57. Insert Interval.cpp

[ajithh404]

PR Title Format: 57.Insert Interval.cpp

Intuition

The key idea is to simplify the insert interval problem by converting it into a standard merge intervals problem.
Instead of figuring out where the new interval fits manually, we can:

1. Add the new interval to the list.
2. Sort all intervals by their start times.
3. Merge overlapping intervals in a single pass.

This ensures all possible overlaps (including those created by the new interval) are correctly merged without needing separate insertion logic.

Approach

1. Append the new interval:
   Add newInterval to the list of existing intervals.

2. Sort the intervals:
   Sort all intervals based on their starting points. This step ensures the merging process works linearly in one pass.

3. Merge overlapping intervals:

   • Initialize a result vector ans with the first interval.
   • Iterate through the sorted intervals from the second one onward:
     • If the current interval’s start is after the end of the last merged interval, there’s no overlap, so add it directly to ans.
     • If there is overlap, merge them by updating the end of the last interval in ans with the maximum of both end times.

4. Return the merged list:
   After processing all intervals, ans will contain the correct set of non-overlapping intervals.

Time Complexity:

• Sorting: (O(n \log n))
• Merging: (O(n))
• Total: (O(n \log n))

Space Complexity:

• (O(n)) for the merged output list.

---

Code Solution (C++)

    class Solution {
public:
    vector<vector<int>> insert(vector<vector<int>>& intervals, vector<int>& newInterval) {
        intervals.emplace_back(newInterval);
        return merge(intervals);
    }

    vector<vector<int>> merge(vector<vector<int>>& intervals) {
        sort(intervals.begin(), intervals.end());
        vector<vector<int>> ans;
        ans.emplace_back(intervals[0]);

        for (int i = 1; i < intervals.size(); ++i) {
            if (ans.back()[1] < intervals[i][0]) {
                ans.emplace_back(intervals[i]);
            } else {
                ans.back()[1] = max(ans.back()[1], intervals[i][1]);
            }
        }
        return ans;
    }
};
    

Related Issues

Closes #264

By submitting this PR, I confirm that:

• [✅] This is my original work not totally AI generated
• [✅] I have tested the solution thoroughly on leetcode
• [✅] I have maintained proper PR description format
• [✅] This is a meaningful contribution, not spam

Summary by Sourcery

New Features:

• Add C++ solution for Leetcode 57 that appends the new interval, sorts intervals, and merges overlaps

[sourcery-ai]

Reviewer's Guide

Adds a C++ solution for LeetCode problem 57 by converting the insert-interval task into a standard merge-intervals workflow: appending the new interval, sorting all intervals, and merging overlaps in a single pass.

Class diagram for the new Solution class (Insert Interval)

classDiagram
class Solution {
  +vector<vector<int>> insert(vector<vector<int>>& intervals, vector<int>& newInterval)
  +vector<vector<int>> merge(vector<vector<int>>& intervals)
}

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Flow diagram for the Insert Interval algorithm

flowchart TD
    A["Start with intervals and newInterval"] --> B["Append newInterval to intervals"]
    B --> C["Sort intervals by start time"]
    C --> D["Initialize ans with first interval"]
    D --> E["Iterate through intervals (from second)"]
    E --> F{Is current interval overlapping with last in ans?}
    F -- No --> G["Add current interval to ans"]
    F -- Yes --> H["Merge: update end of last interval in ans"]
    G --> I["Continue iteration"]
    H --> I
    I --> J["Return ans (merged intervals)"]

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File-Level Changes

Change	Details	Files
Implement Insert Interval solution using merge-interval strategy	Append new interval in insert() and delegate to merge() Sort intervals by start time Merge overlapping intervals in one pass and return result	57. Insert Interval.cpp

Assessment against linked issues

Issue	Objective	Addressed	Explanation
#264	Implement a working C++ solution for LeetCode Problem 57: Insert Interval.	✅
#264	Ensure the filename follows the convention '[Number]. [Problem Title].cpp'.	✅
#264	Include the approach and intuition in the PR description/documentation.	✅

Possibly linked issues

• Diagonal_Traverse.cpp added #57: The PR provides the C++ solution for the Insert Interval problem, which is exactly what issue 57 describes, with identical approach and code.

---

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[ajithh404]

hello again @SjxSubham, i've raised the issue and made the pr, pls review and merge it, don't forget to assign the hacktoberfest-accepted label!! thank you..

[github-actions]

🎉 Congrats on getting your PR merged in, @ajithh404! 🙌🏼

Thanks for your contribution every effort helps improve the project.

Looking forward to seeing more from you! 🥳✨