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        <title>CVBB ACM Team 2020-2021:teams:legal_string:组队训练比赛记录</title>
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        <link>https://wiki.cvbbacm.com/</link>
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       <dc:date>2026-04-30T07:02:47+0800</dc:date>
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    <image rdf:about="https://wiki.cvbbacm.com/lib/exe/fetch.php?media=favicon.ico">
        <title>CVBB ACM Team</title>
        <link>https://wiki.cvbbacm.com/</link>
        <url>https://wiki.cvbbacm.com/lib/exe/fetch.php?media=favicon.ico</url>
    </image>
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        <dc:format>text/html</dc:format>
        <dc:date>2021-10-04T17:00:16+0800</dc:date>
        <dc:creator>Anonymous (anonymous@undisclosed.example.com)</dc:creator>
        <title>2020-2021:teams:legal_string:组队训练比赛记录:缓冲区</title>
        <link>https://wiki.cvbbacm.com/doku.php?id=2020-2021:teams:legal_string:%E7%BB%84%E9%98%9F%E8%AE%AD%E7%BB%83%E6%AF%94%E8%B5%9B%E8%AE%B0%E5%BD%95:%E7%BC%93%E5%86%B2%E5%8C%BA&amp;rev=1633338016&amp;do=diff</link>
        <description>H. travel

题意

给定一棵点权树，从树上选三条不相交的路径，每条路径的权值定义为路径上的点权和，要求最大化三条路径权值和。

题解

设 $\text{dp}(u,0/1/2,i)$ 表示只考虑 $u$ 的子树，结点 $u$ 的状态为 $0/1/2$ 时，已经选中了 $i$$i$$u$$0$$u$$u$$1$$u$$u$$u$$2$$u$$u$$$
\text{dp}(u,0,i+j)\gets \text{dp}(u,0,i)+\text{dp}(v,0,j)\\
\text{dp}(u,1,i+j)\gets \text{dp}(u,0,i)+\text{dp}(v,1,j)+a_u\\
\text{dp}(u,1,i+j)\gets \text{dp}(u,1,i)+\text{dp}(v,0,j)\\
\text{dp}(u,2,i+j)\gets \text{dp}(u,1,i)+\text{dp}(v,1,j)\\
\text{dp}(u,2,i+j)\gets \text{dp}(u,2,i)+\text{dp}(v,0,j)
$$$\gets$$v$$\te…</description>
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        <dc:format>text/html</dc:format>
        <dc:date>2021-07-11T10:01:54+0800</dc:date>
        <dc:creator>Anonymous (anonymous@undisclosed.example.com)</dc:creator>
        <title>2020-2021:teams:legal_string:组队训练比赛记录:contest1</title>
        <link>https://wiki.cvbbacm.com/doku.php?id=2020-2021:teams:legal_string:%E7%BB%84%E9%98%9F%E8%AE%AD%E7%BB%83%E6%AF%94%E8%B5%9B%E8%AE%B0%E5%BD%95:contest1&amp;rev=1625968914&amp;do=diff</link>
        <description>比赛链接

题解

A. Array's Hash

题意

给定一个长度为$n$的数组，这么定义该数组的哈希值：每次从数组开头取出两个数，将后一个数减去前一个数得到的数值放入数组开头，如此重复，直到数组中只剩下一个数，最后这个数便为数组的哈希值。现在有$m$$v$$\sum_{i=1}^n{\left(-1\right)^\left(n-i\right)\times a_i}$$n$$v$$v$$O\left(n+m\right)$$n$$x_i$$t$$1$$0$$O\left(n\log n\right)$$n$$\left(-10^8\le x_i,y_i\le 10^8\right)$$\frac{n\times \left(n-1\right)}{2}$$\left(2\le n\le 100000,1\le k\le \frac{n\times \left(n-1\right)}{2}\right)$$d$$\le d$$45$$\sqrt{2}$$\left(x-y,x+y\right)$$\le d$$2d$$O\left(\log\left(4\times 10^8…</description>
    </item>
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        <dc:format>text/html</dc:format>
        <dc:date>2021-07-18T11:04:58+0800</dc:date>
        <dc:creator>Anonymous (anonymous@undisclosed.example.com)</dc:creator>
        <title>2020-2021:teams:legal_string:组队训练比赛记录:contest2</title>
        <link>https://wiki.cvbbacm.com/doku.php?id=2020-2021:teams:legal_string:%E7%BB%84%E9%98%9F%E8%AE%AD%E7%BB%83%E6%AF%94%E8%B5%9B%E8%AE%B0%E5%BD%95:contest2&amp;rev=1626577498&amp;do=diff</link>
        <description>比赛链接

题解

A. 序列

题意

给定一个 $1\sim n$ 的排列 $a$，该排列的每个子序列 $s=(s_1,s_2\cdot s_p)$ 对 $k$ 的贡献为 $\sum_{i=1}^{p-1}[s_i\lt k\lt s_{i+1}]+[s_i\gt k\gt s_{i+1}]$。

