Add 'Merge Intervals'

Author: nickolashkraus

README.md

@@ -60,6 +60,8 @@ A collection of LeetCode solutions
 
 [Maximum Subarray](./src/maximum_subarray.py)
 
+[Merge Intervals](./src/merge_intervals.py)
+
 [Merge k Sorted Lists](./src/merge_k_sorted_lists.py)
 
 [Merge Sorted Array](./src/merge_sorted_array.py)

src/merge_intervals.py

@@ -0,0 +1,58 @@
+"""
+56. Merge Intervals
+
+https://leetcode.com/problems/merge-intervals
+
+NOTES
+  * A common routine for interval problems is to sort the array of intervals
+    by each interval's starting index.
+"""
+
+
+class Solution:
+    def merge(self, intervals: list[list[int]]) -> list[list[int]]:
+        if not intervals:
+            return []
+        sorted_intervals = sorted(intervals)
+        ans: list[list[int]] = [sorted_intervals[0]]
+        # p1 is a pointer into ans. p2 is a pointer into sorted_intervals.
+        p1, p2 = 0, 1
+        while p2 < len(sorted_intervals):
+            if overlap(ans[p1], sorted_intervals[p2]):
+                ans[p1] = merge(ans[p1], sorted_intervals[p2])
+            else:
+                ans.append(sorted_intervals[p2])
+                p1 += 1
+            p2 += 1
+        return ans
+
+
+def overlap(a: list[int], b: list[int]) -> bool:
+    """
+    Returns True if `a` and `b` overlap, otherwise returns False.
+    """
+    return a[0] <= b[1] and b[0] <= a[1]
+
+
+def merge(a: list[int], b: list[int]) -> list[int]:
+    """
+    Merges two intervals (`a` and `b`).
+    """
+    return [min(a[0], b[0]), max(a[1], b[1])]
+
+
+class OptimizedSolution:
+    """
+    Since the intervals are already sorted, we only need to check if the end
+    index of the last interval is greater than or equal to the start index of
+    the current interval.
+    """
+    def merge(self, intervals: list[list[int]]) -> list[list[int]]:
+        intervals.sort(key=lambda x: x[0])
+        merged: list[list[int]] = []
+        for interval in intervals:
+            if not merged or merged[-1][1] < interval[0]:
+                merged.append(interval)
+            else:
+                merged[-1][1] = max(merged[-1][1], interval[1])
+        return merged

tests/test_merge_intervals.py

@@ -0,0 +1,28 @@
+"""
+56. Merge Intervals
+
+https://leetcode.com/problems/merge-intervals
+"""
+from unittest import TestCase
+
+from src.merge_intervals import Solution, OptimizedSolution
+
+
+class TestSolution(TestCase):
+    def test_1(self):
+        exp = [[1, 6], [8, 10], [15, 18]]
+        assert Solution().merge([[1, 3], [2, 6], [8, 10], [15, 18]]) == exp
+
+    def test_2(self):
+        exp = [[1, 5]]
+        assert Solution().merge([[1, 4], [4, 5]]) == exp
+
+
+class TestOptimizedSolution(TestCase):
+    def test_1(self):
+        exp = [[1, 6], [8, 10], [15, 18]]
+        assert OptimizedSolution().merge([[1, 3], [2, 6], [8, 10], [15, 18]]) == exp
+
+    def test_2(self):
+        exp = [[1, 5]]
+        assert OptimizedSolution().merge([[1, 4], [4, 5]]) == exp