問題
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.
制約
1 ≤ row, column ≤ 1,000,000,000. The value fits a signed 64-bit integer.
例
入力：
row = 3
column = 2
期待される出力：
expected = 6入力：
long long row = 3;
long long column = 2;
期待される出力：
long long expected = 6;入力：
long row = 3;
long column = 2;
期待される出力：
long expected = 6;解説
In the displayed third row, the second value is 6.
入力：
row = 1
column = 4
期待される出力：
expected = 10入力：
long long row = 1;
long long column = 4;
期待される出力：
long long expected = 10;入力：
long row = 1;
long column = 4;
期待される出力：
long expected = 10;解説
The fourth square layer begins at 10 in the top row.
解き方のヒント
まずは自分で考えてから、ヒントを 1 つずつ開いてみましょう。
ヒント 1
The spiral is built in square layers, so a cell belongs to a layer determined by the larger coordinate.
ヒント 2
Use the parity of that layer to decide whether values increase along a row or a column.
ヒント 3
Pay attention to whether the layer reaches from the top-left corner or the opposite corner first.
目安の計算量
O(1) time, O(1) extra space
参考資料
この課題はCodeUtility用に調整されています。上記の説明と制約に従ってください。