docs(content): add Insert Interval page, expand intervals guide, and update array badge

apps/docs/content/(05-decision-space)/intervals/57-insert-interval.mdx

@@ -0,0 +1,56 @@
+---
+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" }
+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
+```