
        int c, f;
    } E[M];
    void init() {
        memset(V, -1, sizeof(V));
        top = 0;
    }
    void add_edge(int u, int v, int c) {
        E[top].v = v;
        E[top].c = c;
        E[top].f = 0;
        E[top].next = V[u].head;
        V[u].head = top++;
    }
    void add(int u, int v, int c) {
        add_edge(u, v, c);
        add_edge(v, u, 0);
    }
    void set_d(int t) {
        queue<int> Q;
        memset(d, -1, sizeof(d));
        memset(gap, 0, sizeof(gap));
        d[t] = 0;
        Q.push(t);
        while (!Q.empty()) {
            int v = Q.front(); Q.pop();
            ++gap[d[v]];
            for (int i = V[v].head; ~i; i = E[i].next) {
                int u = E[i].v;
                if (d[u] == -1) {
                    d[u] = d[v] + 1;
                    Q.push(u);
                }
            }
        }
    }
    int sap(int s, int t, int num) {
        set_d(t);
        int ans = 0, u = s;
        int flow = inf;
        memcpy(cur, V, sizeof(V));
        while (d[s] < num) {
            int &i = cur[u];
            for (; ~i; i = E[i].next) {
                int v = E[i].v;
                if (E[i].c > E[i].f && d[u] == d[v] + 1) {
                    u = v;
                    pre[v] = i;
                    flow = min(flow, E[i].c - E[i].f);
                    if (u == t) {
                        while (u != s) {
                            int j = pre[u];
                            E[j].f += flow;
                            E[j ^ 1].f -= flow;
                            u = E[j ^ 1].v;
                        }
                        ans += flow;
                        flow = inf;
                    }
                    break;
                }
            }
            if (i == -1) {
                if (--gap[d[u]] == 0)
                    break;
                int dmin = num - 1;
                cur[u] = V[u].head;
                for (int j = V[u].head; ~j; j = E[j].next)
                    if (E[j].c > E[j].f)
                        dmin = min(dmin, d[E[j].v]);
                d[u] = dmin + 1;
                ++gap[d[u]];
                if (u != s)
                    u = E[pre[u] ^ 1].v;
            }
        }
        return ans;
    }
};
Isap<100005, 200005> Sap;

int T, n, m, s, t, x, y, z, xx, yy, a[100005], b[100005];

int main(int argc, char const *argv[])
{
    //ios::sync_with_stdio(false);
    int u=0;

        cin >> n >> m;
        Sap.init();
        xx=1,yy=n;
        while (m--) cin >> x >> y >> z, Sap.add(x, y, z);//Sap.add(y, x, z);
        printf("Case %d: %d\n",++u,Sap.sap(xx, yy, n)) ;

}