문제
The infinite spiral starts at the top-left cell. The first four rows and columns are shown below. Continue the same pattern in expanding square layers. Coordinates start at 1.
1 2 9 10
4 3 8 11
5 6 7 12
16 15 14 13Return one cell value without constructing the entire grid.
Implement number_spiral(row, column).
Input
row: The row counted from the top, starting at 1.
column: The column counted from the left, starting at 1.
Output
Return the number at that position.
제약 조건
1 ≤ row, column ≤ 1,000,000,000. The value fits a signed 64-bit integer.
예시
입력:
row = 3
column = 2
예상 출력:
expected = 6입력:
long long row = 3;
long long column = 2;
예상 출력:
long long expected = 6;입력:
long row = 3;
long column = 2;
예상 출력:
long expected = 6;설명
In the displayed third row, the second value is 6.
입력:
row = 1
column = 4
예상 출력:
expected = 10입력:
long long row = 1;
long long column = 4;
예상 출력:
long long expected = 10;입력:
long row = 1;
long column = 4;
예상 출력:
long expected = 10;설명
The fourth square layer begins at 10 in the top row.
접근 방법
먼저 스스로 풀어 본 뒤 힌트를 하나씩 열어 보세요.
힌트 1
The spiral is built in square layers, so a cell belongs to a layer determined by the larger coordinate.
힌트 2
Use the parity of that layer to decide whether values increase along a row or a column.
힌트 3
Pay attention to whether the layer reaches from the top-left corner or the opposite corner first.
예상 복잡도
O(1) time, O(1) extra space
참고 자료
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