From 630d69c8424ffc1c36c9be2290f2cb089391aa08 Mon Sep 17 00:00:00 2001
From: Shubham Kondekar <40213815+kondekarshubham123@users.noreply.github.com>
Date: Wed, 26 Oct 2022 19:37:02 +0530
Subject: [PATCH 01/14] Create combination_sum_iv.py

---
 dynamic_programming/combination_sum_iv.py | 102 ++++++++++++++++++++++
 1 file changed, 102 insertions(+)
 create mode 100644 dynamic_programming/combination_sum_iv.py

diff --git a/dynamic_programming/combination_sum_iv.py b/dynamic_programming/combination_sum_iv.py
new file mode 100644
index 000000000000..c4493cac6345
--- /dev/null
+++ b/dynamic_programming/combination_sum_iv.py
@@ -0,0 +1,102 @@
+"""
+Question:
+You are given an array of distinct integers and you have to tell how many
+different ways of selecting the elements from the array are there such that
+the sum of chosen elements is equal to the target number tar.
+
+Example
+
+Input:
+N = 3
+target = 5
+array = [1, 2, 5]
+
+Output:
+9
+
+Approach:
+The basic idea is to go over recursively to find the way such that the sum
+of chosen elements is “tar”. For every element, we have two choices
+    1. Include the element in our set of chosen elements.
+    2. Don’t include the element in our set of chosen elements.
+"""
+
+
+from typing import List
+
+
+def combination_sum_iv(N: int, array: List[int], target: int) -> int:
+    """
+    Function checks the all possible combinations, and returns the count
+    of possible combination in exponential Time Complexity.
+
+    >>> combination_sum_iv(3, [1,2,5], 5)
+    9
+    """
+    def count_of_possible_combinations(target: int) -> int:
+        if target < 0:
+            return 0
+        if target == 0:
+            return 1
+        count = 0
+        for i in range(len(array)):
+            count += count_of_possible_combinations(target - array[i])
+        return count
+    return count_of_possible_combinations(target)
+
+
+def combination_sum_iv_dp_array(N: int, array: List[int], target: int) -> int:
+    """
+    Function checks the all possible combinations, and returns the count
+    of possible combination in O(N^2) Time Complexity as we are using Dynamic
+    programming array here.
+
+    >>> combination_sum_iv_dp_array(3, [1,2,5], 5)
+    9
+    """
+    def count_of_possible_combinations_with_dp_array(target: int, dp_array: List[int]) -> int:
+        if target < 0:
+            return 0
+        if target == 0:
+            return 1
+        if dp_array[target] != -1:
+            return dp_array[target]
+        answer = 0
+        for i in range(len(array)):
+            answer += count_of_possible_combinations_with_dp_array(
+                target - array[i], dp_array)
+        dp_array[target] = answer
+        return answer
+    dp_array = [-1 for _ in range(target+1)]
+    return count_of_possible_combinations_with_dp_array(target, dp_array)
+
+
+def combination_sum_iv_bottom_up(N: int, array: List[int], target: int) -> int:
+    """
+    Function checks the all possible combinations with using bottom up approach,
+    and returns the count of possible combination in O(N^2) Time Complexity
+    as we are using Dynamic programming array here.
+
+    >>> combination_sum_iv_bottom_up(3, [1,2,5], 5)
+    9
+    """
+
+    dp_array = [0 for _ in range(target + 1)]
+    dp_array[0] = 1
+
+    for i in range(1, target+1):
+        for j in range(N):
+            if (i - array[j] >= 0):
+                dp_array[i] += dp_array[i - array[j]]
+
+    return dp_array[target]
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+    N = 3
+    target = 5
+    array = [1, 2, 5]
+    print(combination_sum_iv(N, array, target))

From 909c704d47f7c81cab314efdce59575cf7a39767 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Wed, 26 Oct 2022 14:09:43 +0000
Subject: [PATCH 02/14] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 dynamic_programming/combination_sum_iv.py | 23 +++++++++++++++--------
 1 file changed, 15 insertions(+), 8 deletions(-)

diff --git a/dynamic_programming/combination_sum_iv.py b/dynamic_programming/combination_sum_iv.py
index c4493cac6345..7bfee928b879 100644
--- a/dynamic_programming/combination_sum_iv.py
+++ b/dynamic_programming/combination_sum_iv.py
@@ -25,7 +25,7 @@
 from typing import List
 
