feat(algorithms, dynamic-programming): counting bits

DIRECTORY.md

@@ -55,6 +55,10 @@
       * [Test Max Profit Three](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/dynamic_programming/buy_sell_stock/test_max_profit_three.py)
       * [Test Max Profit Two](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/dynamic_programming/buy_sell_stock/test_max_profit_two.py)
       * [Test Max Profit With Fee](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/dynamic_programming/buy_sell_stock/test_max_profit_with_fee.py)
+    * Climb Stairs
+      * [Test Climb Stairs](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/dynamic_programming/climb_stairs/test_climb_stairs.py)
+    * Countingbits
+      * [Test Counting Bits](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/dynamic_programming/countingbits/test_counting_bits.py)
     * Domino Tromino Tiling
       * [Test Domino Tromino Tiling](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/dynamic_programming/domino_tromino_tiling/test_domino_tromino_tiling.py)
     * Duffle Bug Value
@@ -138,12 +142,16 @@
     * Spread Stones
       * [Test Minimum Moves To Spread Stones](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/greedy/spread_stones/test_minimum_moves_to_spread_stones.py)
   * Heap
+    * Kclosestelements
+      * [Test Find K Closest Elements](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/heap/kclosestelements/test_find_k_closest_elements.py)
     * Longest Happy String
       * [Test Longest Happy String](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/heap/longest_happy_string/test_longest_happy_string.py)
     * Maximal Score After K Operations
       * [Test Maximal Score](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/heap/maximal_score_after_k_operations/test_maximal_score.py)
     * Maximum Subsequence Score
       * [Test Max Subsequence Score](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/heap/maximum_subsequence_score/test_max_subsequence_score.py)
+    * Mergeksortedlists
+      * [Test Merge K Sorted Lists](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/heap/mergeksortedlists/test_merge_k_sorted_lists.py)
     * Min Cost Hire K Workers
       * [Test Min Cost To Hire Workers](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/heap/min_cost_hire_k_workers/test_min_cost_to_hire_workers.py)
     * Min Cost To Connect Sticks
@@ -676,8 +684,6 @@
     * [Battleship](https://github.com/BrianLusina/PythonSnips/blob/master/puzzles/battleship/battleship.py)
   * Beeramid
     * [Test Bearamid](https://github.com/BrianLusina/PythonSnips/blob/master/puzzles/beeramid/test_bearamid.py)
-  * Climb Stairs
-    * [Test Climb Stairs](https://github.com/BrianLusina/PythonSnips/blob/master/puzzles/climb_stairs/test_climb_stairs.py)
   * Find Missing Elem
     * [Test Find Missing Elem](https://github.com/BrianLusina/PythonSnips/blob/master/puzzles/find_missing_elem/test_find_missing_elem.py)
   * Hashmap

algorithms/dynamic_programming/countingbits/README.md

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+# Counting Bits
+
+Given an integer n, return an array ans of length n + 1 such that for each i (0 <= i <= n), ans[i] is the number of 1's
+in the binary representation of i.
+
+## Examples
+
+```text
+Example 1:
+
+Input: n = 2
+Output: [0,1,1]
+Explanation:
+0 --> 0
+1 --> 1
+2 --> 10
+```
+
+```
+Example 2:
+
+Input: n = 5
+Output: [0,1,1,2,1,2]
+Explanation:
+0 --> 0
+1 --> 1
+2 --> 10
+3 --> 11
+4 --> 100
+5 --> 101
+```
+
+## Constraints
+
+- 0 <= `n` <= 10^5
+
+## Solution
+
+This solution uses a bottom-up dynamic programming approach to solve the problem.
+The key to this problem lies in the fact that any binary number can be broken down into two parts: the least-significant
+(rightmost bit), and the rest of the bits. The rest of the bits can be expressed as the binary number divided by 2
+(rounded down), or `i >> 1`.
+
+For example:
+- 4 in binary = 100
+- rightmost bit = 0
+- rest of bits = 10, which is also (4 // 2) = 2 in binary.
+
+When the number is odd,
+- 5 in binary = 101
+- rightmost bit = 1
+- rest of bits = 10, which is also (5 // 2) = 2 in binary.
+
+in the binary representation of i is that number plus 1 if the rightmost bit is 1. We can tell if the last significant
+bit is 1 by checking if it is odd.
+
+As an example, we know that the number of 1's in 2 is 1. This information can be used to calculate the number of 1's in 4.
+The number of 1's in 4 is the number of 1's in 2 plus 0, because 4 is even.
+
+This establishes a recurrence relationship between the number of 1's in the binary representation of i and the number of
+1's in the binary representation of i // 2: if count[i] is the number of 1's in the binary representation of i, then
+count[i] = count[i // 2] + (i % 2).
+
+With the recurrence relationship established, we can now solve the problem using a bottom-up dynamic programming approach.
+We start with the base case dp[0] = 0, and then build up the solution for dp[i] for i from 1 to n.
+
+![Solution 1](./images/solutions/counting_bits_solution_1.png)
+![Solution 2](./images/solutions/counting_bits_solution_2.png)
+![Solution 3](./images/solutions/counting_bits_solution_3.png)
+![Solution 4](./images/solutions/counting_bits_solution_4.png)
+![Solution 5](./images/solutions/counting_bits_solution_5.png)
+![Solution 6](./images/solutions/counting_bits_solution_6.png)
+![Solution 7](./images/solutions/counting_bits_solution_7.png)
+![Solution 8](./images/solutions/counting_bits_solution_8.png)
+![Solution 9](./images/solutions/counting_bits_solution_9.png)
+![Solution 10](./images/solutions/counting_bits_solution_10.png)
+![Solution 11](./images/solutions/counting_bits_solution_11.png)
+![Solution 12](./images/solutions/counting_bits_solution_12.png)

