2011清華集訓.BZOJ2561 && THU A1277.最小生成樹(最小割)
阿新 • • 發佈:2019-02-16
有一個 n 個點, m 條邊的圖,現在多加入一條邊 <u, v>,求最少要刪去多少條邊,才能使邊 <u, v> 既可能出現在最小生成樹上,也可能出現在最大生成樹上。
設後加入的邊的長度為 L,那麼只有原圖中小於 L 的邊不能再用的時候,<u, v> 才可能出現在最小生成樹上,用最小割可求。最大生成樹時同理。兩次答案相加。
#include <cstdio> #include <cstring> #include <algorithm> using namespace std; const int MAX_N = 20005, MAX_M = 200005; const int inf = 1000000007; struct node { int v, w, next; }E[MAX_M << 1]; struct arr { int x, y, k; }R[MAX_M]; int head[MAX_N], cur[MAX_N], top = 0; int n, m, s, t, l, ans = 0; int dep[MAX_N], q[MAX_M]; inline void add(int u, int v, int x) { int t1 = x << 1, t2 = t1 | 1; E[t1].v = v; E[t1].w = 1; E[t1].next = head[u]; head[u] = t1; E[t2].v = u; E[t2].w = 1; E[t2].next = head[v]; head[v] = t2; } inline bool cmp(arr a, arr b) { return a.k < b.k; } inline bool bfs() { memset(dep, -1, sizeof(dep)); int bg = 0, ed = 1; q[ed] = s; dep[s] = 0; while (bg < ed) { int x = q[++ bg]; for (int i = head[x]; i != -1; i = E[i].next) if (dep[E[i].v] == -1 && E[i].w) { dep[E[i].v] = dep[x] + 1; q[++ ed] = E[i].v; if (E[i].v == t) return 1; } } return 0; } int dfs(int x, int mx) { if (x == t) return mx; int ret; for (int &i = cur[x]; i != -1; i = E[i].next) if (E[i].w && dep[E[i].v] == dep[x] + 1 && (ret = dfs(E[i].v, min(mx, E[i].w)))) { E[i].w -= ret; E[i ^ 1].w += ret; return ret; } return 0; } void dinic() { int ret; while (bfs()) { for (int i = 0; i <= n; i ++) cur[i] = head[i]; while (ret = dfs(s, inf)) ans += ret; } } void init() { scanf("%d%d", &n, &m); for (int i = 1; i <= m; i ++) scanf("%d%d%d", &R[i].x, &R[i].y, &R[i].k); scanf("%d%d%d", &s, &t, &l); } void doit() { sort(R + 1, R + 1 + m, cmp); memset(head, -1, sizeof(head)); top = 0; for (int i = 1; i <= m; i ++) { if (R[i].k < l) add(R[i].x, R[i].y, top ++); else break; } dinic(); memset(head, -1, sizeof(head)); top = 0; for (int i = m; i >= 1; i --) { if (R[i].k > l) add(R[i].x, R[i].y, top ++); else break; } dinic(); printf("%d\n", ans); } int main() { init(); doit(); return 0; }