 
-def combination_sum_iv(N: int, array: List[int], target: int) -> int:
+def combination_sum_iv(N: int, array: list[int], target: int) -> int:
     """
     Function checks the all possible combinations, and returns the count
     of possible combination in exponential Time Complexity.
@@ -33,6 +33,7 @@ def combination_sum_iv(N: int, array: List[int], target: int) -> int:
     >>> combination_sum_iv(3, [1,2,5], 5)
     9
     """
+
     def count_of_possible_combinations(target: int) -> int:
         if target < 0:
             return 0
@@ -42,10 +43,11 @@ def count_of_possible_combinations(target: int) -> int:
         for i in range(len(array)):
             count += count_of_possible_combinations(target - array[i])
         return count
+
     return count_of_possible_combinations(target)
 
 
-def combination_sum_iv_dp_array(N: int, array: List[int], target: int) -> int:
+def combination_sum_iv_dp_array(N: int, array: list[int], target: int) -> int:
     """
     Function checks the all possible combinations, and returns the count
     of possible combination in O(N^2) Time Complexity as we are using Dynamic
@@ -54,7 +56,10 @@ def combination_sum_iv_dp_array(N: int, array: List[int], target: int) -> int:
     >>> combination_sum_iv_dp_array(3, [1,2,5], 5)
     9
     """
-    def count_of_possible_combinations_with_dp_array(target: int, dp_array: List[int]) -> int:
+
+    def count_of_possible_combinations_with_dp_array(
+        target: int, dp_array: list[int]
+    ) -> int:
         if target < 0:
             return 0
         if target == 0:
@@ -64,14 +69,16 @@ def count_of_possible_combinations_with_dp_array(target: int, dp_array: List[int
         answer = 0
         for i in range(len(array)):
             answer += count_of_possible_combinations_with_dp_array(
-                target - array[i], dp_array)
+                target - array[i], dp_array
+            )
         dp_array[target] = answer
         return answer
-    dp_array = [-1 for _ in range(target+1)]
+
+    dp_array = [-1 for _ in range(target + 1)]
     return count_of_possible_combinations_with_dp_array(target, dp_array)
 
 
-def combination_sum_iv_bottom_up(N: int, array: List[int], target: int) -> int:
+def combination_sum_iv_bottom_up(N: int, array: list[int], target: int) -> int:
     """
     Function checks the all possible combinations with using bottom up approach,
     and returns the count of possible combination in O(N^2) Time Complexity
@@ -84,9 +91,9 @@ def combination_sum_iv_bottom_up(N: int, array: List[int], target: int) -> int:
     dp_array = [0 for _ in range(target + 1)]
     dp_array[0] = 1
 
-    for i in range(1, target+1):
+    for i in range(1, target + 1):
         for j in range(N):
-            if (i - array[j] >= 0):
+            if i - array[j] >= 0:
                 dp_array[i] += dp_array[i - array[j]]
 
     return dp_array[target]

From c63e28e6288825b0d76a1e73f2c0381894055165 Mon Sep 17 00:00:00 2001
From: Shubham Kondekar <40213815+kondekarshubham123@users.noreply.github.com>
Date: Wed, 26 Oct 2022 20:22:40 +0530
Subject: [PATCH 03/14] Update dynamic_programming/combination_sum_iv.py

Co-authored-by: Caeden Perelli-Harris <caedenperelliharris@gmail.com>
---
 dynamic_programming/combination_sum_iv.py | 1 -
 1 file changed, 1 deletion(-)

diff --git a/dynamic_programming/combination_sum_iv.py b/dynamic_programming/combination_sum_iv.py
index 7bfee928b879..1b38e4b7f5f2 100644
--- a/dynamic_programming/combination_sum_iv.py
+++ b/dynamic_programming/combination_sum_iv.py
@@ -22,7 +22,6 @@
 """
 
 
-from typing import List
 
 
 def combination_sum_iv(N: int, array: list[int], target: int) -> int:

From 1c35f5caf00f10fbe65487f80389c32b6dd95ee3 Mon Sep 17 00:00:00 2001
From: Shubham Kondekar <40213815+kondekarshubham123@users.noreply.github.com>
Date: Wed, 26 Oct 2022 20:23:00 +0530
Subject: [PATCH 04/14] Update dynamic_programming/combination_sum_iv.py