algorithms/dynamic_programming/countingbits/__init__.py

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+from typing import List
+
+
+def count_bits(n: int) -> List[int]:
+    """
+    Counts the number of 1 bits in the given integer provided returning a list where count[i] stores the count of '1'
+    bits in the binary form of i.
+    Args:
+        n(int): integer
+    Returns:
+        list: count of 1 bits where each index contains the count of 1 bits
+    """
+    dp = [0] * (n + 1)
+
+    for i in range(1, n + 1):
+        # this can also be solved as which is faster in Python
+        # dp[i] = dp[i >> 1] + (i & 1)
+        dp[i] = dp[i // 2] + (i % 2)
+
+    return dp

algorithms/dynamic_programming/countingbits/test_counting_bits.py

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+import unittest
+from typing import List
+from parameterized import parameterized
+from algorithms.dynamic_programming.countingbits import count_bits
+
+COUNTING_BITS_TEST_CASES = [
+    (6, [0, 1, 1, 2, 1, 2, 2]),
+    (2, [0, 1, 1]),
+    (5, [0, 1, 1, 2, 1, 2]),
+    (0, [0]),
+    (7, [0, 1, 1, 2, 1, 2, 2, 3]),
+    (10, [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2]),
+]
+
+
+class CountingBitsTestCase(unittest.TestCase):
+    @parameterized.expand(COUNTING_BITS_TEST_CASES)
+    def test_counting_bits(self, n: int, expected: List[int]):
+        actual = count_bits(n)
+        self.assertEqual(expected, actual)
+
+
+if __name__ == "__main__":
+    unittest.main()

algorithms/heap/kclosestelements/README.md

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+# Find K Closest Elements
+
+Given a sorted array nums, a target value target, and an integer k, find the k closest elements to target in the array,
+where "closest" is the absolute difference between each element and target. Return these elements in an array, sorted in
+ascending order.
+
+## Examples
+
+```text
+nums = [-1, 0, 1, 4, 6]
+target = 1
+k = 3
+
+Output
+[-1, 0, 1]
+
+Explanation
+Explanation: -1 is 2 away from 1, 0 is 1 away from 1, and 1 is 0 away from 1. All other elements are more than 2 away. 
+Since we need to return the elements in ascending order, the answer is [-1, 0, 1]
+```
+
+```text
+nums = [5, 6, 7, 8, 9]
+target = 10
+k = 2
+
+Output:
+[8, 9]
+```

algorithms/heap/kclosestelements/__init__.py

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+from typing import List
+import heapq
+
+
+def k_closest(nums: List[int], k: int, target: int):
+    heap = []
+
+    for num in nums:
+        diff = abs(num - target)
+
+        if len(heap) < k:
+            heapq.heappush(heap, (-diff, num))
+        elif diff < -heap[0][0]:
+            heapq.heappushpop(heap, (-diff, num))
+
+    distances = [pair[1] for pair in heap]
+    distances.sort()
+    return distances

