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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,28 @@ | ||
| \section{技巧总结} | ||
| \subsection{最大流} | ||
| \begin{itemize} | ||
| \item 若一个点只能被经过有限次，将其拆为入点和出点，入点到出点连流量为 | ||
| 经过次数限制的边。 | ||
| \item 树形最大流可以贪心解决。 | ||
| \end{itemize} | ||
| \subsection{最小割} | ||
| \begin{itemize} | ||
| \item 最大化收益可以理解为已经拿到所有收益，最小化损失。然后将其转化为最小割解决。 | ||
| \item 使用$+\infty$边描述依赖关系，可以保证这条边不出现在最小割中。 | ||
| \item 用$S,T$与点的连边来表示点的权。 | ||
| \end{itemize} | ||
| \subsection{费用流} | ||
| \begin{itemize} | ||
| \item 要求费用最小且边数最小：类比进制的思想，实际费用乘以一个大于总边数的因子，再加上 | ||
| 1作为该边边权。 | ||
| \item 若已知走一条边之前必定已经走完了另外几条边，则考虑动态加边。 | ||
| \item 对于层数较少，结构简单的图，考虑使用其它数据结构贪心模拟费用流。 | ||
| \item （待验证）判断一条边是否一定被选：在残量网络上跑SPFA，若距离差不等于边权则必选。 | ||
| \item 餐巾计划问题： | ||
| \end{itemize} | ||
|
|
||
| 上述内容参考了胡伯涛的2007年国家集训队论文《最小割模型在信息学竞赛中的应用》 | ||
| \cite{MCIOI}和租酥雨的博客\footnote{ | ||
| 网络流总结\\ | ||
| \url{https://www.cnblogs.com/zhoushuyu/p/8137534.html} | ||
| }。 |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,93 @@ | ||
| #include <algorithm> | ||
| #include <cstdio> | ||
| int read() { | ||
| int res = 0, c; | ||
| do | ||
| c = getchar(); | ||
| while(c < '0' || c > '9'); | ||
| while('0' <= c && c <= '9') { | ||
| res = res * 10 + c - '0'; | ||
| c = getchar(); | ||
| } | ||
| return res; | ||
| } | ||
| const int size = 70000; | ||
| template <int esiz> | ||
| struct G { | ||
| struct Edge { | ||
| int to, nxt; | ||
| } E[esiz]; | ||
| int last[size], cnt; | ||
| G() : cnt(0) {} | ||
| void addEdge(int u, int v) { | ||
| ++cnt; | ||
| E[cnt].to = v, E[cnt].nxt = last[u]; | ||
| last[u] = cnt; | ||
| } | ||
| }; | ||
| G<size * 2> A; | ||
| G<size> B; | ||
| int in[size], q[size], d[size], p[size][16], siz[size]; | ||
| void DFS(int u) { | ||
| siz[u] = 1; | ||
| for(int i = B.last[u]; i; i = B.E[i].nxt) { | ||
| int v = B.E[i].to; | ||
| if(v != p[u][0]) { | ||
| DFS(v); | ||
| siz[u] += siz[v]; | ||
| } | ||
| } | ||
| } | ||
| int getLCA(int u, int v) { | ||
| if(u == 0 || v == 0) | ||
| return u | v; | ||
| if(d[u] < d[v]) | ||
| std::swap(u, v); | ||
| int delta = d[u] - d[v]; | ||
| for(int i = 0; i < 16; ++i) | ||
| if(delta & (1 << i)) | ||
| u = p[u][i]; | ||
| if(u == v) | ||
| return u; | ||
| for(int i = 15; i >= 0; --i) | ||
| if(p[u][i] != p[v][i]) | ||
| u = p[u][i], v = p[v][i]; | ||
| return p[u][0]; | ||
| } | ||
| int main() { | ||
| int n = read(); | ||
| for(int i = 1; i <= n; ++i) { | ||
| int k = read(); | ||
| while(k) { | ||
| ++in[i]; | ||
| A.addEdge(k, i); | ||
| k = read(); | ||
| } | ||
| } | ||
| int qcnt = 0, rt = n + 1; | ||
| for(int i = 1; i <= n; ++i) | ||
| if(!in[i]) { | ||
| B.addEdge(rt, i); | ||
| p[i][0] = rt; | ||
| q[++qcnt] = i; | ||
| d[i] = 1; | ||
| } | ||
| for(int i = 1; i <= qcnt; ++i) { | ||
| int u = q[i]; | ||
| for(int j = A.last[u]; j; j = A.E[j].nxt) { | ||
| int v = A.E[j].to; | ||
| p[v][0] = getLCA(p[v][0], u); | ||
| if(--in[v] == 0) { | ||
| B.addEdge(p[v][0], v); | ||
| d[v] = d[p[v][0]] + 1; | ||
| for(int k = 1; k < 16; ++k) | ||
| p[v][k] = p[p[v][k - 1]][k - 1]; | ||
| q[++qcnt] = v; | ||
| } | ||
| } | ||
| } | ||
| DFS(rt); | ||
| for(int i = 1; i <= n; ++i) | ||
| printf("%d\n", siz[i] - 1); | ||
| return 0; | ||
| } |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,154 @@ | ||
| #include <algorithm> | ||
| #include <cassert> | ||
| #include <cmath> | ||
| #include <csetjmp> | ||
| #include <cstdio> | ||
| #include <cstring> | ||
| namespace IO { | ||
| void init() { | ||
| assert(setvbuf(stdin, 0, _IONBF, 0) == 0); | ||
| assert(setvbuf(stdout, 0, _IONBF, 0) == 0); | ||
| } | ||
| const int size = 1 << 21; | ||
| char in[size]; | ||
