Python program to test whether all elements in a list are at most K apart

In many programming scenarios, we will encounter situations where we need to determine whether all elements in a list are at most K positions apart. This problem arises in various fields such as data analysis, sequence processing, and algorithmic challenges. Being able to test and verify these conditions is critical to ensuring the integrity and correctness of our programs.

In this article, we will explore a Python program to solve this problem efficiently. We will discuss the concept, present a step-by-step approach to solving the problem, and provide a working code implementation. After reading this article, you will have a clear understanding of how to check if elements in a list are at most K positions apart using Python.

Understanding Questions

Before we delve into the solution, let’s first understand the problem statement in detail.

Given a list of elements, we need to determine whether each element is at most K positions away from any other largest element in the list. In other words, we want to check if the largest element of the list and any other largest element are within a distance of K positions.

To illustrate this, consider the following example -

Input: [2, 7, 4, 9, 5, 1]
K = 2

In this example, the largest element is 9 and is 2 or less positions away from the other largest element (7). Therefore, the condition is met.

Now, let’s give another example−

Input: [3, 8, 6, 1, 9, 2]
K = 3

In this example, the largest element is 9, but it is 4 positions away from the next largest element (8), so the condition is not met.

Our task is to write a Python program that takes as input a list of elements and K values ​​and returns whether a given condition is met.

Methods and Algorithms

To solve this problem, we can adopt a simple method, which is to iterate the list and compare each element with the largest element found so far. As we iterate over the list, we keep track of the largest element and its position.

This is a step-by-step algorithm for implementing our method -

• Initialize two variables -

• max_element stores the largest element found so far (initialized to the first element of the list).

• max_index stores the index of the largest element (initialized to 0).

• Iterate over the remaining elements of the list from index 1 to n-1.

  If the current element is greater than max_element, update max_element to the current element and max_index to the current index.

• After the iteration ends, we get the largest element in the list and its index.

• Now, iterate over the list again, and for each element, check if it is the largest element, or if it is at most K positions away from the largest element. If any element does not meet this condition, False is returned.

• Returns True if all elements meet the condition.

By following this approach, we can efficiently determine whether all elements in a list are at most K positions away from any other largest element.

In the next section, we will implement this algorithm in Python.

Implementation

Now, let us implement the algorithm discussed in the previous section using Python code. Below is a code snippet demonstrating the solution−

def test_k_apart(nums, k):
   max_element = nums[0]
   max_index = 0

   # Find the maximum element and its index
   for i in range(1, len(nums)):
      if nums[i] > max_element:
         max_element = nums[i]
         max_index = i

   # Check if all elements are at most K positions away
   for i in range(len(nums)):
      if nums[i] != max_element and abs(i - max_index) > k:
         return False

   return True

In this code, we define a function test_k_apart that takes a list of numbers (nums) and the value k as parameters. This function iterates the list to find the largest element and its index using a simple comparison. Then, it iterates the list again to check if each element is the maximum element or is at most K positions away from the maximum element. If any element does not meet this condition, the function returns False. Otherwise, returns True, indicating that all elements satisfy the condition.

Example

Let's test this function with an example and see how it works -

nums = [5, 9, 7, 12, 9, 3, 7]
k = 2

result = test_k_apart(nums, k)
print(result)  # Output: True

In this example, the list nums contains elements at most 2 positions away from the largest element (12), so the function returns True.

Output

True

Test Case

To demonstrate how the program works, let's consider some test cases with different input lists and k values ​​-

Test Case 1 −

nums = [5, 2, 7, 1, 8]
k = 2

In this example, the maximum element in the list is 8. The position of the elements relative to the largest element is as follows: [3, 0, 1, 2, 0]. The absolute difference is [3, 0, 1, 2, 0]. Since the absolute difference of all elements is within the range k=2, the expected output is True.

Test Case 2 −

nums = [10, 4, 5, 8, 2]
k = 1

In this example, the maximum element in the list is 10. The position of the elements relative to the largest element is as follows: [0, 1, 2, 1, 3]. The absolute difference is [0, 1, 2, 1, 3]. The element at index 4 (value 2) has an absolute difference of 3, which is greater than k=1. Therefore, the expected output is False.

Test Case 3−

nums = [3, 6, 9, 12, 15]
k = 3

在本例中，列表中的最大元素为 15。元素相对于最大元素的位置如下：[3, 2, 1, 0, 0]。绝对差为 [3, 2, 1, 0, 0]。由于所有元素的绝对差异在 k=3 范围内，因此预期输出为 True。

结论

在本文中，我们讨论了一个 Python 程序，用于测试列表中的所有元素是否是除最大元素之外的 k 个位置中的最大值。我们探索了一种利用查找最大元素并计算每个元素相对于最大值的绝对差的概念的方法。

通过使用简单的循环并检查绝对差异，我们能够确定是否所有元素都满足给定条件。通过理解和应用这个程序，您可以有效地检查列表中的元素是否在距最大元素的指定范围内。这在各种场景中都很有用，例如验证数据完整性或识别序列中的模式。

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