From e96b4a30e86b67a34b030bc78603ea4f28265357 Mon Sep 17 00:00:00 2001
From: obelisk0114 <obelisk0114@gmail.com>
Date: Wed, 26 Jun 2019 14:15:17 -0700
Subject: [PATCH 1/4] Update Bucket Sort time complexity analysis

---
 sorts/bucket_sort.py | 7 ++++++-
 1 file changed, 6 insertions(+), 1 deletion(-)

diff --git a/sorts/bucket_sort.py b/sorts/bucket_sort.py
index c4d61874fc47..bd212ede4e10 100644
--- a/sorts/bucket_sort.py
+++ b/sorts/bucket_sort.py
@@ -11,7 +11,12 @@
 # involve the number of buckets.
 
 #  Time Complexity of Solution:
-#  Best Case O(n); Average Case O(n); Worst Case O(n)
+#  Worst case scenario occurs when all the elements are placed in a single bucket. The overall performance 
+#  would then be dominated by the algorithm used to sort each bucket. In this case, O(n log n), because of TimSort 
+#
+#  Average Case O(n + (n^2)/k + k), where k is the number of buckets
+#
+#  If k = O(n), time complexity is O(n)
 
 DEFAULT_BUCKET_SIZE=5
 

From 27ba11a1e58f76c06286d15a69e8ba5edf582f21 Mon Sep 17 00:00:00 2001
From: obelisk0114 <obelisk0114@gmail.com>
Date: Sat, 13 Jul 2019 21:29:24 -0700
Subject: [PATCH 2/4] Add combinations

---
 backtracking/all_combinations.py | 35 ++++++++++++++++++++++++++++++++
 1 file changed, 35 insertions(+)
 create mode 100644 backtracking/all_combinations.py

diff --git a/backtracking/all_combinations.py b/backtracking/all_combinations.py
new file mode 100644
index 000000000000..b0c3f9020e68
--- /dev/null
+++ b/backtracking/all_combinations.py
@@ -0,0 +1,35 @@
+# -*- coding: utf-8 -*-
+
+"""
+	In this problem, we want to determine all possible combinations of k
+	numbers out of 1 ... n. We use backtracking to solve this problem.
+	Time complexity: O(C(n,k)) which is O(n choose k) = O((n!/(k! * (n - k)!)))
+"""
+
+
+def generate_all_combinations(n: int, k: int) -> [[int]]:
+    result = []
+    create_all_state(1, n, k, [], result)
+    return result
+
+
+def create_all_state(increment, total_number, level, current_list, total_list):
+    if level == 0:
+        total_list.append(current_list[:])
+        return
+
+    for i in range(increment, total_number - level + 2):
+        current_list.append(i)
+        create_all_state(i + 1, total_number, level - 1, current_list, total_list)
+        current_list.pop()
+
+
+def print_all_state(total_list):
+    for i in total_list:
+        print(*i)
+
+
+n = 4
+k = 2
+total_list = generate_all_combinations(n, k)
+print_all_state(total_list)

From a175ca342d4a7dcb559ac28db2679f4ec897e303 Mon Sep 17 00:00:00 2001
From: obelisk0114 <obelisk0114@gmail.com>
Date: Sat, 13 Jul 2019 22:19:36 -0700
Subject: [PATCH 3/4] Adding doctest

---
 backtracking/all_combinations.py | 19 +++++++++++++++----
 1 file changed, 15 insertions(+), 4 deletions(-)

diff --git a/backtracking/all_combinations.py b/backtracking/all_combinations.py
index b0c3f9020e68..56c84fcf9be4 100644
--- a/backtracking/all_combinations.py
+++ b/backtracking/all_combinations.py
@@ -8,6 +8,16 @@
 
 
 def generate_all_combinations(n: int, k: int) -> [[int]]:
+    """
+    >>> generate_all_combinations(n=4, k=2)
+    1 2
+    1 3
+    1 4
+    2 3
+    2 4
+    3 4
+    """
+    
     result = []
     create_all_state(1, n, k, [], result)
     return result
@@ -29,7 +39,8 @@ def print_all_state(total_list):
         print(*i)
 
 
-n = 4
-k = 2
-total_list = generate_all_combinations(n, k)
-print_all_state(total_list)
+if __name__ == '__main__':
+    n = 4
+    k = 2
+    total_list = generate_all_combinations(n, k)
+    print_all_state(total_list)

From 6c699111daccc4c839b8121d0335e4157be9ad3d Mon Sep 17 00:00:00 2001
From: obelisk0114 <obelisk0114@gmail.com>
Date: Sat, 13 Jul 2019 22:29:01 -0700
Subject: [PATCH 4/4] Fix doctest problem

---
 backtracking/all_combinations.py | 7 +------
 1 file changed, 1 insertion(+), 6 deletions(-)

diff --git a/backtracking/all_combinations.py b/backtracking/all_combinations.py
index 56c84fcf9be4..63425aeabbd1 100644
--- a/backtracking/all_combinations.py
+++ b/backtracking/all_combinations.py
@@ -10,12 +10,7 @@
 def generate_all_combinations(n: int, k: int) -> [[int]]:
     """
     >>> generate_all_combinations(n=4, k=2)
-    1 2
-    1 3
-    1 4
-    2 3
-    2 4
-    3 4
+    [[1, 2], [1, 3], [1, 4], [2, 3], [2, 4], [3, 4]]
     """
     
     result = []