feat: refactored docs structure

docs/(05-decision-space)/intervals/(problems)/435_non-overlapping-intervals.mdx

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+---
+title: '435. Non-overlapping Intervals'
+description: Given an array of intervals intervals where intervals[i] = [starti, endi], return the minimum number of intervals you need to remove to make the rest of the intervals non-overlapping
+icon: dot
+topics:
+  - { name: "Array", slug: "array" }
+  - { name: "Dynamic Programming", slug: "dynamic-programming" }
+  - { name: "Greedy", slug: "greedy" }
+  - { name: "Sorting", slug: "sorting" }
+issue: "https://github.com/prdlk/leetcode/issues/183"
+sidebar:
+  label: 'Non-overlapping Intervals'
+  badge: 'Medium'
+---
+
+### Example 1:
+- Input: `intervals = [[1,2],[2,3],[3,4],[1,3]]`
+- Output: `1`
+- Explanation: `[1,3]` can be removed and the rest of the `intervals` are non-overlapping.
+
+### Example 2:
+- Input: `intervals = [[1,2],[1,2],[1,2]]`
+- Output: `2`
+- Explanation: You need to remove two `[1,2]` to make the rest of the `intervals` non-overlapping.
+
+### Example 3:
+- Input: `intervals = [[1,2],[2,3]]`
+- Output: `0`
+- Explanation: You don't need to remove any of the `intervals` since they're already non-overlapping.
+
+### Constraints:
+
+- `1 <= intervals.length <= 10^5`
+- `intervals[i].length == 2`
+- `-5 * 10^4 <= starti < endi <= 5 * 10^4`
+
+## Solution
+
+```py
+class Solution:
+    def eraseOverlapIntervals(self, intervals: list[list[int]]) -> int:
+        intervals.sort(key=lambda x: x[0])
+        result = []
+
+        for start, end in intervals:
+            # Use '<' to avoid intervals which touch
+            if result and start < result[-1][1]:
+                result[-1][1] = min(result[-1][1], end)
+            else:
+                result.append([start, end])
+
+        # Difference between original and result is to remove
+        return len(intervals) - len(result)
+```

docs/(05-decision-space)/intervals/(problems)/56_merge-intervals.mdx

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+---
+title: '56. Merge Intervals'
+description: Given an array of intervals where intervals[i] = [starti, endi], merge all overlapping intervals, and return an array of the non-overlapping intervals that cover all the intervals in the input
+icon: dot
+topics:
+  - { name: "Array", slug: "array" }
+  - { name: "Sorting", slug: "sorting" }
+  - { name: "Quicksort", slug: "quicksort" }
+issue: "https://github.com/prdlk/leetcode/issues/182"
+sidebar:
+  label: 'Merge Intervals'
+  badge: 'Medium'
+---
+
+### Example 1:
+- Input: `intervals = [[1,3],[2,6],[8,10],[15,18]]`
+- Output: `[[1,6],[8,10],[15,18]]`
+- Explanation: Since `intervals [1,3]` and `[2,6]` overlap, merge them into `[1,6]`.
+
+### Example 2:
+- Input: `intervals = [[1,4],[4,5]]`
+- Output: `[[1,5]]`
+- Explanation: Intervals `[1,4]` and `[4,5]` are considered overlapping.
+
+### Example 3:
+- Input: `intervals = [[4,7],[1,4]]`
+- Output: `[[1,7]]`
+- Explanation: Intervals `[1,4]` and `[4,7]` are considered overlapping.
+
+### Constraints:
+
+- `1 <= intervals.length <= 10^4`
+- `intervals[i].length == 2`
+- `0 <= starti <= endi <= 10^4`
+
+## Solution
+
+```py
+class Solution:
+    def merge(self, intervals: list[list[int]]) -> list[list[int]]:
+        intervals.sort(key=lambda x: x[0])
+        result = []
+
+        for start, end in intervals:
+            if result and start <= result[-1][1]:
+                result[-1][1] = max(result[-1][1], end)
+            else:
+                result.append([start, end])
+
+        return result
+```

docs/(05-decision-space)/intervals/(problems)/57_insert-interval.mdx

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+---
+title: '57. Insert Interval'
+description: You are given an array of non-overlapping intervals intervals where intervals[i] = [starti, endi] represent the start and the end of the i^th 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
+icon: dot
+topics:
+  - { name: "Array", slug: "array" }
+issue: "https://github.com/prdlk/leetcode/issues/181"
+sidebar:
+  label: 'Insert Interval'
+  badge: 'Medium'
+---
+
+### 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 <= starti <= endi <= 10^5`
+- intervals is sorted by starti in ascending order.
+- `newInterval.length == 2`
+- `0 <= start <= end <= 10^5`
+
+## Solution
+
+```py
+class Solution:
+    def insert(
+        self, intervals: list[list[int]], newInterval: list[int]
+    ) -> list[list[int]]:
+        result = []
+        i, n = 0, len(intervals)
+        start, end = newInterval
+
+        # Everything before
+        while i < n and intervals[i][1] < start:
+            result.append(intervals[i])
+            i += 1
+
+        # Everything merged
+        while i < n and intervals[i][0] <= end:
+            start = min(start, intervals[i][0])
+            end = max(end, intervals[i][1])
+            i += 1
+        result.append([start, end])
+
+        # Everything after
+        result.extend(intervals[i:])
+        return result
+```