From 46f151a0d9bf07d5501e3698e4ecfb15e4674c01 Mon Sep 17 00:00:00 2001 From: TooYoungTooSimp <6648049+TooYoungTooSimp@users.noreply.github.com> Date: Mon, 6 Mar 2017 19:41:04 +0800 Subject: [PATCH] Section 7.3 --- OnlineJudges/poj/3041.cpp | 33 +++++++++++++++++++++++++++++++ 省选准备/assets/day7/poj3041.cpp | 33 +++++++++++++++++++++++++++++++ 省选准备/省选基础算法.pdf | Bin 945617 -> 952132 bytes 省选准备/省选基础算法.tex | 9 +++++++++ 4 files changed, 75 insertions(+) create mode 100644 OnlineJudges/poj/3041.cpp create mode 100644 省选准备/assets/day7/poj3041.cpp diff --git a/OnlineJudges/poj/3041.cpp b/OnlineJudges/poj/3041.cpp new file mode 100644 index 0000000..bf15dd6 --- /dev/null +++ b/OnlineJudges/poj/3041.cpp @@ -0,0 +1,33 @@ +#include +int adj[505], nxt[10005], to[10005], ecnt, mate[505], vis[505], idx, n, m; +inline void addEdge(int f, int t) +{ + nxt[++ecnt] = adj[f], adj[f] = ecnt, to[ecnt] = t; +} +bool hungry(int u) +{ + for (int e = adj[u]; e; e = nxt[e]) + if (!mate[to[e]]) + return mate[to[e]] = u, true; + for (int e = adj[u]; e; e = nxt[e]) + if (vis[to[e]] != idx) + { + vis[to[e]] = idx; + if (hungry(mate[to[e]])) return mate[to[e]] = u, true; + } + return false; +} +int main() +{ + scanf("%d%d", &n, &m); + for (int i = 0, x, y; i < m; i++) + scanf("%d%d", &x, &y), addEdge(x, y); + int ans = 0; + for (int i = 1; i <= n; i++) + { + idx++; + if (hungry(i)) ans++; + } + printf("%d", ans); + return 0; +} \ No newline at end of file diff --git a/省选准备/assets/day7/poj3041.cpp b/省选准备/assets/day7/poj3041.cpp new file mode 100644 index 0000000..bf15dd6 --- /dev/null +++ b/省选准备/assets/day7/poj3041.cpp @@ -0,0 +1,33 @@ +#include +int adj[505], nxt[10005], to[10005], ecnt, mate[505], vis[505], idx, n, m; +inline void addEdge(int f, int t) +{ + nxt[++ecnt] = adj[f], adj[f] = ecnt, to[ecnt] = t; +} +bool hungry(int u) +{ + for (int e = adj[u]; e; e = nxt[e]) + if (!mate[to[e]]) + return mate[to[e]] = u, true; + for (int e = adj[u]; e; e = nxt[e]) + if (vis[to[e]] != idx) + { + vis[to[e]] = idx; + if (hungry(mate[to[e]])) return mate[to[e]] = u, true; + } + return false; +} +int main() +{ + scanf("%d%d", &n, &m); + for (int i = 0, x, y; i < m; i++) + scanf("%d%d", &x, &y), addEdge(x, y); + int ans = 0; + for (int i = 1; i <= n; i++) + { + idx++; + if (hungry(i)) ans++; + } + printf("%d", ans); + return 0; +} \ No newline at end of file diff --git a/省选准备/省选基础算法.pdf b/省选准备/省选基础算法.pdf index 09aeb181ad158a22a2c9511f842f413e8f1b195d..6dc3160400166b178feebceb6f2028f9900293ee 100644 GIT binary patch delta 259397 zcmZU(19WCh(=Hs_wrv{|Oq@(?