Introduction

In this blog post, we will explore how to solve the LeetCode problem "2145" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

You are given a 0-indexed array of n integers differences, which describes the differences between each pair of consecutive integers of a hidden sequence of length (n + 1). More formally, call the hidden sequence hidden, then we have that differences[i] = hidden[i + 1] - hidden[i]. You are further given two integers lower and upper that describe the inclusive range of values [lower, upper] that the hidden sequence can contain. For example, given differences = [1, -3, 4], lower = 1, upper = 6, the hidden sequence is a sequence of length 4 whose elements are in between 1 and 6 (inclusive). [3, 4, 1, 5] and [4, 5, 2, 6] are possible hidden sequences. [5, 6, 3, 7] is not possible since it contains an element greater than 6. [1, 2, 3, 4] is not possible since the differences are not correct. Return the number of possible hidden sequences there are. If there are no possible sequences, return 0. Example 1: Input: differences = [1,-3,4], lower = 1, upper = 6 Output: 2 Explanation: The possible hidden sequences are: - [3, 4, 1, 5] - [4, 5, 2, 6] Thus, we return 2. Example 2: Input: differences = [3,-4,5,1,-2], lower = -4, upper = 5 Output: 4 Explanation: The possible hidden sequences are: - [-3, 0, -4, 1, 2, 0] - [-2, 1, -3, 2, 3, 1] - [-1, 2, -2, 3, 4, 2] - [0, 3, -1, 4, 5, 3] Thus, we return 4. Example 3: Input: differences = [4,-7,2], lower = 3, upper = 6 Output: 0 Explanation: There are no possible hidden sequences. Thus, we return 0. Constraints: n == differences.length 1 <= n <= 105 -105 <= differences[i] <= 105 -105 <= lower <= upper <= 105

Explanation

Here's the approach, followed by the code:

• Calculate Prefix Sums: Iterate through the differences array, calculating the prefix sums. Each prefix sum represents the value of a hidden sequence element relative to the first element.
• Find Min/Max Offsets: Track the minimum and maximum prefix sums encountered. These represent the smallest and largest possible offsets from the initial hidden sequence value.

• Determine Valid Range: Using the min/max offsets and the lower and upper bounds, determine the range of possible starting values for the hidden sequence. The number of integers within this range is the answer.

• Runtime Complexity: O(n), where n is the length of the differences array.

• Storage Complexity: O(1) - constant extra space is used.

Code

    def numberOfArrays(differences, lower, upper):
    """
    Calculates the number of possible hidden sequences given the differences, lower bound, and upper bound.

    Args:
        differences (list of int): The differences between consecutive elements of the hidden sequence.
        lower (int): The lower bound of the hidden sequence elements.
        upper (int): The upper bound of the hidden sequence elements.

    Returns:
        int: The number of possible hidden sequences.
    """

    min_offset = 0
    max_offset = 0
    current_offset = 0

    for diff in differences:
        current_offset += diff
        min_offset = min(min_offset, current_offset)
        max_offset = max(max_offset, current_offset)

    min_start = lower - min_offset
    max_start = upper - max_offset

    count = max(0, max_start - min_start + 1)  # Ensure non-negative result

    return count