feat: add kth next greater element script to /data_structures/stacks/.

data_structures/stacks/kth_next_greater_element.py

@@ -0,0 +1,93 @@
+"""
+Implement the function to find kth Next Greatest Element (NGE) for all elements.
+Idea comes from my blog:
+https://starsexpress.github.io/SkyHorse/docs/stack/2454_hard/second_next_greater
+"""
+
+test_k = 10
+test_array = list(range(10000))
+expected_answers = [value + test_k for value in range(10000 - test_k)] + [None] * test_k
+
+
+def find_kth_next_greater_element(
+    array: list[int | float], kth_ord: int
+) -> list[int | float | None]:
+    """
+    Efficient general method to seek the kth NGE for all elements.
+    Approach is entirely based on k stacks, which are actually very easy to understand.
+    These k stacks symbolize how many NGEs an element has already found.
+
+    For example, for 1 <= j <= k, if an element is currently at the jth stack,
+    it means that this element has found its (j - 1)th NGE, now looking for jth NGE.
+
+    By processing stacks from higher to lower ordinals, we can always ensure that
+    each stack secures decreasing monotonicity in terms of element value.
+
+    Time complexity: O(kn) where n is the length of input array.
+    However, if k >= n, all elements won't find their respective kth NGE.
+    As a result, worst case time complexity is O(n^2) when k < n but k ≈ n.
+
+    Space complexity: O(n), since at any point, an element is only in one of k stacks.
+
+    Args:
+        array (list[int | float]): A list for which the kth NGE is computed.
+                                   A mix of integers and floats in list is allowed.
+
+        kth_ord (int): Ordinal of the NGE to find. k must be a positive integer.
+
+    Returns:
+        A list containing each element's kth NGE. If an element can't find its kth NGE,
+        None, instead of -1, is put as its entry, because input array might have -1.
+
+    Example:
+    >>> find_kth_next_greater_element([1, 2, 3, 4, 5], 3) == [4, 5, None, None, None]
+    True
+    >>> find_kth_next_greater_element([2.5, 1.9, 4.3, 6.0], 1) == [4.3, 4.3, 6.0, None]
+    True
+    >>> find_kth_next_greater_element(list(range(1000)), 1000) == [None] * 1000
+    True
+    >>> find_kth_next_greater_element(test_array, test_k) == expected_answers
+    True
+    """
+    if not isinstance(kth_ord, int) or kth_ord < 1:
+        raise ValueError("k must be a positive integer.")
+
+    kth_next_greater_elements: list[int | float | None] = [None] * len(array)
+    if kth_ord >= len(array):  # Trivial cases: nobody can have kth NGE.
+        return kth_next_greater_elements
+
+    # For 1 <= j <= k, the jth stack is at the jth idx of stacks list.
+    # stacks[0]: a transporter that transfer entries between stacks.
+    # Each stack's entry is a tuple of (element, idx).
+    stacks: list[list[tuple[int | float, int]]] = [[] for _ in range(kth_ord + 1)]
+
+    for idx, element in enumerate(array):
+        # From kth stack to answer found.
+        while stacks[kth_ord] and stacks[kth_ord][-1][0] < element:
+            _, prev_idx = stacks[kth_ord].pop()
+            kth_next_greater_elements[prev_idx] = element
+
+        for stack_ord in range(kth_ord - 1, 0, -1):  # From (k - 1)th to 1st stack.
+            while stacks[stack_ord] and stacks[stack_ord][-1][0] < element:
+                stacks[0].append(stacks[stack_ord].pop())
+
+            while stacks[0]:  # Move to the next ordered stack.
+                stacks[stack_ord + 1].append(stacks[0].pop())
+
+        unvisited_elements_count = len(array) - 1 - idx
+        if unvisited_elements_count >= kth_ord:  # Element has a chance to find kth NGE.
+            stacks[1].append((element, idx))  # Always join 1st stack to begin search.
+
+    return kth_next_greater_elements
+
+
+if __name__ == "__main__":
+    from doctest import testmod
+    from timeit import timeit
+
+    testmod()
+    setup = "from __main__ import test_array, test_k, find_kth_next_greater_element"
+    print(
+        "find_kth_next_greater_element():",
+        timeit("find_kth_next_greater_element(test_array, test_k)", setup=setup),
+    )