对 $k=1\sim n$，问所有子序列对 $k$ 的贡献总和。

题解

考虑所有子序列中 $(a_i,a_j)(i\lt j)$ 相邻的情况，易知共有 $2^{n-j+i+1}$ 个子序列满足条件。$(a_i,a_j)(i\lt j)$$k\in (\min(a_i,a_j),\max(a_i,a_j))$$2^{n-j+i+1}$$(i,j)$$O(n^2)$$(a_i,a_j)(i\lt j)$$k$$2^{n-j+i+1}$$k\in [1,\min(a_i,a_j)]\bigcup [\max(a_i,a_j),n]$$\sum_{i=1}^{n-1} (n-i)2^{n-i-1}$$1\sim n$$j$$1\le i\lt j$$c_{a_i}=2^ia_i(i\lt j…</description>
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        <dc:format>text/html</dc:format>
        <dc:date>2021-07-18T17:26:45+0800</dc:date>
        <dc:creator>Anonymous (anonymous@undisclosed.example.com)</dc:creator>
        <title>2020-2021:teams:legal_string:组队训练比赛记录:contest3</title>
        <link>https://wiki.cvbbacm.com/doku.php?id=2020-2021:teams:legal_string:%E7%BB%84%E9%98%9F%E8%AE%AD%E7%BB%83%E6%AF%94%E8%B5%9B%E8%AE%B0%E5%BD%95:contest3&amp;rev=1626600405&amp;do=diff</link>
        <description>比赛链接

题解

E. Escape along Water Pipe

题意

给一张 $n×m$ 的图，起点在 $(1,1)$ 坐标点的上方，终点在 $(n,m)$ 坐标点的下方。每个点有一个水管，其中 $(0,3)$ 是垂直的管，连接两个方向， $4$ 是水平管， $5$ 是竖直管，每个管子可以旋转 $90,180,270$$NO$$YES$$(x,y)$$0,x,y$$1,$$,$$,$$20mn$$T$$T≤10000,2≤m,n≤1000$$n×m$$10^{6}$$BFS$$dx,dy$$BFS$$O(n×m)$$n$$A,B$$k$$a_i,a_j$$k$$\sum_{i=1}^n|a_i-b_i|$$k$$a_i,b_i$$n$$+$$n$$-$$a_i,b_i$$2n$$n$$+$$a_i,b_i$$(+a_i,+b_i),(-a_j,-b_j)$$a_i,a_j$$k$$(+a_i,+b_i),(-a_j,-b_j)$$2(\min(a_i,b_i)-\max(a_j,b_j))$$\min(a_i,b_i)$$\max(a_i,b_i)$$k$$(+a_i,+…</description>
    </item>
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        <dc:format>text/html</dc:format>
        <dc:date>2021-07-25T00:00:27+0800</dc:date>
        <dc:creator>Anonymous (anonymous@undisclosed.example.com)</dc:creator>
        <title>2020-2021:teams:legal_string:组队训练比赛记录:contest4</title>
        <link>https://wiki.cvbbacm.com/doku.php?id=2020-2021:teams:legal_string:%E7%BB%84%E9%98%9F%E8%AE%AD%E7%BB%83%E6%AF%94%E8%B5%9B%E8%AE%B0%E5%BD%95:contest4&amp;rev=1627142427&amp;do=diff</link>
        <description>比赛链接

题解

A. Arithmetic Progression

题意

给定一个序列，问有多少连续子串从小到大排列后可以构成等差序列。

题解

给定一个序列 $a_1,a_2\cdots a_n$，则 $\max(a_i)-\min(a_i)\ge (n-1)\times \text{gcd}(a_2-a_1,a_3-a_2\cdots a_n-a_{n-1})$。

等号成立充要条件为 $a_1,a_2\cdots a_n$ 从小到大排列后可以构成等差序列。具体见 $\max(a[l\sim r])-\min(a[l\sim r])=(r-l)\text{gcd}(a_{l+1}-a_l\cdots a_r-a_{r-1})$$b_i=\max(a[i\sim r])-\min(a[i\sim r])+i\times \text{gcd}(a_{i+1}-a_i\cdots a_r-a_{r-1})$$r$$[i,r](i\lt r)$$\text{gcd}(a_{i+1}-a_i\cdots a_r-a_{r-1})$$b_i=r\times \text{gcd}(a_…</description>
    </item>
    <item rdf:about="https://wiki.cvbbacm.com/doku.php?id=2020-2021:teams:legal_string:%E7%BB%84%E9%98%9F%E8%AE%AD%E7%BB%83%E6%AF%94%E8%B5%9B%E8%AE%B0%E5%BD%95:contest5&amp;rev=1628045568&amp;do=diff">
        <dc:format>text/html</dc:format>
        <dc:date>2021-08-04T10:52:48+0800</dc:date>
        <dc:creator>Anonymous (anonymous@undisclosed.example.com)</dc:creator>
        <title>2020-2021:teams:legal_string:组队训练比赛记录:contest5</title>
        <link>https://wiki.cvbbacm.com/doku.php?id=2020-2021:teams:legal_string:%E7%BB%84%E9%98%9F%E8%AE%AD%E7%BB%83%E6%AF%94%E8%B5%9B%E8%AE%B0%E5%BD%95:contest5&amp;rev=1628045568&amp;do=diff</link>
        <description>比赛链接

