Added Kth largest element algorithm (#10687)

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* Added test case for tuple

* Update kth_largest_element.py

---------

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

data_structures/arrays/kth_largest_element.py

@@ -0,0 +1,117 @@
+"""
+Given an array of integers and an integer k, find the kth largest element in the array.
+
+https://stackoverflow.com/questions/251781
+"""
+
+
+def partition(arr: list[int], low: int, high: int) -> int:
+    """
+    Partitions list based on the pivot element.
+
+    This function rearranges the elements in the input list 'elements' such that
+    all elements greater than or equal to the chosen pivot are on the right side
+    of the pivot, and all elements smaller than the pivot are on the left side.
+
+    Args:
+        arr: The list to be partitioned
+        low: The lower index of the list
+        high: The higher index of the list
+
+    Returns:
+        int: The index of pivot element after partitioning
+
+        Examples:
+        >>> partition([3, 1, 4, 5, 9, 2, 6, 5, 3, 5], 0, 9)
+        4
+        >>> partition([7, 1, 4, 5, 9, 2, 6, 5, 8], 0, 8)
+        1
+        >>> partition(['apple', 'cherry', 'date', 'banana'], 0, 3)
+        2
+        >>> partition([3.1, 1.2, 5.6, 4.7], 0, 3)
+        1
+    """
+    pivot = arr[high]
+    i = low - 1
+    for j in range(low, high):
+        if arr[j] >= pivot:
+            i += 1
+            arr[i], arr[j] = arr[j], arr[i]
+    arr[i + 1], arr[high] = arr[high], arr[i + 1]
+    return i + 1
+
+
+def kth_largest_element(arr: list[int], position: int) -> int:
+    """
+    Finds the kth largest element in a list.
+    Should deliver similar results to:
+    ```python
+    def kth_largest_element(arr, position):
+        return sorted(arr)[-position]
+    ```
+
+    Args:
+        nums: The list of numbers.
+        k: The position of the desired kth largest element.
+
+    Returns:
+        int: The kth largest element.
+
+    Examples:
+        >>> kth_largest_element([3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5], 3)
+        5
+        >>> kth_largest_element([2, 5, 6, 1, 9, 3, 8, 4, 7, 3, 5], 1)
+        9
+        >>> kth_largest_element([2, 5, 6, 1, 9, 3, 8, 4, 7, 3, 5], -2)
+        Traceback (most recent call last):
+        ...
+        ValueError: Invalid value of 'position'
+        >>> kth_largest_element([9, 1, 3, 6, 7, 9, 8, 4, 2, 4, 9], 110)
+        Traceback (most recent call last):
+        ...
+        ValueError: Invalid value of 'position'
+        >>> kth_largest_element([1, 2, 4, 3, 5, 9, 7, 6, 5, 9, 3], 0)
+        Traceback (most recent call last):
+        ...
+        ValueError: Invalid value of 'position'
+        >>> kth_largest_element(['apple', 'cherry', 'date', 'banana'], 2)
+        'cherry'
+        >>> kth_largest_element([3.1, 1.2, 5.6, 4.7,7.9,5,0], 2)
+        5.6
+        >>> kth_largest_element([-2, -5, -4, -1], 1)
+        -1
+        >>> kth_largest_element([], 1)
+        -1
+        >>> kth_largest_element([3.1, 1.2, 5.6, 4.7, 7.9, 5, 0], 1.5)
+        Traceback (most recent call last):
+        ...
+        ValueError: The position should be an integer
+        >>> kth_largest_element((4, 6, 1, 2), 4)
+        Traceback (most recent call last):
+        ...
+        TypeError: 'tuple' object does not support item assignment
+    """
+    if not arr:
+        return -1
+    if not isinstance(position, int):
+        raise ValueError("The position should be an integer")
+    if not 1 <= position <= len(arr):
+        raise ValueError("Invalid value of 'position'")
+    low, high = 0, len(arr) - 1
+    while low <= high:
+        if low > len(arr) - 1 or high < 0:
+            return -1
+        pivot_index = partition(arr, low, high)
+        if pivot_index == position - 1:
+            return arr[pivot_index]
+        elif pivot_index > position - 1:
+            high = pivot_index - 1
+        else:
+            low = pivot_index + 1
+    return -1
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()