Introduction

In this blog post, we will explore how to solve the LeetCode problem "1630" 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

A sequence of numbers is called arithmetic if it consists of at least two elements, and the difference between every two consecutive elements is the same. More formally, a sequence s is arithmetic if and only if s[i+1] - s[i] == s[1] - s[0] for all valid i. For example, these are arithmetic sequences: 1, 3, 5, 7, 9 7, 7, 7, 7 3, -1, -5, -9 The following sequence is not arithmetic: 1, 1, 2, 5, 7 You are given an array of n integers, nums, and two arrays of m integers each, l and r, representing the m range queries, where the ith query is the range [l[i], r[i]]. All the arrays are 0-indexed. Return a list of boolean elements answer, where answer[i] is true if the subarray nums[l[i]], nums[l[i]+1], ... , nums[r[i]] can be rearranged to form an arithmetic sequence, and false otherwise. Example 1: Input: nums = [4,6,5,9,3,7], l = [0,0,2], r = [2,3,5] Output: [true,false,true] Explanation: In the 0th query, the subarray is [4,6,5]. This can be rearranged as [6,5,4], which is an arithmetic sequence. In the 1st query, the subarray is [4,6,5,9]. This cannot be rearranged as an arithmetic sequence. In the 2nd query, the subarray is [5,9,3,7]. This can be rearranged as [3,5,7,9], which is an arithmetic sequence. Example 2: Input: nums = [-12,-9,-3,-12,-6,15,20,-25,-20,-15,-10], l = [0,1,6,4,8,7], r = [4,4,9,7,9,10] Output: [false,true,false,false,true,true] Constraints: n == nums.length m == l.length m == r.length 2 <= n <= 500 1 <= m <= 500 0 <= l[i] < r[i] < n -105 <= nums[i] <= 105

Explanation

Here's the breakdown of the approach, complexities, and the Python code:

• High-Level Approach:

  • For each query (l[i], r[i]), extract the corresponding subarray from nums.
  • Check if the subarray can be rearranged into an arithmetic sequence. This involves finding the minimum and maximum values, calculating the common difference, and verifying if all elements fit the arithmetic progression. Using a set to check for existence is crucial for efficiency.
  • Store the boolean result (True/False) for each query in a list and return it.

• Complexity:

  • Runtime: O(m * n), where m is the number of queries and n is the maximum size of a subarray.
  • Storage: O(n), where n is the maximum size of a subarray (for the set).

Code

    def canMakeArithmeticProgression(arr):
    """
    Checks if an array can be rearranged to form an arithmetic progression.
    """
    if len(arr) <= 1:
        return True

    min_val = min(arr)
    max_val = max(arr)
    n = len(arr)

    if min_val == max_val:
        return True

    if (max_val - min_val) % (n - 1) != 0:
        return False

    diff = (max_val - min_val) // (n - 1)

    if diff == 0:  # all numbers must be same.
       return len(set(arr)) == 1

    seen = set()
    for num in arr:
        if (num - min_val) % diff != 0:
            return False
        if (num - min_val) // diff >= n:
            return False
        seen.add(num)

    return len(seen) == n

def solve():
    """
    Solves the arithmetic sequence query problem.
    """
    nums = [4,6,5,9,3,7]
    l = [0,0,2]
    r = [2,3,5]
    # nums = [-12,-9,-3,-12,-6,15,20,-25,-20,-15,-10]
    # l = [0,1,6,4,8,7]
    # r = [4,4,9,7,9,10]


    result = []
    for i in range(len(l)):
        sub_array = nums[l[i]:r[i] + 1]
        result.append(canMakeArithmeticProgression(sub_array))
    return result

def areArithmetic(nums, l, r):
    """
    Given an array of n integers, nums, and two arrays of m integers each, l and r, representing the m range queries, where the ith query is the range [l[i], r[i]].
    Return a list of boolean elements answer, where answer[i] is true if the subarray nums[l[i]], nums[l[i]+1], ... , nums[r[i]] can be rearranged to form an arithmetic sequence, and false otherwise.
    """
    result = []
    for i in range(len(l)):
        sub_array = nums[l[i]:r[i] + 1]
        result.append(canMakeArithmeticProgression(sub_array))
    return result

# Example Usage (inside the code for demonstration):
if __name__ == "__main__":
    nums = [4, 6, 5, 9, 3, 7]
    l = [0, 0, 2]
    r = [2, 3, 5]
    print(areArithmetic(nums, l, r))

    nums = [-12,-9,-3,-12,-6,15,20,-25,-20,-15,-10]
    l = [0,1,6,4,8,7]
    r = [4,4,9,7,9,10]
    print(areArithmetic(nums, l, r))