题解

C. Cover the Paths

题意

给定一棵树和若干路径，要求选出最小的点集，使得每条路径上至少有一个点。

题解

强制以 $1$ 为根，根据每条路径两端点的 $\text{LCA}$ 深度从大到小排序。

对于 $\text{LCA}$ 深度最大的路径，显然必须选择一个点，由于其他路径的 $\text{LCA}$$\text{LCA}$$\text{LCA}$$\text{LCA}$$\text{LCA}$$x_v+b_i\le x_u+T$$T$$(x_1,x_2\cdots x_n)$$x_i$$x_v\le x_u+T-b_i$$T$$s$$x_i$$(s,i,\infty),(i,s,\infty)$$-\infty\le x_i\le \infty$$x_i$$(s,i,v),(i,s,-v)$$v\le x_i\le v$$O(nm\log V)$$n$$q$$[l,r]$$m$$[lef,rig]$$mid=\frac {lef+rig}2$$[l,r]\in [lef,mid],[mid+1,rig]$$\text{mid}$$O\l…</description>
    </item>
    <item rdf:about="https://wiki.cvbbacm.com/doku.php?id=2020-2021:teams:legal_string:%E7%BB%84%E9%98%9F%E8%AE%AD%E7%BB%83%E6%AF%94%E8%B5%9B%E8%AE%B0%E5%BD%95:contest6&amp;rev=1628686076&amp;do=diff">
        <dc:format>text/html</dc:format>
        <dc:date>2021-08-11T20:47:56+0800</dc:date>
        <dc:creator>Anonymous (anonymous@undisclosed.example.com)</dc:creator>
        <title>2020-2021:teams:legal_string:组队训练比赛记录:contest6</title>
        <link>https://wiki.cvbbacm.com/doku.php?id=2020-2021:teams:legal_string:%E7%BB%84%E9%98%9F%E8%AE%AD%E7%BB%83%E6%AF%94%E8%B5%9B%E8%AE%B0%E5%BD%95:contest6&amp;rev=1628686076&amp;do=diff</link>
        <description>比赛链接

补题情况
  题目    蒋贤蒙    王赵安    王智彪    A    2    1    0    B    1    2    2    C    1    1    2    D    2    0    0    E    2    0    2    F    2    0    1    G    2    1    0    H    0    0    0    I    2    0    1    J    2  $x\in [1,n]$$A$$B$$B$$y$$y\le x$$A$$A$$B$$B$$i$$A$$i\le x$$B$$y$$A$$i\le x$$[1,y)$$+1$$[y,n]$$+1$$1$$B$$[1,n]$$A$$+1$$1$$11100011$$a$$1$$b$$0$$c$$1$$\text{dp}(a,b,c)$$O\left(n^4\right)$$f(a,b,c,k)$$k$$f(a,b,c,k)$$p(a,b,c)$$c_1\le c_2\to p(a,b,c_1)\le p(a,b,c_2)$$O\left(n^…</description>
    </item>
    <item rdf:about="https://wiki.cvbbacm.com/doku.php?id=2020-2021:teams:legal_string:%E7%BB%84%E9%98%9F%E8%AE%AD%E7%BB%83%E6%AF%94%E8%B5%9B%E8%AE%B0%E5%BD%95:contest7&amp;rev=1627637011&amp;do=diff">
        <dc:format>text/html</dc:format>
        <dc:date>2021-07-30T17:23:31+0800</dc:date>
        <dc:creator>Anonymous (anonymous@undisclosed.example.com)</dc:creator>
        <title>2020-2021:teams:legal_string:组队训练比赛记录:contest7</title>
        <link>https://wiki.cvbbacm.com/doku.php?id=2020-2021:teams:legal_string:%E7%BB%84%E9%98%9F%E8%AE%AD%E7%BB%83%E6%AF%94%E8%B5%9B%E8%AE%B0%E5%BD%95:contest7&amp;rev=1627637011&amp;do=diff</link>
        <description>比赛链接

补题情况
  题目    蒋贤蒙    王赵安    王智彪    A    0    0    0    B    2    0    2    C    2    0    1    D    2    1    0    E    2    0    1    F    2    0    2    G    2    0    2    H    0    1    2    I    2    0    2    J    2  $k$$k$$k$$k+1$$i$$s_i$$(s_1,s_2\cdots s_{k+1})$$\text{prufer}$$i$$d_i$$$
\prod_{i=1}^{k+1}s_i^{d_i}
$$$p_i$$i$$\text{prufer}$$\text{prufer}$$d_i=p_i+1$$$
\prod_{i=1}^{k+1}s_i^{d_i}=
\left(\prod_{i=1}^{k+1}s_i\right)\left(\prod_{i=1}^{k+1}s_i^{p_i}\right)
$$$\prod_{i=1}^{k…</description>
    </item>
    <item rdf:about="https://wiki.cvbbacm.com/doku.php?id=2020-2021:teams:legal_string:%E7%BB%84%E9%98%9F%E8%AE%AD%E7%BB%83%E6%AF%94%E8%B5%9B%E8%AE%B0%E5%BD%95:contest8&amp;rev=1627746652&amp;do=diff">
        <dc:format>text/html</dc:format>
        <dc:date>2021-07-31T23:50:52+0800</dc:date>
        <dc:creator>Anonymous (anonymous@undisclosed.example.com)</dc:creator>
        <title>2020-2021:teams:legal_string:组队训练比赛记录:contest8</title>
        <link>https://wiki.cvbbacm.com/doku.php?id=2020-2021:teams:legal_string:%E7%BB%84%E9%98%9F%E8%AE%AD%E7%BB%83%E6%AF%94%E8%B5%9B%E8%AE%B0%E5%BD%95:contest8&amp;rev=1627746652&amp;do=diff</link>
        <description>比赛链接

