시간 제한 | 메모리 제한 | 제출 | 정답 | 맞힌 사람 | 정답 비율 |
---|---|---|---|---|---|
20 초 (추가 시간 없음) | 1024 MB | 0 | 0 | 0 | 0.000% |
Indicium means "trace" in Latin. In this problem we work with Latin squares and matrix traces.
A Latin square is an N-by-N square matrix in which each cell contains one of N different values, such that no value is repeated within a row or a column. In this problem, we will deal only with "natural Latin squares" in which the N values are the integers between 1 and N.
The trace of a square matrix is the sum of the values on the main diagonal (which runs from the upper left to the lower right).
Given values N and K, produce any N-by-N "natural Latin square" with trace K, or say it is impossible. For example, here are two possible answers for N = 3, K = 6. In each case, the values that contribute to the trace are underlined.
2 1 3 3 1 2
3 2 1 1 2 3
1 3 2 2 3 1
The first line of the input gives the number of test cases, T. T test cases follow. Each consists of one line containing two integers N and K: the desired size of the matrix and the desired trace.
For each test case, output one line containing Case #x: y
, where x
is the test case number (starting from 1) and y
is IMPOSSIBLE
if there is no answer for the given parameters or POSSIBLE
otherwise. In the latter case, output N more lines of N integers each, representing a valid "natural Latin square" with a trace of K, as described above.
2 3 6 2 3
Case #1: POSSIBLE 2 1 3 3 2 1 1 3 2 Case #2: IMPOSSIBLE
Sample Case #1 is the one described in the problem statement.
Sample Case #2 has no answer. The only possible 2-by-2 "natural Latin squares" are as follows:
1 2 2 1
2 1 1 2
These have traces of 2 and 4, respectively. There is no way to get a trace of 3.
Contest > Google > Code Jam > Google Code Jam 2020 > Qualification Round E번