+qUjFnb@{%+qP{^Y$yLb-}^q_`p-FQ_1bH9chyx@ zS5>dwecwH|!95tw;}--R1QG-q1QrC|2r(j=QfC554q#?yXA%&AadLJvF|dJgU%$-c zkGbc7^Lze+`Sw>DLR3JxArbL+JyqRp&JPr9LHPWZF6;b_FCCo(g1;VN54GQsAi3r# z5tn#$RfE7&Avo)C(J6{*$oaMQ`LOo+0_&n5buN%{1)52G&f5&(-!XIcY{x|$2s>~T zGo#l;52&_Ti$GS5D@$tXUBM6pRI}7n$!EX@N6Y-60pHGWnhQoG6JfBO7c`9Y9Ml!G zuEJHzic$M9H&~^H$~<70Q)&n-B3e{Fa=ZbKYid&g!)Igj2#SdB-^5-&$9vO7$fVH7 zADCqiLCGJHrP12rAM{zj%VqBXDB$$7?dmyX1UPnmIbX{4lx#33mKXH7^Tz2vNG$WW zQOpXF#eUT9-u10?WJN1$@V;?IM~CVcF_E4p3R6Pl=FVm*rk+X{uFaB;#<4*HbR6+ns^eLvUXgRi z;1-h?dx@bGA8;4pA#v7h?B;ZAbGc>}|KLsa>Zc61|I19%T z{LC(_dI5)&Z%Olk?%SiQP^>**+vaR-D$8YkKBHb&)*1;I^Vuz94Plb@*_)p9ARm12xQf)Y%_EY zuuU^M(aR9cAyx~3RUFDO^~9;a{%t0y<Zl27dUJ0xfB-kTu6&yKS-PvQ`vv!k$Q_cQTp zw&VGHenX#L?v0vL02W7VO;>`Ic&+b=?Y=d#Wf^fhJBqLKnS$1ha1!R-cG!}Dh{`nU z_-)0Kk}tCC!rey&Mv0GFXj={4O*1{JGp^`T>Z~zrEN@BXC^O%t`(Ce6 zzaNReZ+3>3FdSSdz*sQkEoAZ#Ah5v9|8yu?WVIkVpn=){Gs9p4p$C)v&v1hsgeXkP zemxXL3%)0W2^{c$bxT7ayrF?v{v$3G3xN#-%$Wk50Y%>OI~{@s{y(VXEo&tZvatW6 z$}~V=!2Sym)(ue)^)G<_2n5IfignII$V2}%PT9h`36Tj6%=#ZAk4F$L(7+u3>BL?` zu)~6|GX1A_@dlv;^&cw~DSrb&YHiZ}_IzWSP{#PGe3o;Yt z-$++XAoZaCMbNf`6o>u~g=6lJi*Wzy4+KNr!GLi8SAR1WQtf~J)JTU6hx$i9<1g

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z@-wPGmM*!e&p&Jbr87GHqxvZSO7y-mHE|AcaPFbH`bzZvo}%5hlFR8b-&h;B&r7HN zLHiy7-d}%zH92TD_^G(>1Q5e)xAHd4TB!2Mjr$& zZ|c-_4M88P)&rjoy(OMF8pswpYoMs2pc a=kBpWNak*nT?i!VC~~KT#aXQT&i?_H?dbFX diff --git a/省选准备/省选基础算法.tex b/省选准备/省选基础算法.tex index 30db6a6..60e5870 100644 --- a/省选准备/省选基础算法.tex +++ b/省选准备/省选基础算法.tex @@ -523,4 +523,13 @@ Manacher 模板题 若确定了底面半径,则其他值都可以依次计算出来,同时根据上面几个有关圆锥的公式也可以看出,$V$是关于$r$的一个单峰函数,因此三分底面半径求解 \codeinput[\href{http://poj.org/problem?id=3737}{POJ3737} - UmBasketella]{assets/day7/poj3737.cpp} \subsection{Hash} 人品算法,没有什么意思,附一个UOJ模数:$998244353=7*17*2^{23}+1$ +\subsection{二分图匹配} + 给定一个二分图$G$,在$G$的一个子图$M$中,$M$的边集$E$中的任意两条边都不依附于同一个顶点,则称$M$是一个匹配。在二分图$G$中所有的匹配$M$中,边数最多的匹配,称为二分图的最大匹配。 +\paragraph{求解二分图最大匹配} +\subparagraph{使用网络流算法} 实际上,可以将二分图最大匹配问题看成是最大流问题的一种特殊情况。首先:建立源点$s$和汇点$t$,从$s$向$X$集合的所有顶点引一条边,容量为$1$,从$Y$集合的所有顶点向$t$引一条边,容量为$1$。然后将二分图的所有边看成是从$X_i$到$Y_j$的一条有向边,容量为$1$。求最大匹配就是求$s$到$t$的最大流。 +\subparagraph{使用匈牙利算法:} +利用所有边的容量都是$1$以及二分图的性质,我们还可以将二分图最大匹配算法更简单地实现:\\ +假设$M$是二分图$G$的一个匹配,则称$M$中边所依附的顶点是已匹配的顶点,若$P$是图$G$中一条连通两个未匹配顶点的路径,并且不属于$M$的边和属于$M$的边(即待匹配的边和已匹配边)在$P$上交替出现,则称$P$为相对于$M$的一条增广路径。如果我们将$P$的路径看着边的集合,我们令$M'=M \mathop{xor} P$,则$M'$是比$M$多一条边的匹配,即更大的匹配$M'$包含了,或者属于$M$,或者属于$P$,但不同时属于$M$和$P$的边。当找不到增广路的时候,则这时候的$M$是最大匹配。 +\paragraph{例题} 把光束当作图的顶点,小行星当作连接对应光束的边。 +\codeinput[\href{http://poj.org/problem?id=3041}{POJ3041} - Asteroids]{assets/day7/poj3041.cpp} \end{document} \ No newline at end of file