Co-authored-by: Caeden Perelli-Harris <caedenperelliharris@gmail.com>
---
 dynamic_programming/combination_sum_iv.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/dynamic_programming/combination_sum_iv.py b/dynamic_programming/combination_sum_iv.py
index 1b38e4b7f5f2..76634118cd39 100644
--- a/dynamic_programming/combination_sum_iv.py
+++ b/dynamic_programming/combination_sum_iv.py
@@ -73,7 +73,7 @@ def count_of_possible_combinations_with_dp_array(
         dp_array[target] = answer
         return answer
 
-    dp_array = [-1 for _ in range(target + 1)]
+    dp_array = [-1]  * (target + 1)
     return count_of_possible_combinations_with_dp_array(target, dp_array)
 
 

From 81bd35f51983ceda04fdcbed57d49eefc2062dac Mon Sep 17 00:00:00 2001
From: Shubham Kondekar <40213815+kondekarshubham123@users.noreply.github.com>
Date: Wed, 26 Oct 2022 20:23:24 +0530
Subject: [PATCH 05/14] Update dynamic_programming/combination_sum_iv.py

Co-authored-by: Caeden Perelli-Harris <caedenperelliharris@gmail.com>
---
 dynamic_programming/combination_sum_iv.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/dynamic_programming/combination_sum_iv.py b/dynamic_programming/combination_sum_iv.py
index 76634118cd39..250a1c045d66 100644
--- a/dynamic_programming/combination_sum_iv.py
+++ b/dynamic_programming/combination_sum_iv.py
@@ -87,7 +87,7 @@ def combination_sum_iv_bottom_up(N: int, array: list[int], target: int) -> int:
     9
     """
 
-    dp_array = [0 for _ in range(target + 1)]
+    dp_array = [0] * (target + 1)
     dp_array[0] = 1
 
     for i in range(1, target + 1):

From 463f99ec882a02da210690122cef81c0d514629e Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Wed, 26 Oct 2022 14:54:08 +0000
Subject: [PATCH 06/14] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 dynamic_programming/combination_sum_iv.py | 4 +---
 1 file changed, 1 insertion(+), 3 deletions(-)

diff --git a/dynamic_programming/combination_sum_iv.py b/dynamic_programming/combination_sum_iv.py
index 250a1c045d66..99d7a2b6bfa6 100644
--- a/dynamic_programming/combination_sum_iv.py
+++ b/dynamic_programming/combination_sum_iv.py
@@ -22,8 +22,6 @@
 """
 
 
-
-
 def combination_sum_iv(N: int, array: list[int], target: int) -> int:
     """
     Function checks the all possible combinations, and returns the count
@@ -73,7 +71,7 @@ def count_of_possible_combinations_with_dp_array(
         dp_array[target] = answer
         return answer
 
-    dp_array = [-1]  * (target + 1)
+    dp_array = [-1] * (target + 1)
     return count_of_possible_combinations_with_dp_array(target, dp_array)
 
 

From 194ff68283d6b1518f60dae924cb2cab901c3b38 Mon Sep 17 00:00:00 2001
From: Shubham Kondekar <40213815+kondekarshubham123@users.noreply.github.com>
Date: Wed, 26 Oct 2022 20:43:06 +0530
Subject: [PATCH 07/14] Update combination_sum_iv.py

---
 dynamic_programming/combination_sum_iv.py | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/dynamic_programming/combination_sum_iv.py b/dynamic_programming/combination_sum_iv.py
index 99d7a2b6bfa6..4dff586bd228 100644
--- a/dynamic_programming/combination_sum_iv.py
+++ b/dynamic_programming/combination_sum_iv.py
@@ -22,7 +22,7 @@
 """
 
 
-def combination_sum_iv(N: int, array: list[int], target: int) -> int:
+def combination_sum_iv(n: int, array: list[int], target: int) -> int:
     """
     Function checks the all possible combinations, and returns the count
     of possible combination in exponential Time Complexity.
@@ -44,7 +44,7 @@ def count_of_possible_combinations(target: int) -> int:
     return count_of_possible_combinations(target)
 
 
-def combination_sum_iv_dp_array(N: int, array: list[int], target: int) -> int:
+def combination_sum_iv_dp_array(n: int, array: list[int], target: int) -> int:
     """
     Function checks the all possible combinations, and returns the count
     of possible combination in O(N^2) Time Complexity as we are using Dynamic
@@ -75,7 +75,7 @@ def count_of_possible_combinations_with_dp_array(
     return count_of_possible_combinations_with_dp_array(target, dp_array)
 
