S2. Sunflowers
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Barbara plants \(N\) different
sunflowers, each with a unique height, ordered from smallest to largest,
and records their heights for \(N\)
consecutive days. Each day, all of her flowers grow taller than they
were the day before.
She records each of these measurements in a table, with one row for
each plant, with the first row recording the shortest sunflower’s growth
and the last row recording the tallest sunflower’s growth. The leftmost
column is the first measurement for each sunflower, and the rightmost
column is the last measurement for each sunflower.
If a sunflower was smaller than another when initially planted, it
remains smaller for every measurement.
Unfortunately, her children may have altered her measurements by
rotating her table by a multiple of 90 degrees.
Your job is to help Barbara determine her original data.
\((2 \leq N \leq 100)\)
The first line of input contains the number \(N\) \((2 \leq N \leq 100)\). The next \(N\)
lines each contain \(N\) positive
integers, each of which is at most \(10^9\). It is guaranteed that the input
grid represents a rotated version of Barbara’s grid.
Output Barbara’s original data, consisting of \(N\) lines, each of which contain \(N\) positive integers.
2
1 3
2 91 3
2 9The data has been rotated a multiple of 360 degrees, meaning that the
input arrangement is the original arrangement.
3
4 3 1
6 5 2
9 7 31 2 3
3 5 7
4 6 9The original data was rotated 90 degrees to the right/clockwise.
3
3 7 9
2 5 6
1 3 41 2 3
3 5 7
4 6 9The original data was rotated 90 degrees to the
left/counter-clockwise.
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S2. Sunflowers
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S2. Sunflowers