Maximum Gap

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class Solution:
    def maximumGap(self, nums: List[int]) -> int:
        n = len(nums)
        if n < 2:
            return 0

        min_num, max_num = min(nums), max(nums)
        # Calculate the bucket size and number of buckets
        bucket_size = max(1, (max_num - min_num) // (n - 1))
        bucket_count = (max_num - min_num) // bucket_size + 1
        buckets = [[float('inf'), float('-inf')] for _ in range(bucket_count)]

        # Put the numbers into the buckets
        for num in nums:
            idx = (num - min_num) // bucket_size
            buckets[idx][0] = min(buckets[idx][0], num)
            buckets[idx][1] = max(buckets[idx][1], num)

        # Calculate the maximum gap between adjacent non-empty buckets
        max_gap = 0
        prev_max = min_num
        for i in range(bucket_count):
            if buckets[i][0] == float('inf'):
                continue
            max_gap = max(max_gap, buckets[i][0] - prev_max)
            prev_max = buckets[i][1]

        return max_gap

Identifying Problem Isomorphism

“164. Maximum Gap” belongs to the category of sorting and array manipulation. The task is to find the maximum difference between two consecutive elements in a sorted version of the given array, which involves sorting and scanning the array linearly.

Here are 10 problems to prepare for tackling this problem:

  1. Problem 283. Move Zeroes: This problem helps understand how to manipulate elements in an array, a skill useful for the Maximum Gap problem.

  2. Problem 88. Merge Sorted Array: This problem involves merging two sorted arrays, providing insight into how sorted arrays behave.

  3. Problem 26. Remove Duplicates from Sorted Array: This problem helps understand the characteristics of sorted arrays, and how to manipulate and analyze them.

  4. Problem 167. Two Sum II - Input array is sorted: The skill of operating on a sorted array is necessary for solving the Maximum Gap problem.

  5. Problem 349. Intersection of Two Arrays: This problem requires sorting and scanning, two key operations in the Maximum Gap problem.

  6. Problem 215. Kth Largest Element in an Array: This problem can be solved through sorting, which is a crucial step in solving the Maximum Gap problem.

  7. Problem 75. Sort Colors: This problem provides practice for in-place sorting, which can be helpful for the Maximum Gap problem.

  8. Problem 350. Intersection of Two Arrays II: This problem requires sorting and scanning arrays, similar to the Maximum Gap problem.

  9. Problem 217. Contains Duplicate: This problem gives practice in sorting and linearly scanning an array.

  10. Problem 414. Third Maximum Number: In this problem, you have to find the third maximum number in a non-sorted array, which involves sorting and array manipulation.

These cover how to manipulate arrays and work with sorted arrays, skills that are key to solving the Maximum Gap problem. Starting from the basics, these problems gradually increase in complexity, preparing you for more challenging problems.

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class Solution:
    def maximumGap(self, nums: List[int]) -> int:
        nums = sorted(nums)
        min = float("-inf")
        if len(nums)<2:
            return 0
        for i in range(len(nums)-1):
            x = abs(nums[i]-nums[i+1])
            if min < x:
                min=x
        return min

Problem Classification

The problem asks for the largest difference between consecutive numbers in a sorted version of a given list. It’s about finding the largest gap in a list, so it’s a Gap Finding Problem.

Language Agnostic Coding Drills

  1. Using Lists or Arrays: This is a fundamental concept in most modern languages. The list is a most versatile datatype available in Python which can be written as a list of comma-separated values (items) between square brackets.

    Drill: Create a list of integers, print the list, add a new element to the end, and remove an element from the list based on an index provided.

  2. Sorting Algorithms: Sorting is arranging of data (integer, float, string etc.) in some particular order. The order could be either ascending order or descending order. This is a common functionality in most modern languages.

    Drill: Implement a sorting algorithm, such as Bubble Sort or Quick Sort, to sort a list of integers in ascending order.

  3. Iterating through Lists/Arrays: Iteration is a fundamental programming concept, and in Python, you can iterate over a list using a for loop.

    Drill: Given a list of integers, write a function that iterates through the list and prints each integer.

  4. Using Conditionals: Conditionals (if, elif, else) are used in Python for decision making.

    Drill: Write a function that takes an integer as input. The function should print “Positive” if the number is positive, “Negative” if it’s negative, and “Zero” if it’s 0.

  5. Finding the Maximum/Minimum: Finding the maximum or minimum value in a list or array is a common operation in most programming languages.

    Drill: Write a function that takes a list of integers as input and returns the maximum and minimum integer in the list.

  6. Mathematical Operations: In the given code, subtraction (-) is used to calculate the difference between numbers. This is a basic operation in all modern programming languages.

    Drill: Write a function that takes two integers as input and returns their sum, difference, product, and quotient.

When you’ve practiced these drills separately, you can combine them to write the given function. The function first checks if there are enough elements in the list, then sorts the list, and finally finds the maximum difference between adjacent elements.

Targeted Drills in Python

  1. Using Lists or Arrays: Drill: Create a list of integers, print the list, add a new element to the end, and remove an element from the list based on an index provided.

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    nums = [3, 2, 7, 8, 1]
print(nums)  # Prints: [3, 2, 7, 8, 1]
nums.append(10)
print(nums)  # Prints: [3, 2, 7, 8, 1, 10]
del nums[2]
print(nums)  # Prints: [3, 2, 8, 1, 10]

  2. Sorting Algorithms: Drill: Implement a sorting algorithm, such as Bubble Sort or Quick Sort, to sort a list of integers in ascending order.

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    def bubble_sort(nums):
    for i in range(len(nums)):
        for j in range(len(nums) - i - 1):
            if nums[j] > nums[j + 1]:
                nums[j], nums[j + 1] = nums[j + 1], nums[j]
    return nums

nums = [3, 2, 7, 8, 1]
print(bubble_sort(nums))  # Prints: [1, 2, 3, 7, 8]

  3. Iterating through Lists/Arrays: Drill: Given a list of integers, write a function that iterates through the list and prints each integer.

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    def print_elements(nums):
    for num in nums:
        print(num)

nums = [3, 2, 7, 8, 1]
print_elements(nums)  # Prints: 3 2 7 8 1

  4. Using Conditionals: Drill: Write a function that takes an integer as input. The function should print “Positive” if the number is positive, “Negative” if it’s negative, and “Zero” if it’s 0.

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    def classify_number(n):
    if n > 0:
        print("Positive")
    elif n < 0:
        print("Negative")
    else:
        print("Zero")

classify_number(10)  # Prints: Positive
classify_number(-5)  # Prints: Negative
classify_number(0)  # Prints: Zero

  5. Finding the Maximum/Minimum: Drill: Write a function that takes a list of integers as input and returns the maximum and minimum integer in the list.

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    def find_max_min(nums):
    return max(nums), min(nums)

nums = [3, 2, 7, 8, 1]
print(find_max_min(nums))  # Prints: (8, 1)

  6. Mathematical Operations: Drill: Write a function that takes two integers as input and returns their sum, difference, product, and quotient.

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    def compute_ops(a, b):
    return a + b, a - b, a * b, a / b if b != 0 else "Undefined"

print(compute_ops(10, 2))  # Prints: (12, 8, 20, 5.0)