补题情况
  题目    蒋贤蒙    王赵安    王智彪    D    2    0    1    E    0    1    2    L    0    1    2  
题解

D. Contest Strategy

题意

给定 $n$ 道题以及完成每道题需要的时间。对固定读题顺序，一个队伍会先按顺序读 $k$$1\sim n$$t_1,t_2\cdots t_n$$\sum_{i=1}^n (n+1-i)t_i$$i$$a_i$$k-1$$i$$i$$n-k+1$$f(i,j)$$i$$j$$i$$j$$j$$i$$k-1$$i$$j$$i$$p$$i$$$
f(i,j)=j!(n-j)!\sum_{p=k-1}^{j-1}{n-i\choose p}{i-1\choose j-p-1}
$$$i$$j$$f(i,j)-f(i,j-1)$$$
(n+k-j)a_i\times (f(i,j)-f(i,j-1))
$$$O\left(n^3\right)$$k$$n-k$$3≤k＜n≤100,100$$10^{9}$$k$$n-k$$O(logn)$$n…</description>
    </item>
    <item rdf:about="https://wiki.cvbbacm.com/doku.php?id=2020-2021:teams:legal_string:%E7%BB%84%E9%98%9F%E8%AE%AD%E7%BB%83%E6%AF%94%E8%B5%9B%E8%AE%B0%E5%BD%95:contest9&amp;rev=1628255270&amp;do=diff">
        <dc:format>text/html</dc:format>
        <dc:date>2021-08-06T21:07:50+0800</dc:date>
        <dc:creator>Anonymous (anonymous@undisclosed.example.com)</dc:creator>
        <title>2020-2021:teams:legal_string:组队训练比赛记录:contest9</title>
        <link>https://wiki.cvbbacm.com/doku.php?id=2020-2021:teams:legal_string:%E7%BB%84%E9%98%9F%E8%AE%AD%E7%BB%83%E6%AF%94%E8%B5%9B%E8%AE%B0%E5%BD%95:contest9&amp;rev=1628255270&amp;do=diff</link>
        <description>比赛链接

补题情况
  题目    蒋贤蒙    王赵安    王智彪    A    0    0    0    C    2    1    0    E    2    0    1    F    0    1    2    G    2    0    2    I    2    1    0    J    2    1    1  
题解

C. Cheating and Stealing

题意

给定一个长度为 $n$$01$$S$$i=1\sim n$$0$$i$$0$$i$$1$$0$$1$$2$$1$$0$$2$$i$$i$$O\left(\frac ni\right)$$O(n\log n)$$O(1)$$O(n\log n)$$i$$0$$i$$1$$k$$0$$1$$p(0,k)$$p(1,k)$$O(1)$$0$$1$$2$$1$$0$$2$$2$$0$$\text{next}$$\text{next}(i)=(s[i]==s[i+1])?(i+1):\text{next}(i+2)$$O(1)$$1$$i$$a_i$$\text{OR},\te…</description>
    </item>
    <item rdf:about="https://wiki.cvbbacm.com/doku.php?id=2020-2021:teams:legal_string:%E7%BB%84%E9%98%9F%E8%AE%AD%E7%BB%83%E6%AF%94%E8%B5%9B%E8%AE%B0%E5%BD%95:contest10&amp;rev=1628668816&amp;do=diff">
        <dc:format>text/html</dc:format>
        <dc:date>2021-08-11T16:00:16+0800</dc:date>
        <dc:creator>Anonymous (anonymous@undisclosed.example.com)</dc:creator>
        <title>2020-2021:teams:legal_string:组队训练比赛记录:contest10</title>
        <link>https://wiki.cvbbacm.com/doku.php?id=2020-2021:teams:legal_string:%E7%BB%84%E9%98%9F%E8%AE%AD%E7%BB%83%E6%AF%94%E8%B5%9B%E8%AE%B0%E5%BD%95:contest10&amp;rev=1628668816&amp;do=diff</link>
        <description>比赛链接

补题情况
  题目    蒋贤蒙    王赵安    王智彪    A    0    1    2    B    0    0    0    C    1    0    2    D    2    1    0    E    2    0    0    G    0    1    2    J    2    0    1    K    2    0    0  
题解

A.  Contracting Convex Hull
$n(n≤1000)$$1$$q$$(q≤100000)$$(×)$$O(n)$$O(1)$$2$$n$$2$$0$$(×)$$x$$0$$y$$y\in [0\sim n-1]$$y=i$$p_i$$x\gets \max(x,x\oplus y)$$x$$n-1$$n$$2$$\text{dp}(i)$$i$$n-1$$\text{dp}(n-1)=0$$\text{dp}(0)$$$
\text{dp}(i)=1+\sum_{j\oplus i\gt i}p_j\text{dp}(j\oplus i)+\sum_{j\oplu…</description>
    </item>
    <item rdf:about="https://wiki.cvbbacm.com/doku.php?id=2020-2021:teams:legal_string:%E7%BB%84%E9%98%9F%E8%AE%AD%E7%BB%83%E6%AF%94%E8%B5%9B%E8%AE%B0%E5%BD%95:contest11&amp;rev=1628402791&amp;do=diff">
        <dc:format>text/html</dc:format>
        <dc:date>2021-08-08T14:06:31+0800</dc:date>
        <dc:creator>Anonymous (anonymous@undisclosed.example.com)</dc:creator>
        <title>2020-2021:teams:legal_string:组队训练比赛记录:contest11</title>
        <link>https://wiki.cvbbacm.com/doku.php?id=2020-2021:teams:legal_string:%E7%BB%84%E9%98%9F%E8%AE%AD%E7%BB%83%E6%AF%94%E8%B5%9B%E8%AE%B0%E5%BD%95:contest11&amp;rev=1628402791&amp;do=diff</link>
        <description>比赛链接

