|
| 1 | +# Insert Interval |
| 2 | + |
| 3 | +Page on leetcode: https://leetcode.com/problems/insert-interval/ |
| 4 | + |
| 5 | +## Problem Statement |
| 6 | + |
| 7 | +You are given an array of non-overlapping intervals intervals where intervals[i] = [starti, endi] represent the start and the end of the ith interval and intervals is sorted in ascending order by starti. You are also given an interval newInterval = [start, end] that represents the start and end of another interval. |
| 8 | + |
| 9 | +Insert newInterval into intervals such that intervals is still sorted in ascending order by starti and intervals still does not have any overlapping intervals (merge overlapping intervals if necessary). |
| 10 | + |
| 11 | +Return intervals after the insertion. |
| 12 | + |
| 13 | +### Constraints |
| 14 | + |
| 15 | +- 0 <= intervals.length <= 104 |
| 16 | +- intervals[i].length == 2 |
| 17 | +- 0 <= starti <= endi <= 105 |
| 18 | +- intervals is sorted by starti in ascending order. |
| 19 | +- newInterval.length == 2 |
| 20 | +- 0 <= start <= end <= 105 |
| 21 | + |
| 22 | +### Example |
| 23 | + |
| 24 | +``` |
| 25 | +Input: intervals = [[1,3],[6,9]], newInterval = [2,5] |
| 26 | +Output: [[1,5],[6,9]] |
| 27 | +``` |
| 28 | + |
| 29 | +``` |
| 30 | +Input: intervals = [[1,2],[3,5],[6,7],[8,10],[12,16]], newInterval = [4,8] |
| 31 | +Output: [[1,2],[3,10],[12,16]] |
| 32 | +Explanation: Because the new interval [4,8] overlaps with [3,5],[6,7],[8,10]. |
| 33 | +``` |
| 34 | + |
| 35 | +## Solution |
| 36 | + |
| 37 | +- Need to take care of null case (no intervals provided) |
| 38 | +- Need to find either interval before (if no overlap) or interval with overlap of start interval |
| 39 | +- Check for overlap of end and subsequent intervals |
| 40 | +- Remove intervals that get merged |
| 41 | +- If new interval is entirely contained in single existing interval, return original intervals |
| 42 | +- Can I use two pointers? |
| 43 | + |
| 44 | +### Pseudocode |
| 45 | + |
| 46 | +1. Create two pointers left, right |
| 47 | +2. Iterate thru the array |
| 48 | +3. Check if left pointer[1] is greater than start |
| 49 | +4. right pointer = left point + 1 |
| 50 | +5. Check if right pointer[0] is less than end, if not merge with previous |
| 51 | +6. Check if right pointer[1] is greater than end, if true merge |
| 52 | + |
| 53 | +### Initial Attempt |
| 54 | + |
| 55 | +```javascript |
| 56 | +const insert = function (intervals, newInterval) { |
| 57 | + // No existing intervals |
| 58 | + if (intervals.length === 0) { |
| 59 | + intervals.push(newInterval); |
| 60 | + return intervals; |
| 61 | + } |
| 62 | + |
| 63 | + let l = 0, |
| 64 | + r = 0; |
| 65 | + while (r < intervals.length) { |
| 66 | + r++; |
| 67 | + // New interval completely contained within a single interval |
| 68 | + if (intervals[l][0] <= newInterval[0] && intervals[l][1] >= newInterval[1]) { |
| 69 | + return intervals; |
| 70 | + } |
| 71 | + // New interval start overlaps with existing interval |
| 72 | + if (intervals[l][1] >= newInterval[0]) { |
| 73 | + r--; |
| 74 | + while (r < intervals.length) { |
| 75 | + r++; |
| 76 | + // new interval start overlaps on start, but not end |
| 77 | + if (intervals[r] === undefined || intervals[r][0] > newInterval[1]) { |
| 78 | + const start = intervals[l][0]; |
| 79 | + const end = newInterval[1]; |
| 80 | + intervals.splice(l, r - l, [start, end]); |
| 81 | + return intervals; |
| 82 | + // new interval spans and overlaps 2+ intervals, including start |
| 83 | + } else if (intervals[r][0] <= newInterval[1] && intervals[r][1] > newInterval[1]) { |
| 84 | + const start = intervals[l][0]; |
| 85 | + const end = intervals[r][1]; |
| 86 | + intervals.splice(l, r - l + 1, [start, end]); |
| 87 | + return intervals; |
| 88 | + } |
| 89 | + r++; |
| 90 | + } |
| 91 | + // No overlaps |
| 92 | + } else if (intervals[l][1] < newInterval[0] && intervals[r][0] > newInterval[1]) { |
| 93 | + intervals.splice(l + 1, 0, newInterval); |
| 94 | + return intervals; |
| 95 | + } |
| 96 | + // New interval end overlaps with existing interval |
| 97 | + if (intervals[r][0] <= newInterval[1] && intervals[r][1] > newInterval[1]) { |
| 98 | + const start = newInterval[0]; |
| 99 | + const end = intervals[r][1]; |
| 100 | + intervals.splice(r, 1, [start, end]); |
| 101 | + return intervals; |
| 102 | + } |
| 103 | + l++; |
| 104 | + } |
| 105 | +}; |
| 106 | +``` |
| 107 | + |
| 108 | +### Optimized Solution |
| 109 | + |
| 110 | +This solution has a time and space complexity of O(n). You can see an explanation of the solution here: https://www.youtube.com/watch?v=A8NUOmlwOlM |
| 111 | + |
| 112 | +```javascript |
| 113 | +const insert = function (intervals, newInterval) { |
| 114 | + let result = []; |
| 115 | + for (let i = 0; i < intervals.length; i++) { |
| 116 | + // Check if new interval is before element without overlap |
| 117 | + if (intervals[i][0] > newInterval[1]) { |
| 118 | + result.push(newInterval); |
| 119 | + return result.concat(intervals.slice(i)); |
| 120 | + // Check if new interval is after element without overlap |
| 121 | + } else if (intervals[i][1] < newInterval[0]) { |
| 122 | + result.push(intervals[i]); |
| 123 | + // Update new interval based on min and max values of overlapping intervals |
| 124 | + } else { |
| 125 | + newInterval[0] = Math.min(intervals[i][0], newInterval[0]); |
| 126 | + newInterval[1] = Math.max(intervals[i][1], newInterval[1]); |
| 127 | + } |
| 128 | + } |
| 129 | + // Need to add new interval to result if the above return never fired. This accounts for cases where new interval is at the end or overlaps with the end element. |
| 130 | + result.push(newInterval); |
| 131 | + return result; |
| 132 | +}; |
| 133 | +``` |
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