add solution: insert-interval

Author: dusunax

insert-interval/dusunax.py

@@ -0,0 +1,38 @@
+'''
+# 57. Insert Interval
+
+use binary search to find the index of the new interval.(bisect_left)
+insert the new interval into the list.
+iterate through the list and merge the intervals.
+
+=> insert first, merge later
+
+## Time and Space Complexity
+
+```
+TC: O(n)
+SC: O(n)
+```
+
+#### TC is O(n):
+- do binary search to find correct index of the new interval. = O(log n)
+- inserting the new interval into the list. = O(n)
+- iterating through the list to merge the intervals. = O(n)
+
+#### SC is O(n):
+- using a list to store the intervals. = O(n)
+'''
+class Solution:
+    def insert(self, intervals: List[List[int]], newInterval: List[int]) -> List[List[int]]:
+        start_idx = bisect_left([interval[0] for interval in intervals], newInterval[0]) # TC: O(log n)
+        
+        intervals.insert(start_idx, newInterval) # TC: O(n)
+
+        result = []  # SC: O(n)
+        for interval in intervals: # TC: O(n)
+            if not result or result[-1][1] < interval[0]:
+                result.append(interval)
+            else:
+                result[-1][1] = max(result[-1][1], interval[1])
+            
+        return result