补题情况
  题目    蒋贤蒙    王赵安    王智彪    B    2    1    0    D    2    0    1    E    2    0    1    G    0    0    0    I    0    0    0    J    2    0    1    L    2    0    1  
题解

B. Bipartite Blanket

题意

给定一个二分图，左部有 $n$$m$$t$$t$$S$$f(S)$$S$$S$$\forall T(T\subseteq S\to |T|\le |f(T)|)$$O(n2^n)$$A$$B$$A\cup B$$A$$A$$B$$1$$A,B$$6\times 6$$(r,c)$$(r+1,c)$$(r,c+1)$$(1,1)$$a_1,a_2\cdots a_n$$a_1,a_2\cdots a_n$$1\sim n$$(6,6)$$(6,6)$$n,n-1\cdots 1$$n\le 40000$$f(r,c)$$f(r,c)$$(6,6)$$(6,6)$$f(6,6)=…</description>
    </item>
    <item rdf:about="https://wiki.cvbbacm.com/doku.php?id=2020-2021:teams:legal_string:%E7%BB%84%E9%98%9F%E8%AE%AD%E7%BB%83%E6%AF%94%E8%B5%9B%E8%AE%B0%E5%BD%95:contest12&amp;rev=1628909778&amp;do=diff">
        <dc:format>text/html</dc:format>
        <dc:date>2021-08-14T10:56:18+0800</dc:date>
        <dc:creator>Anonymous (anonymous@undisclosed.example.com)</dc:creator>
        <title>2020-2021:teams:legal_string:组队训练比赛记录:contest12</title>
        <link>https://wiki.cvbbacm.com/doku.php?id=2020-2021:teams:legal_string:%E7%BB%84%E9%98%9F%E8%AE%AD%E7%BB%83%E6%AF%94%E8%B5%9B%E8%AE%B0%E5%BD%95:contest12&amp;rev=1628909778&amp;do=diff</link>
        <description>比赛链接

补题情况
  题目    蒋贤蒙    王赵安    王智彪    A    0    0    0    B    2    2    0    C    0    0    0    D    0    0    0    E    1    0    2    G    0    0    0    J    2    2    0    K    2    1    0  
题解

B. xay loves monotonicity
$A$$B$$0\le b_i\le 1$$a_i\gets t$$l\le i\le r$$b_i\gets b_i\oplus 1$$l,r$$l\le i_1\le i_2\le \cdots i_k\le r$$a_{i_1}\le a_{i_2}\le\cdots \le a_{i_k}$$i_t\lt j\lt i_{t+1}$$a_j\lt a_{i_t}$$3$$b_{i_t}\neq b_{i_{t+1}}$$ma(L,R)=\max(a[L\sim R]),mb(L,R)$$ma(L,R)$$b_i$$\text{q…</description>
    </item>
    <item rdf:about="https://wiki.cvbbacm.com/doku.php?id=2020-2021:teams:legal_string:%E7%BB%84%E9%98%9F%E8%AE%AD%E7%BB%83%E6%AF%94%E8%B5%9B%E8%AE%B0%E5%BD%95:contest13&amp;rev=1628998820&amp;do=diff">
        <dc:format>text/html</dc:format>
        <dc:date>2021-08-15T11:40:20+0800</dc:date>
        <dc:creator>Anonymous (anonymous@undisclosed.example.com)</dc:creator>
        <title>2020-2021:teams:legal_string:组队训练比赛记录:contest13</title>
        <link>https://wiki.cvbbacm.com/doku.php?id=2020-2021:teams:legal_string:%E7%BB%84%E9%98%9F%E8%AE%AD%E7%BB%83%E6%AF%94%E8%B5%9B%E8%AE%B0%E5%BD%95:contest13&amp;rev=1628998820&amp;do=diff</link>
        <description>比赛链接

补题情况
  题目    蒋贤蒙    王赵安    王智彪    B    0    0    0    C    2    0    1    F    2    0    1    G    0    0    0    H    1    0    2    I    0    0    0    J    2    1    0  
题解

