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57. Insert Interval

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Insert Interval

題目連結

題目描述

原文:

You are given an array of non-overlapping intervals intervals where intervals[i] = [start_i, end_i] represent the start and the end of the ith interval and intervals is sorted in ascending order by start_i. You are also given an interval newInterval = [start, end] that represents the start and end of another interval.

Insert newInterval into intervals such that intervals is still sorted in ascending order by start_i and intervals still does not have any overlapping intervals (merge overlapping intervals if necessary).

Return intervals after the insertion.


GPT 4 翻譯:

你給定了一個非重疊區間數組 intervals,其中 intervals[i] = [start_i, end_i] 代表第 i 個區間的開始和結束,且 intervalsstart_i 升序排序。你還給定了一個區間 newInterval = [start, end],代表另一個區間的開始和結束。

newInterval 插入到 intervals 中,使得 intervals 仍按 start_i 升序排序,且 intervals 仍然沒有任何重疊的區間(必要時合併重疊的區間)。

返回插入後的 intervals


Example 1

Input: intervals = [[1,3],[6,9]], newInterval = [2,5]
Output: [[1,5],[6,9]]

Example 2

Input: intervals = [[1,2],[3,5],[6,7],[8,10],[12,16]], newInterval = [4,8]
Output: [[1,2],[3,10],[12,16]]
Explanation: Because the new interval [4,8] overlaps with [3,5],[6,7],[8,10].

Constraints:

  • 0 <= intervals.length <= 10^4
  • intervals[i].length == 2
  • 0 <= start_i <= end_i <= 10^5
  • intervals is sorted by start_i in ascending order.
  • newInterval.length == 2
  • 0 <= start <= end <= 10^5

思路:

如果還沒做過 56. Merge Intervals 建議可以先去做,這題只差了一點點,插在原先就已經排序好了,今天要把新的區間插入並重新合併他。

最簡單的做法,就是用 O(N) 的時間,把新的區間放進去,在用 O(N) 的時間一一合併,這樣就和 56 題一樣了,但這樣做有什麼問題呢?就是當把新區間插入陣列時,首先陣列在操作插入時需要 O(N) 的時間,而且在不同程式語言下,要插入元素可能會造成不同的空間複雜度影響,可能會需要開一個新的陣列,並把舊的元素複製過去,導致空間複雜度上升。

比較好得作法是,其實 newInterval 不需要真的插入進去,而是那他跟原本的陣列不斷地比較,判斷他會影響、重疊的區間做處理即可。

複雜度:

  • 時間複雜度:O(N)
  • 空間複雜度:O(1)