USACO

USACO 2015 December Contest, Platinum

Problem 1. Max Flow

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Farmer John has installed a new system of

$N-1$ pipes to transport milk between the

$N$ stalls in his barn (

$2 \leq N \leq 50,000$ ), conveniently numbered

$1 \ldots N$ . Each pipe connects a pair of stalls, and all stalls are connected to each-other via paths of pipes.

FJ is pumping milk between $K$ pairs of stalls ( $1 \leq K \leq 100,000$ ). For the $i$ th such pair, you are told two stalls $s_i$ and $t_i$ , endpoints of a path along which milk is being pumped at a unit rate. FJ is concerned that some stalls might end up overwhelmed with all the milk being pumped through them, since a stall can serve as a waypoint along many of the $K$ paths along which milk is being pumped. Please help him determine the maximum amount of milk being pumped through any stall. If milk is being pumped along a path from $s_i$ to $t_i$ , then it counts as being pumped through the endpoint stalls $s_i$ and $t_i$ , as well as through every stall along the path between them.

INPUT FORMAT (file maxflow.in):

The first line of the input contains

$N$ and

$K$ .

The next $N-1$ lines each contain two integers $x$ and $y$ ( $x \ne y$ ) describing a pipe between stalls $x$ and $y$ .

The next $K$ lines each contain two integers $s$ and $t$ describing the endpoint stalls of a path through which milk is being pumped.

OUTPUT FORMAT (file maxflow.out):

An integer specifying the maximum amount of milk pumped through any stall in the barn.

SAMPLE INPUT:

SAMPLE OUTPUT:

Problem credits: Brian Dean

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