C. Fuzzy Graph

题意

给定一个连通图，要求将图上每个点染成 $\text{RGB}$$(u,v)$$u,v$$u,v$$\text{RGB}$$3\mid n$$\text{X}$$\text{X}$$\text{dfs}$$\text{RG}$$c_0$$\text{R}$$c_1$$\text{G}$$c_0\le \frac n3$$c_1\le \frac n3$$\text{B}$$\text{dfs}$$\text{B}$$c_0\le \frac n3$$G$$R$$G$$\frac n3$$R$$R$$c_0$$R$$\frac n3$$\frac n3$$B$$B$$c_0\ge \frac…</description>
    </item>
    <item rdf:about="https://wiki.cvbbacm.com/doku.php?id=2020-2021:teams:legal_string:%E7%BB%84%E9%98%9F%E8%AE%AD%E7%BB%83%E6%AF%94%E8%B5%9B%E8%AE%B0%E5%BD%95:contest14&amp;rev=1628853188&amp;do=diff">
        <dc:format>text/html</dc:format>
        <dc:date>2021-08-13T19:13:08+0800</dc:date>
        <dc:creator>Anonymous (anonymous@undisclosed.example.com)</dc:creator>
        <title>2020-2021:teams:legal_string:组队训练比赛记录:contest14</title>
        <link>https://wiki.cvbbacm.com/doku.php?id=2020-2021:teams:legal_string:%E7%BB%84%E9%98%9F%E8%AE%AD%E7%BB%83%E6%AF%94%E8%B5%9B%E8%AE%B0%E5%BD%95:contest14&amp;rev=1628853188&amp;do=diff</link>
        <description>比赛链接

补题情况
  题目    蒋贤蒙    王赵安    王智彪    B    0    0    0    C    0    0    0    D    2    0    0    E    0    0    0    G    2    0    0    J    2    0    0    K    0    0    0    M    0    0    0  
题解

D. Dumae

题意
$1\sim n$$i$$p_i$$L_i\le p_i\le R_i$$m$$p_u\lt p_v$$p_u\lt p_v$$u\to v$$u\to v$$L_i$$R_i$$u\to v$$u$$v$$R_u=\min(R_u,R_v-1)$$0$$L_i$$R_u$$O(n\log n+m)$$n$$i$$w_i$$k$$i$$j$$x\le k$$x$$\text{dp}(i,0/1,0/1,k_1,k_2)$$i$$i-1$$i-1,i$$k_1$$k_2$$\text{dp}$$\text{dp}(0,1,0,0,0)=0$$\min_{j_1+j…</description>
    </item>
    <item rdf:about="https://wiki.cvbbacm.com/doku.php?id=2020-2021:teams:legal_string:%E7%BB%84%E9%98%9F%E8%AE%AD%E7%BB%83%E6%AF%94%E8%B5%9B%E8%AE%B0%E5%BD%95:contest15&amp;rev=1630071772&amp;do=diff">
        <dc:format>text/html</dc:format>
        <dc:date>2021-08-27T21:42:52+0800</dc:date>
        <dc:creator>Anonymous (anonymous@undisclosed.example.com)</dc:creator>
        <title>2020-2021:teams:legal_string:组队训练比赛记录:contest15</title>
        <link>https://wiki.cvbbacm.com/doku.php?id=2020-2021:teams:legal_string:%E7%BB%84%E9%98%9F%E8%AE%AD%E7%BB%83%E6%AF%94%E8%B5%9B%E8%AE%B0%E5%BD%95:contest15&amp;rev=1630071772&amp;do=diff</link>
        <description>比赛链接

补题情况
  题目    蒋贤蒙    王赵安    王智彪    A    2    1    0    B    2    1    0    C    2    1    0    D    0    0    0    F    0    0    0    G    2    2    0    I    1    0    2    J    2    0    2  
题解

A. A Math Challenge
$$
\sum_{i=0}^n\sum_{1\le cj\le ai+b}i^pj^q
$$$F(n)=\sum_{i=1}^n i^q$$$
\sum_{i=0}^ni^pF(\lfloor \frac {ai+b}c\rfloor)
$$$F(n)$$q+1$$F(n)$$\sum_{i=0}^ni^p(\lfloor \frac {ai+b}c\rfloor)^k(0\le k\le q)$$O\left(p^2q^2\log c\right)$$O\left((p+q)^3\log c\right)$$k-\text{degree}$$k$…</description>
    </item>
    <item rdf:about="https://wiki.cvbbacm.com/doku.php?id=2020-2021:teams:legal_string:%E7%BB%84%E9%98%9F%E8%AE%AD%E7%BB%83%E6%AF%94%E8%B5%9B%E8%AE%B0%E5%BD%95:contest16&amp;rev=1630111802&amp;do=diff">
        <dc:format>text/html</dc:format>
        <dc:date>2021-08-28T08:50:02+0800</dc:date>
        <dc:creator>Anonymous (anonymous@undisclosed.example.com)</dc:creator>
        <title>2020-2021:teams:legal_string:组队训练比赛记录:contest16</title>
        <link>https://wiki.cvbbacm.com/doku.php?id=2020-2021:teams:legal_string:%E7%BB%84%E9%98%9F%E8%AE%AD%E7%BB%83%E6%AF%94%E8%B5%9B%E8%AE%B0%E5%BD%95:contest16&amp;rev=1630111802&amp;do=diff</link>
        <description>比赛链接