 
-def combination_sum_iv_bottom_up(N: int, array: list[int], target: int) -> int:
+def combination_sum_iv_bottom_up(n: int, array: list[int], target: int) -> int:
     """
     Function checks the all possible combinations with using bottom up approach,
     and returns the count of possible combination in O(N^2) Time Complexity
@@ -100,7 +100,7 @@ def combination_sum_iv_bottom_up(N: int, array: list[int], target: int) -> int:
     import doctest
 
     doctest.testmod()
-    N = 3
+    n = 3
     target = 5
     array = [1, 2, 5]
-    print(combination_sum_iv(N, array, target))
+    print(combination_sum_iv(n, array, target))

From 6435bef3206a4a7c5eb29029a34e59b865455d55 Mon Sep 17 00:00:00 2001
From: Shubham Kondekar <40213815+kondekarshubham123@users.noreply.github.com>
Date: Wed, 26 Oct 2022 21:06:12 +0530
Subject: [PATCH 08/14] Update combination_sum_iv.py

---
 dynamic_programming/combination_sum_iv.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/dynamic_programming/combination_sum_iv.py b/dynamic_programming/combination_sum_iv.py
index 4dff586bd228..def23075d0c0 100644
--- a/dynamic_programming/combination_sum_iv.py
+++ b/dynamic_programming/combination_sum_iv.py
@@ -89,7 +89,7 @@ def combination_sum_iv_bottom_up(n: int, array: list[int], target: int) -> int:
     dp_array[0] = 1
 
     for i in range(1, target + 1):
-        for j in range(N):
+        for j in range(n):
             if i - array[j] >= 0:
                 dp_array[i] += dp_array[i - array[j]]
 

From 9817a4407dad59035b87fbbf2af6ecf0d016e3bd Mon Sep 17 00:00:00 2001
From: Shubham Kondekar <40213815+kondekarshubham123@users.noreply.github.com>
Date: Fri, 28 Oct 2022 20:12:15 +0530
Subject: [PATCH 09/14] Resolved PR Comments

---
 dynamic_programming/combination_sum_iv.py | 11 ++---------
 1 file changed, 2 insertions(+), 9 deletions(-)

diff --git a/dynamic_programming/combination_sum_iv.py b/dynamic_programming/combination_sum_iv.py
index def23075d0c0..03dbd6a7b8d0 100644
--- a/dynamic_programming/combination_sum_iv.py
+++ b/dynamic_programming/combination_sum_iv.py
@@ -36,10 +36,7 @@ def count_of_possible_combinations(target: int) -> int:
             return 0
         if target == 0:
             return 1
-        count = 0
-        for i in range(len(array)):
-            count += count_of_possible_combinations(target - array[i])
-        return count
+        return sum([count_of_possible_combinations(target - each) for each in array])
 
     return count_of_possible_combinations(target)
 
@@ -63,11 +60,7 @@ def count_of_possible_combinations_with_dp_array(
             return 1
         if dp_array[target] != -1:
             return dp_array[target]
-        answer = 0
-        for i in range(len(array)):
-            answer += count_of_possible_combinations_with_dp_array(
-                target - array[i], dp_array
-            )
+        answer = sum([count_of_possible_combinations_with_dp_array(target - each) for each in array])
         dp_array[target] = answer
         return answer
 

From de2969319016a8b7d23c63c272cbd1fe8876a25d Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Fri, 28 Oct 2022 14:44:15 +0000
Subject: [PATCH 10/14] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 dynamic_programming/combination_sum_iv.py | 7 ++++++-
 1 file changed, 6 insertions(+), 1 deletion(-)

diff --git a/dynamic_programming/combination_sum_iv.py b/dynamic_programming/combination_sum_iv.py
index 03dbd6a7b8d0..dcaa793941d3 100644
--- a/dynamic_programming/combination_sum_iv.py
+++ b/dynamic_programming/combination_sum_iv.py
@@ -60,7 +60,12 @@ def count_of_possible_combinations_with_dp_array(
             return 1
         if dp_array[target] != -1:
             return dp_array[target]
-        answer = sum([count_of_possible_combinations_with_dp_array(target - each) for each in array])
+        answer = sum(
+            [
+                count_of_possible_combinations_with_dp_array(target - each)
+                for each in array
+            ]
+        )
         dp_array[target] = answer
         return answer
 

