문제
번역본 보기For each board size k from 1 through n, count unordered pairs of distinct squares on a k by k board where two knights cannot attack each other. A knight moves two squares in one axis and one in the other.
. x . x .
x . . . x
. . K . .
x . . . x
. x . x .K marks a knight and x its possible destinations, when those squares lie on the board. Swapping the two knights does not create another placement.
Implement two_knights(n).
Input
n: The largest board size to consider.
Output
Return n counts in order, for board sizes 1 through n.
제약 조건
1 ≤ n ≤ 10,000. Counts fit signed 64-bit integers.
예시
입력:
n = 3
예상 출력:
expected = [0, 6, 28]입력:
long long n = 3;
예상 출력:
std::vector<long long> expected = {0, 6, 28};입력:
long n = 3;
예상 출력:
long[] expected = new long[] {0, 6, 28};설명
A 1 × 1 board cannot hold two knights. A 2 × 2 board has six pairs and no attacks. A 3 × 3 board has 36 pairs, of which eight attack, leaving 28.
입력:
n = 1
예상 출력:
expected = [0]입력:
long long n = 1;
예상 출력:
std::vector<long long> expected = {0};입력:
long n = 1;
예상 출력:
long[] expected = new long[] {0};설명
Two distinct squares are required, but the board has only one.
참고 자료
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