add: Minimum Deviation in Array to greedy_methods (#10860)

* add: Minimum Deviation in Array in greedy methods

* min deviation

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* min deviation

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* min deviation

* min deviation

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* min deviation

* min deviation

* min deviation

* updating DIRECTORY.md

---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>
Co-authored-by: cclauss <cclauss@users.noreply.github.com>

Author: 3 people

DIRECTORY.md

@@ -670,6 +670,7 @@
   * [Fractional Knapsack](greedy_methods/fractional_knapsack.py)
   * [Fractional Knapsack 2](greedy_methods/fractional_knapsack_2.py)
   * [Gas Station](greedy_methods/gas_station.py)
+  * [Minimize Deviation In Array](greedy_methods/minimize_deviation_in_array.py)
   * [Minimum Coin Change](greedy_methods/minimum_coin_change.py)
   * [Minimum Waiting Time](greedy_methods/minimum_waiting_time.py)
   * [Optimal Merge Pattern](greedy_methods/optimal_merge_pattern.py)

greedy_methods/minimize_deviation_in_array.py

@@ -0,0 +1,60 @@
+"""
+You are given an array nums of n positive integers.
+
+You can perform two types of operations on any
+element of the array any number of times:
+
+If the element is even, divide it by 2.
+For example, if the array is [1,2,3,4], then you can do this operation
+on the last element, and the array will be [1,2,3,2].
+If the element is odd, multiply it by 2.
+For example, if the array is [1,2,3,4], then you can do this operation
+on the first element, and the array will be [2,2,3,4].
+The deviation of the array is the maximum difference between
+any two elements in the array.
+
+Return the minimum deviation the array can have after performing
+some number of operations.
+"""
+
+from heapq import heapify, heappop, heappush
+
+
+class Solution:
+    def minimum_deviation(self, nums: list[int]) -> int:
+        """
+        Function to find the minimum deviation of an array after performing operations.
+
+        Args:
+            nums (List[int]): A list of positive integers.
+
+        Returns:
+            temp_mindeviation (int): The minimum deviation of array after operations.
+
+        Examples:
+            >>> solution = Solution()
+            >>> solution.minimum_deviation([1, 2, 3, 4])
+            1
+            >>> solution.minimum_deviation([5, 10, 20, 30, 30])
+            5
+            >>> solution.minimum_deviation([8, 8, 8, 8, 8])
+            0
+        """
+        heapque = [-n * 2 if n % 2 else -n for n in nums]
+        heapify(heapque)
+        temp_min = -min(heapque, key=lambda num: -num)
+        temp_mindeviation = -heapque[0] - temp_min
+
+        while heapque and heapque[0] % 2 == 0:
+            n = heappop(heapque) // 2
+            heappush(heapque, n)
+            temp_min = min(temp_min, -n)
+            temp_mindeviation = min(temp_mindeviation, -heapque[0] - temp_min)
+
+        return temp_mindeviation
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()