补题情况
  题目    蒋贤蒙    王赵安    王智彪    A    2    2    0    B    0    0    0    C    2    2    0    D    2    1    0    E    0    0    0    G    2    1    0    I    2    1    0    J    2    0    2    K    2    1    0  
题解
$n$$i=1\sim n$$i$$n-i$$32\text{ megabytes}$$i$$n-i$$i$$1$$i=1\sim n$$n-i$$i=n$$O(n)$$2n-1$$1$$n\times 2$$k_i$$k=\max_{i=1}^n k_i$$\text{set}$$O(nk\log n)$$k$$O(km)$$O(m)\sim O(n^2)$$i$$i$$i$$O(m)\sim O(nk)$$O\left(nk^2\right)$$i$$i$$i$$i$$i$$n$$\times 2$$\times 2+1$$f(i,j)$$j$$…</description>
    </item>
    <item rdf:about="https://wiki.cvbbacm.com/doku.php?id=2020-2021:teams:legal_string:%E7%BB%84%E9%98%9F%E8%AE%AD%E7%BB%83%E6%AF%94%E8%B5%9B%E8%AE%B0%E5%BD%95:contest17&amp;rev=1630808458&amp;do=diff">
        <dc:format>text/html</dc:format>
        <dc:date>2021-09-05T10:20:58+0800</dc:date>
        <dc:creator>Anonymous (anonymous@undisclosed.example.com)</dc:creator>
        <title>2020-2021:teams:legal_string:组队训练比赛记录:contest17</title>
        <link>https://wiki.cvbbacm.com/doku.php?id=2020-2021:teams:legal_string:%E7%BB%84%E9%98%9F%E8%AE%AD%E7%BB%83%E6%AF%94%E8%B5%9B%E8%AE%B0%E5%BD%95:contest17&amp;rev=1630808458&amp;do=diff</link>
        <description>比赛链接

补题情况
  题目    蒋贤蒙    王赵安    王智彪    C    0    0    0    D    0    0    0    E    2    2    0    H    2    0    0    J    2    0    0    M    0    0    0  
题解

E. Easy Math Problem

题意

$$
\sum_{i=1}^n\sum_{j=1}^n {i+j\choose j}f(i+j,i)\\
f(i,j)=
\begin{cases}
0, &amp;i=0\\
a, &amp;i=1\\
b\times f(i-1,j)+c\times f(i-2,j), &amp;2\le i\le j\\
d\times f(i-1,j)+e\times f(i-2,j), &amp;i\gt j
\end{cases}
$$

题解

设 

$$
A=\begin{pmatrix}b &amp; 1 \\ c &amp; 0\\ \end{pmatrix},B=\begin{pmatrix}d &amp; 1 \\ e &amp; 0\\ \end{pmatrix}
…</description>
    </item>
    <item rdf:about="https://wiki.cvbbacm.com/doku.php?id=2020-2021:teams:legal_string:%E7%BB%84%E9%98%9F%E8%AE%AD%E7%BB%83%E6%AF%94%E8%B5%9B%E8%AE%B0%E5%BD%95:contest18&amp;rev=1630832142&amp;do=diff">
        <dc:format>text/html</dc:format>
        <dc:date>2021-09-05T16:55:42+0800</dc:date>
        <dc:creator>Anonymous (anonymous@undisclosed.example.com)</dc:creator>
        <title>2020-2021:teams:legal_string:组队训练比赛记录:contest18</title>
        <link>https://wiki.cvbbacm.com/doku.php?id=2020-2021:teams:legal_string:%E7%BB%84%E9%98%9F%E8%AE%AD%E7%BB%83%E6%AF%94%E8%B5%9B%E8%AE%B0%E5%BD%95:contest18&amp;rev=1630832142&amp;do=diff</link>
        <description>比赛链接

补题情况
  题目    蒋贤蒙    王赵安    王智彪    B    0    0    0    F    0    0    0    G    2    0    0    H    0    0    0    L    0    0    0  
题解

G. Ball

题意

给定一个斜坡，有 $n$ 个洞。再给定 $m$ 个球，依次抛球，每次抛球可以决定球的初始下落位置，然后球从斜坡向下运动。$k$$f(i,j)$$i$$j$$g(i,j)$$i$$j$$i$$[i+1,n]$$i$$[1,i-1]$$k$$i-1+k$$$
\text{ans}\gets \sum_{i=1}^{n} g(i-1,i-1+k)f(n-i,m-i-k+1){m\choose i-1+k}
$$$$
\text{ans}\gets [m=n+k]g(n,m)
$$$f(i,j),g(i,j)$$f(i,j)(i\ge j)$$k$$i$$j-k$$f(i-1,j-k)$$k$$j-k$$i-j+k\ge k$$k$$$
f(i,j)=\sum_{k=0}^j f(i-1…</description>
    </item>
    <item rdf:about="https://wiki.cvbbacm.com/doku.php?id=2020-2021:teams:legal_string:%E7%BB%84%E9%98%9F%E8%AE%AD%E7%BB%83%E6%AF%94%E8%B5%9B%E8%AE%B0%E5%BD%95:contest19&amp;rev=1631415214&amp;do=diff">
        <dc:format>text/html</dc:format>
        <dc:date>2021-09-12T10:53:34+0800</dc:date>
        <dc:creator>Anonymous (anonymous@undisclosed.example.com)</dc:creator>
        <title>2020-2021:teams:legal_string:组队训练比赛记录:contest19</title>
        <link>https://wiki.cvbbacm.com/doku.php?id=2020-2021:teams:legal_string:%E7%BB%84%E9%98%9F%E8%AE%AD%E7%BB%83%E6%AF%94%E8%B5%9B%E8%AE%B0%E5%BD%95:contest19&amp;rev=1631415214&amp;do=diff</link>
        <description>比赛链接

补题情况
  题目    蒋贤蒙    王赵安    王智彪    A    2    0    0    D    0    0    0    E    2    0    0    F    0    0    0    J    0    0    0    K    0    0    0  
题解

