From 747ecc12fd7b4671472badc4c36cd01e6ee27f6e Mon Sep 17 00:00:00 2001 From: Lusina <12752833+BrianLusina@users.noreply.github.com> Date: Mon, 5 Jan 2026 15:02:00 +0300 Subject: [PATCH 1/3] doc(algorithms, intervals): insert interval solution write up --- .../intervals/insert_interval/README.md | 51 ++++++++++++++++++ .../solutions/insert_interval_solution_1.png | Bin 0 -> 52437 bytes .../solutions/insert_interval_solution_10.png | Bin 0 -> 52712 bytes .../solutions/insert_interval_solution_2.png | Bin 0 -> 66479 bytes .../solutions/insert_interval_solution_3.png | Bin 0 -> 66817 bytes .../solutions/insert_interval_solution_4.png | Bin 0 -> 66113 bytes .../solutions/insert_interval_solution_5.png | Bin 0 -> 66344 bytes .../solutions/insert_interval_solution_6.png | Bin 0 -> 66885 bytes .../solutions/insert_interval_solution_7.png | Bin 0 -> 71748 bytes .../solutions/insert_interval_solution_8.png | Bin 0 -> 64747 bytes .../solutions/insert_interval_solution_9.png | Bin 0 -> 73895 bytes 11 files changed, 51 insertions(+) create mode 100644 algorithms/intervals/insert_interval/images/solutions/insert_interval_solution_1.png create mode 100644 algorithms/intervals/insert_interval/images/solutions/insert_interval_solution_10.png create mode 100644 algorithms/intervals/insert_interval/images/solutions/insert_interval_solution_2.png create mode 100644 algorithms/intervals/insert_interval/images/solutions/insert_interval_solution_3.png create mode 100644 algorithms/intervals/insert_interval/images/solutions/insert_interval_solution_4.png create mode 100644 algorithms/intervals/insert_interval/images/solutions/insert_interval_solution_5.png create mode 100644 algorithms/intervals/insert_interval/images/solutions/insert_interval_solution_6.png create mode 100644 algorithms/intervals/insert_interval/images/solutions/insert_interval_solution_7.png create mode 100644 algorithms/intervals/insert_interval/images/solutions/insert_interval_solution_8.png create mode 100644 algorithms/intervals/insert_interval/images/solutions/insert_interval_solution_9.png diff --git a/algorithms/intervals/insert_interval/README.md b/algorithms/intervals/insert_interval/README.md index c6e3e5b0..2694b935 100644 --- a/algorithms/intervals/insert_interval/README.md +++ b/algorithms/intervals/insert_interval/README.md @@ -22,3 +22,54 @@ Return the updated list of intervals. ![Example 1](./images/examples/insert_interval_example_1.png) ![Example 2](./images/examples/insert_interval_example_2.png) + +## Solution + +We first want to create a new list merged to store the merged intervals we will return at the end. + +This solution operates in 3 phases: +1. Add all the intervals ending before newInterval starts to merged. +2. Merge all overlapping intervals with newInterval and add that merged interval to merged. +3. Add all the intervals starting after newInterval to merged. + +### Phase 1 + +In this phase, we add all the intervals that end before newInterval starts to merged. This involves iterating through the +intervals list until the current interval no longer ends before newInterval starts (i.e. intervals[i][1] >= newInterval[0]). + +![Solution 1](./images/solutions/insert_interval_solution_1.png) +![Solution 2](./images/solutions/insert_interval_solution_2.png) + +### Phase 2 + +In this phase, we merge all the intervals that overlap with newInterval together into a single interval by updating +newInterval to be the minimum start and maximum end of all the overlapping intervals. This involves iterating through +the intervals list until the current interval starts after newInterval ends (i.e. intervals[i][0] > newInterval[1]). +When that condition is met, we add newInterval to merged and move onto phase 3. + +![Solution 3](./images/solutions/insert_interval_solution_3.png) +![Solution 4](./images/solutions/insert_interval_solution_4.png) +![Solution 5](./images/solutions/insert_interval_solution_5.png) +![Solution 6](./images/solutions/insert_interval_solution_6.png) +![Solution 7](./images/solutions/insert_interval_solution_7.png) + +### Phase 3 + +Phase 3 involves adding all the intervals starting after newInterval to merged. This involves iterating through the +intervals list until the end of the list, and adding each interval to merged. + +After completing these 3 phases, we return merged as the final result. + +![Solution 8](./images/solutions/insert_interval_solution_8.png) +![Solution 9](./images/solutions/insert_interval_solution_9.png) +![Solution 10](./images/solutions/insert_interval_solution_10.png) + +### Complexity Analysis + +#### Time Complexity + +O(n) where n is the number of intervals. We iterate through all intervals once to merge them. + +#### Space Complexity + +O(n) where n is the number of intervals. 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