## USACO 2011 December Contest, Gold Division

## Problem 1. Cow Photography

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**Not submitted**

Problem 1: Cow Photography [Brian Dean, 2011]
The cows are in a particularly mischievous mood today! All Farmer John
wants to do is take a photograph of the cows standing in a line, but they
keep moving right before he has a chance to snap the picture.
Specifically, each of FJ's N (1 <= N <= 20,000) cows has a unique
integer ID number. FJ wants to take a picture of the cows standing in
a line in a very specific ordering, represented by the contents of an
array A[1...N], where A[j] gives the ID number of the jth cow in the
ordering. He arranges the cows in this order, but just before he can
press the button on his camera to snap the picture, a group of zero or
more cows (not necessarily a contiguous group) moves to a set of new
positions in the lineup. More precisely, a group of zero or more cows
steps away from the line, with the remaining cows shifting over to
close the resulting gaps in the lineup. The cows who stepped away
then re-insert themselves at different positions in the lineup (not
necessarily at the locations they originally occupied). Frustrated
but not deterred, FJ again arranges his cows according to the ordering
in A, but again, right before he can snap a picture, a different group
of zero or more cows moves to a set of new positions in the lineup.
The process above repeats for a total of five photographs before FJ gives
up. Given the contents of each photograph, see if you can reconstruct the
original intended ordering A. Each photograph shows an ordering of the
cows that differs from A in that some group of zero or more cows has moved.
However, a cow only moves in at most one photograph: if a cow is part of
the group that moves in one photograph, she will not actively move in any
of the other four photographs (although she could end up at a different
index as a consequence of other cows around her moving, of course).
PROBLEM NAME: photo
INPUT FORMAT:
* Line 1: The number of cows, N (1 <= N <= 20,000).
* Lines 2..5N+1: The next 5N lines describe five orderings, each one a
block of N contiguous lines. Each line contains the ID of a
cow, an integer in the range 0...1,000,000,000.
SAMPLE INPUT (file photo.in):
5
10
20
30
40
50
20
10
30
40
50
30
10
20
40
50
40
10
20
30
50
50
10
20
30
40
INPUT DETAILS:
There are 5 cows, with IDs 10, 20, 30, 40, and 50. In each of the 5
photos, a different cow moves to the front of the line (at most one cow
moves in each photo here, but it is possible in other inputs that multiple
cows could move in a particular photo).
OUTPUT FORMAT:
* Lines 1..N: The intended ordering A, one ID per line.
SAMPLE OUTPUT (file photo.out):
10
20
30
40
50
OUTPUT DETAILS:
The correct original ordering A[1..5] is 10, 20, 30, 40, 50.

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