A. Bags of Candies

题意

多组数据。每组数据给定 $n\le 10^{11}$$1\sim n$$D(n)$$\lfloor \frac n2\rfloor$$\lfloor\frac {n-D(n)-1}2\rfloor$$1$$\lfloor \frac n2\rfloor$$P$$P,2P$$2P$$2$$D(n)$$10^7$$[L,R]$$O(\sqrt n)$$O\left((r-l)\log\log(r-l)\right)$$O(n\log\log n)$$O(10^7\log\log n)$$n$$q$$P(x,y),Q(x,y),y_1,y_2$$P$$Q$$y$$[y_1,y_2]$$P,Q$$P_x\le Q_x$$P$$…</description>
    </item>
    <item rdf:about="https://wiki.cvbbacm.com/doku.php?id=2020-2021:teams:legal_string:%E7%BB%84%E9%98%9F%E8%AE%AD%E7%BB%83%E6%AF%94%E8%B5%9B%E8%AE%B0%E5%BD%95:contest20&amp;rev=1632388622&amp;do=diff">
        <dc:format>text/html</dc:format>
        <dc:date>2021-09-23T17:17:02+0800</dc:date>
        <dc:creator>Anonymous (anonymous@undisclosed.example.com)</dc:creator>
        <title>2020-2021:teams:legal_string:组队训练比赛记录:contest20</title>
        <link>https://wiki.cvbbacm.com/doku.php?id=2020-2021:teams:legal_string:%E7%BB%84%E9%98%9F%E8%AE%AD%E7%BB%83%E6%AF%94%E8%B5%9B%E8%AE%B0%E5%BD%95:contest20&amp;rev=1632388622&amp;do=diff</link>
        <description>比赛链接

补题情况
  题目    蒋贤蒙    王赵安    王智彪    A    0    0    0    B    0    0    0    E    1    0    0    F    0    0    0    H    0    0    0    K    0    0    0    L    0    0    0  
题解

E. Brief Statements Union

题意

给定 $k$$a_l\And a_{l+1}\And a_{l+2}\cdots \And a_r=x$$i$$n$$a$$1$$0$$0$$O(n)$$O(n\log v)$</description>
    </item>
    <item rdf:about="https://wiki.cvbbacm.com/doku.php?id=2020-2021:teams:legal_string:%E7%BB%84%E9%98%9F%E8%AE%AD%E7%BB%83%E6%AF%94%E8%B5%9B%E8%AE%B0%E5%BD%95:contest21&amp;rev=1633338281&amp;do=diff">
        <dc:format>text/html</dc:format>
        <dc:date>2021-10-04T17:04:41+0800</dc:date>
        <dc:creator>Anonymous (anonymous@undisclosed.example.com)</dc:creator>
        <title>2020-2021:teams:legal_string:组队训练比赛记录:contest21</title>
        <link>https://wiki.cvbbacm.com/doku.php?id=2020-2021:teams:legal_string:%E7%BB%84%E9%98%9F%E8%AE%AD%E7%BB%83%E6%AF%94%E8%B5%9B%E8%AE%B0%E5%BD%95:contest21&amp;rev=1633338281&amp;do=diff</link>
        <description>比赛链接

补题情况
  题目    蒋贤蒙    王赵安    王智彪    B    2    0    0    E    0    0    0    F    0    0    0    G    2    0    0    H    2    0    0    K    0    0    0  
题解

B. discount

题意

给定 $n$ 种商品，对于每个商品 $i$$a_i$$j$$b_i$$(b_i\le a_i)$$a_i$$i$$j$$j\to i$$i$$j$$0/1/2$$b_i$$a_i$$0$$2$$\text{dp}(u,0/1/2)$$u$$2$$\text{dp}$$+$$\to$$\text{dp}(u,0/1/2,i)$$u$$u$$0/1/2$$i$$i$$u$$0$$u$$u$$1$$u$$u$$u$$2$$u$$u$$$
\text{dp}(u,0,i+j)\gets \text{dp}(u,0,i)+\text{dp}(v,0,j)\\
\text{dp}(u,1,i+j)\gets \text{dp}(u,0,i)+\…</description>
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    <item rdf:about="https://wiki.cvbbacm.com/doku.php?id=2020-2021:teams:legal_string:%E7%BB%84%E9%98%9F%E8%AE%AD%E7%BB%83%E6%AF%94%E8%B5%9B%E8%AE%B0%E5%BD%95:contest22&amp;rev=1633943313&amp;do=diff">
        <dc:format>text/html</dc:format>
        <dc:date>2021-10-11T17:08:33+0800</dc:date>
        <dc:creator>Anonymous (anonymous@undisclosed.example.com)</dc:creator>
        <title>2020-2021:teams:legal_string:组队训练比赛记录:contest22</title>
        <link>https://wiki.cvbbacm.com/doku.php?id=2020-2021:teams:legal_string:%E7%BB%84%E9%98%9F%E8%AE%AD%E7%BB%83%E6%AF%94%E8%B5%9B%E8%AE%B0%E5%BD%95:contest22&amp;rev=1633943313&amp;do=diff</link>
        <description>比赛链接

补题情况
  题目    蒋贤蒙    王赵安    王智彪    A    0    0    0    C    0    0    0    G    0    0    0    I    2    0    0    L    0    0    0  
题解</description>
    </item>
</rdf:RDF>