algorithms/heap/kclosestelements/test_find_k_closest_elements.py

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+import unittest
+from typing import List
+from parameterized import parameterized
+from algorithms.heap.kclosestelements import k_closest
+
+K_CLOSEST_ELEMENTS_TEST_CASES = [
+    ([1, 2, 3, 4, 5], 4, 3, [1, 2, 3, 4]),
+    ([1, 3, 5, 8, 10], 2, 5, [3, 5]),
+    ([3, 4, 7, 10, 15], 3, 8, [4, 7, 10]),
+    ([5, 6, 7, 8, 9], 3, 7, [6, 7, 8]),
+    ([1, 1, 1, 10, 10, 10], 1, 9, [10]),
+    ([1, 2, 3, 4, 5], 2, 6, [4, 5]),
+]
+
+
+class KClosestElementsTestCase(unittest.TestCase):
+    @parameterized.expand(K_CLOSEST_ELEMENTS_TEST_CASES)
+    def test_k_closest_elements(
+        self, nums: List[int], k: int, target: int, expected: List[int]
+    ):
+        actual = k_closest(nums, k, target)
+        self.assertEqual(expected, actual)
+
+
+if __name__ == "__main__":
+    unittest.main()

algorithms/heap/mergeksortedlists/README.md

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+# Merge K Sorted Lists
+
+Given k linked lists, each sorted in ascending order, in a list lists, write a function to merge the input lists into
+one sorted linked list.
+
+## Examples
+
+```text
+lists = [[3,4,6],[2,3,5],[-1,6]]
+3 -> 4 -> 6
+2 -> 3 -> 5
+-1 -> 6
+
+Output
+[-1,2,3,3,4,5,6,6]
+
+-1 -> 2 -> 3 -> 3 -> 4 -> 5 -> 6 -> 6
+```

algorithms/heap/mergeksortedlists/__init__.py

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+from typing import List
+import heapq
+
+
+def merge_k_lists(lists: List[List[int]]) -> List[int]:
+    """
+    Merges k sorted lists into one list
+    Args:
+        lists(list): list of lists
+    Returns:
+        list: Combined list from the input list that is sorted
+    """
+    # Validate that the input provided is not empty. If it is empty, return an empty list. Nothing more to do here
+    if not lists:
+        return []
+
+    # Check if any of the lists provided is empty. If we have an empty list, we return, as there is nothing more to do
+    has_non_empty = any(lst for lst in lists)
+    if not has_non_empty:
+        return []
+
+    # Initialize our heap. This will be used to keep the lowest value from each list at the root of the heap. Whenever
+    # a value is popped from the root, the next value is added to the list and if it is the lowest value it will be
+    # at the root of the heap
+    min_heap = []
+
+    # We will iterate through the list storing only the first values from each list, including the list index and the
+    # element index which we will use to iterate through a given list. The list index will be used to iterate through
+    # the provided lists
+    for idx, lst in enumerate(lists):
+        if lst:
+            value, list_index, element_index = lst[0], idx, 0
+            heapq.heappush(min_heap, (value, list_index, element_index))
+
+    # Result will store the final output
+    result: List[int] = []
+
+    # While we still have elements in the heap
+    while min_heap:
+        # We get the top element from the heap
+        value, list_index, element_index = heapq.heappop(min_heap)
+        # Add the value to the result, at this point, we know this is the smallest value in the lists of lists
+        result.append(value)
+
+        # We check if the element index is less than the current list it can be found in. This means that there are
+        # still other elements within this list
+        if element_index + 1 < len(lists[list_index]):
+            # We add the next value to the heap
+            next_value = lists[list_index][element_index + 1]
+            heapq.heappush(min_heap, (next_value, list_index, element_index + 1))
+
+    # Return the result
+    return result

algorithms/heap/mergeksortedlists/test_merge_k_sorted_lists.py

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+import unittest
+from typing import List
+from parameterized import parameterized
+from algorithms.heap.mergeksortedlists import merge_k_lists
+
+MERGE_K_LISTS_TEST_CASES = [
+    ([[3, 4, 6], [2, 3, 5], [-1, 6]], [-1, 2, 3, 3, 4, 5, 6, 6]),
+    ([[2, 4, 6], [1, 3, 5]], [1, 2, 3, 4, 5, 6]),
+    ([[1, 4, 5], [1, 3, 4], [2, 6]], [1, 1, 2, 3, 4, 4, 5, 6]),
+    ([], []),
+    ([[]], []),
+    ([[1, 2, 3]], [1, 2, 3]),
+]
+
+
+class MergeKListsTestCase(unittest.TestCase):
+    @parameterized.expand(MERGE_K_LISTS_TEST_CASES)
+    def test_merge_k_lists(self, lists: List[List[int]], expected: List[int]):
+        actual = merge_k_lists(lists)
+        self.assertEqual(expected, actual)
+
+
+if __name__ == "__main__":
+    unittest.main()