ISAP模板邻接表_isap5300-ch-优快云博客

本文链接：https://blog.youkuaiyun.com/keroro520/article/details/9669389

本文介绍了一种高效的增广路径寻找算法——ISAP算法，并详细解释了其数据结构和实现细节。该算法通过维护顶点的距离标号和间隙数组来加速最大流问题的求解过程。

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/*
ISAP模板
邻接表
*/
int cur[MAXN], head[MAXN], aug[MAXN], pre[MAXN], gap[MAXN], dis[MAXN];

struct Edge {
int u, v, next, cap;
Edge () { }
Edge (int u, int v, int next, int cap) : u(u), v(v), next(next), cap(cap) { }
} edge[MAXM];
int edge_num;

void init()
{
edge_num = 0;
memset(head, -1, sizeof(head));
}
void add_edge(int u, int v, int cap)
{
edge[edge_num] = Edge(u, v, head[u], cap);
head[u] = edge_num++;
edge[edge_num] = Edge(v, u, head[v], 0);
head[v] = edge_num++;
}
int SAP(int s, int sink, int n)
{
aug[s] = INF;
pre[s] = -1;
memset(dis, 0, sizeof(dis));
memset(gap, 0, sizeof(gap));
gap[0] = n;
memcpy(cur, head, sizeof(head));
int max_flow = 0, u = s;
while(dis[s] < n) {
bool flag = false;
if(u == sink) {
max_flow += aug[sink];
for(int v = pre[sink]; v != -1; v = pre[v]) {
int k = cur[v];
edge[k].cap -= aug[sink];
edge[k ^ 1].cap += aug[sink];
aug[v] -= aug[sink];
if(edge[k].cap == 0) u = v;
}
}

for(int k = cur[u]; k != -1; k = edge[k].next) {
int v = edge[k].v;
if(edge[k].cap > 0 && dis[u] == dis[v] + 1) {
flag = true;
pre[v] = u;
cur[u] = k;
aug[v] = min(aug[u], edge[k].cap);
u = v;
break;
}
}

if(!flag) {
if(--gap[dis[u]] == 0) break; /* gap优化，层次树出现断层则结束算法 */
int mindis = n;
cur[u] = head[u];
for(int k = head[u]; k != -1; k = edge[k].next) {
int v = edge[k].v;
if(edge[k].cap > 0 && dis[v] < mindis) {
mindis = dis[v];
cur[u] = k;
}
}
dis[u] = mindis + 1;
gap[dis[u]]++;
if(u != s) u = pre[u];
}
}
return max_flow;
}