| char getc() { | ||
| static char *S = in, *T = in; | ||
| if(S == T) | ||
| S = in, T = in + fread(in, 1, size, stdin); | ||
| return S == T ? EOF : *S++; | ||
| } | ||
| } | ||
| int read() { | ||
| int res = 0, c; | ||
| bool flag = false; | ||
| do { | ||
| c = IO::getc(); | ||
| flag |= c == '-'; | ||
| } while(c < '0' || c > '9'); | ||
| while('0' <= c && c <= '9') { | ||
| res = res * 10 + c - '0'; | ||
| c = IO::getc(); | ||
| } | ||
| return flag ? -res : res; | ||
| } | ||
| const int size = 105, maxk = 1005, inf = 0x3f3f3f3f; | ||
| typedef double FT; | ||
| const FT eps = 1e-2; | ||
| struct Edge { | ||
| int to, nxt; | ||
| FT w; | ||
| } E[size * size]; | ||
| int last[size], cnt; | ||
| void addEdge(int u, int v, FT w) { | ||
| ++cnt; | ||
| E[cnt].to = v, E[cnt].nxt = last[u], E[cnt].w = w; | ||
| last[u] = cnt; | ||
| } | ||
| FT dis[size]; | ||
| bool vis[size]; | ||
| jmp_buf buf; | ||
| bool pre(int u) { | ||
| FT cd = dis[u]; | ||
| vis[u] = true; | ||
| bool res = false; | ||
| for(int i = last[u]; i; i = E[i].nxt) { | ||
| int v = E[i].to; | ||
| FT dv = cd + E[i].w; | ||
| if(dv < dis[v]) { | ||
| if(vis[v]) | ||
| longjmp(buf, 1); | ||
| dis[v] = dv; | ||
| pre(v); | ||
| res = true; | ||
| break; | ||
| } | ||
| } | ||
| vis[u] = false; | ||
| return res; | ||
| } | ||
| void DFS(int u, int d) { | ||
| if(d == 0) | ||
| return; | ||
| FT cd = dis[u]; | ||
| vis[u] = true; | ||
| for(int i = last[u]; i; i = E[i].nxt) { | ||
| int v = E[i].to; | ||
| FT dv = cd + E[i].w; | ||
| if(dv < dis[v]) { | ||
| if(vis[v]) | ||
| longjmp(buf, 1); | ||
| dis[v] = dv; | ||
| DFS(v, d - 1); | ||
| } | ||
| } | ||
| vis[u] = false; | ||
| } | ||
| int link[size][size], off[size][size]; | ||
| bool check(int n, int K, FT x) { | ||
| cnt = 0; | ||
| memset(last + 1, 0, sizeof(int) * n); | ||
| for(int i = 1; i <= n; ++i) | ||
| for(int j = 1; j <= n; ++j) { | ||
| if(off[i][j] != inf && link[i][j] != inf) | ||
| addEdge(i, j, | ||
| off[i][j] + link[i][j] * x); | ||
| } | ||
| memset(vis + 1, 0, sizeof(bool) * n); | ||
| memset(dis + 1, 0, sizeof(double) * n); | ||
| if(setjmp(buf)) | ||
| return true; | ||
| else { | ||
| for(int i = 1; i <= n; ++i) | ||
| while(pre(i)) | ||
| ; | ||
| int end = 2 * n; | ||
| for(int k = 1; k < end; k <<= 1) | ||
| for(int i = 1; i <= n; ++i) | ||
| DFS(i, k); | ||
| return false; | ||
| } | ||
| } | ||
| int b[size][maxk], s[size][maxk]; | ||
| int main() { | ||
| IO::init(); | ||
| int n = read(); | ||
| int m = read(); | ||
| int K = read(); | ||
| for(int i = 1; i <= n; ++i) | ||
| for(int j = 1; j <= K; ++j) { | ||
| b[i][j] = read(); | ||
| s[i][j] = read(); | ||
| } | ||
| for(int i = 1; i <= n; ++i) | ||
| for(int j = 1; j <= n; ++j) { | ||
| int& mind = off[i][j]; | ||
| mind = inf; | ||
| if(i == j) | ||
| continue; | ||
| for(int k = 1; k <= K; ++k) | ||
| if(b[i][k] != -1 && s[j][k] != -1) | ||
| mind = std::min(mind, | ||
| b[i][k] - s[j][k]); | ||
| } | ||
| memset(link, 0x3f, sizeof(link)); | ||
| for(int i = 1; i <= m; ++i) { | ||
| int u = read(); | ||
| int v = read(); | ||
| int t = read(); | ||
| link[u][v] = std::min(link[u][v], t); | ||
| } | ||
| for(int k = 1; k <= n; ++k) | ||
| for(int i = 1; i <= n; ++i) | ||
| if(link[i][k] != inf) | ||
| for(int j = 1; j <= n; ++j) | ||
| link[i][j] = std::min( | ||
| link[i][j], | ||
| link[i][k] + link[k][j]); | ||
| FT l = 100.0, r = 350.0; | ||
| while(floor(r + eps) - floor(l + eps) >= eps) { | ||
| FT m = (l + r) / 2.0; | ||
| (check(n, K, m) ? l : r) = m; | ||
| } | ||
| printf("%.0lf\n", floor(r + eps)); | ||
| return 0; | ||
| } |
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