An Old Stone Game
Time Limit: 2 Seconds
Memory Limit: 65536 KB
There is an old stone game, played on an arbitrary general tree T. The goal
is to put one stone on the root of T observing the following rules:
1. At the beginning of the game, the player picks K stones and puts them all
in one bucket.
2. At each step of the game, the player can pick one stone from the bucket and
put it on any empty leaf.
3. When all of the r immediate children of a node p each has one stone, the
player may remove all of these r stones, and put one of the stones on p. The
other r -1 stones are put back into the bucket, and can be used in the later
steps of the game.
The player wins the game if by following the above rules, he succeeds to put
one stone on the root of the tree.
You are to write a program to determine the least number of stones to be picked
at the beginning of the game (K), so that the player can win the game on the
given input tree.
The input file describes several trees. The first line of this file is M, the
number of trees (1 <= M <= 10). Description of these M trees comes next
in the file. Each tree has N < 200 nodes, labeled 1, 2, ... N, and each node
can have any possible number of children. Root has label 1. Description of each
tree starts with N in a separate line. The following N lines describe the children
of all nodes in order of their labels. Each line starts with a number p (1 <=
p <= N, the label of one of the nodes), r the number of the immediate children
of p, and then the labels of these r children.
One line for each input tree showing the minimum number of stones to be picked
in step 1 above, in order to win the game on that input tree.
1 2 2 3
2 2 5 4
3 2 6 7
1 3 2 3 4
3 2 5 6
4 3 7 8 9
5 3 10 11 12
Source: Asia 1999, Tehran (Iran)