From d42eafd7aded004b05be73c78da8e11cf989e27c Mon Sep 17 00:00:00 2001
From: Shubham Kondekar <40213815+kondekarshubham123@users.noreply.github.com>
Date: Fri, 28 Oct 2022 20:18:06 +0530
Subject: [PATCH 11/14] minor change, argument missing in function

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

diff --git a/dynamic_programming/combination_sum_iv.py b/dynamic_programming/combination_sum_iv.py
index dcaa793941d3..a81aa2c6a9b1 100644
--- a/dynamic_programming/combination_sum_iv.py
+++ b/dynamic_programming/combination_sum_iv.py
@@ -60,12 +60,7 @@ def count_of_possible_combinations_with_dp_array(
             return 1
         if dp_array[target] != -1:
             return dp_array[target]
-        answer = sum(
-            [
-                count_of_possible_combinations_with_dp_array(target - each)
-                for each in array
-            ]
-        )
+        answer = sum([count_of_possible_combinations_with_dp_array(target - each, dp_array) for each in array])
         dp_array[target] = answer
         return answer
 

From 0c3b8cab7c8ffb2212b8b79bc4880fb6469c1e88 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Fri, 28 Oct 2022 14:52:17 +0000
Subject: [PATCH 12/14] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 dynamic_programming/combination_sum_iv.py | 7 ++++++-
 1 file changed, 6 insertions(+), 1 deletion(-)

diff --git a/dynamic_programming/combination_sum_iv.py b/dynamic_programming/combination_sum_iv.py
index a81aa2c6a9b1..14feb78edc57 100644
--- a/dynamic_programming/combination_sum_iv.py
+++ b/dynamic_programming/combination_sum_iv.py
@@ -60,7 +60,12 @@ def count_of_possible_combinations_with_dp_array(
             return 1
         if dp_array[target] != -1:
             return dp_array[target]
-        answer = sum([count_of_possible_combinations_with_dp_array(target - each, dp_array) for each in array])
+        answer = sum(
+            [
+                count_of_possible_combinations_with_dp_array(target - each, dp_array)
+                for each in array
+            ]
+        )
         dp_array[target] = answer
         return answer
 

From 2e846dc354859dd4727b5632c1865530b76b48fd Mon Sep 17 00:00:00 2001
From: Shubham Kondekar <40213815+kondekarshubham123@users.noreply.github.com>
Date: Fri, 28 Oct 2022 20:36:35 +0530
Subject: [PATCH 13/14] Update dynamic_programming/combination_sum_iv.py

Co-authored-by: Christian Clauss <cclauss@me.com>
---
 dynamic_programming/combination_sum_iv.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/dynamic_programming/combination_sum_iv.py b/dynamic_programming/combination_sum_iv.py
index 14feb78edc57..76392fec3542 100644
--- a/dynamic_programming/combination_sum_iv.py
+++ b/dynamic_programming/combination_sum_iv.py
@@ -36,7 +36,7 @@ def count_of_possible_combinations(target: int) -> int:
             return 0
         if target == 0:
             return 1
-        return sum([count_of_possible_combinations(target - each) for each in array])
+        return sum(count_of_possible_combinations(target - item) for item in array)
 
     return count_of_possible_combinations(target)
 

From 8cf9c1a593396641da64f081d192295e12e34e45 Mon Sep 17 00:00:00 2001
From: Shubham Kondekar <40213815+kondekarshubham123@users.noreply.github.com>
Date: Fri, 28 Oct 2022 21:56:28 +0530
Subject: [PATCH 14/14] minor change

---
 dynamic_programming/combination_sum_iv.py | 6 ++----
 1 file changed, 2 insertions(+), 4 deletions(-)

diff --git a/dynamic_programming/combination_sum_iv.py b/dynamic_programming/combination_sum_iv.py
index 76392fec3542..b2aeb0824f64 100644
--- a/dynamic_programming/combination_sum_iv.py
+++ b/dynamic_programming/combination_sum_iv.py
@@ -61,10 +61,8 @@ def count_of_possible_combinations_with_dp_array(
         if dp_array[target] != -1:
             return dp_array[target]
         answer = sum(
-            [
-                count_of_possible_combinations_with_dp_array(target - each, dp_array)
-                for each in array
-            ]
+            count_of_possible_combinations_with_dp_array(target - item, dp_array)
+            for item in array
         )
         dp_array[target] = answer
         return answer