Hurdle Jump in Python

Given an array of hurdle heights and a jumper's jump height, determine whether or not the hurdler can clear all the hurdles. If they can, return True; otherwise return False.

A hurdler can clear a hurdle if their jump height is greater than or equal to the hurdle height.

Examples:

hurdleJump([1, 2, 3, 4, 5], 5) ➞ true

hurdleJump([5, 5, 3, 4, 5], 3) ➞ false

hurdleJump([5, 4, 5, 6], 10) ➞ true

hurdleJump([1, 2, 1], 1) ➞ false

Note: Return True for the edge case of an empty array of hurdles. (Zero hurdles means that any jump height can clear them).

Understanding the Problem

The core challenge of this problem is to determine if the jumper's height is sufficient to clear all the hurdles in the given array. This problem is significant in scenarios where we need to check if a certain threshold is met across a series of values, which is a common requirement in various applications such as gaming, sports analytics, and more.

Potential pitfalls include not handling the edge case of an empty array correctly or misunderstanding the comparison condition (greater than or equal to).

Approach

To solve this problem, we need to check if the jumper's height is greater than or equal to the maximum height of the hurdles. If it is, the jumper can clear all the hurdles; otherwise, they cannot.

Let's discuss a naive solution and then an optimized solution:

Naive Solution

The naive approach would be to iterate through each hurdle and check if the jumper's height is sufficient for each one. This approach is not optimal because it involves multiple comparisons even if we find a hurdle that the jumper cannot clear early in the array.

Optimized Solution

A more optimized approach is to find the maximum height of the hurdles and compare it with the jumper's height. This way, we only need to make a single comparison after finding the maximum height.

Algorithm

Here is a step-by-step breakdown of the optimized algorithm:

Check if the array of hurdles is empty. If it is, return True.
Find the maximum height in the array of hurdles.
Compare the maximum height with the jumper's height.
If the jumper's height is greater than or equal to the maximum height, return True; otherwise, return False.

Code Implementation

def hurdleJump(hurdles, jump_height):
    # Check if the array of hurdles is empty
    if not hurdles:
        return True
    
    # Find the maximum height in the array of hurdles
    max_hurdle = max(hurdles)
    
    # Compare the maximum height with the jumper's height
    return jump_height >= max_hurdle

# Test cases
print(hurdleJump([1, 2, 3, 4, 5], 5))  # ➞ True
print(hurdleJump([5, 5, 3, 4, 5], 3))  # ➞ False
print(hurdleJump([5, 4, 5, 6], 10))    # ➞ True
print(hurdleJump([1, 2, 1], 1))        # ➞ False

Complexity Analysis

The time complexity of the optimized solution is O(n), where n is the number of hurdles. This is because we need to iterate through the array once to find the maximum height. The space complexity is O(1) as we are not using any additional space that scales with the input size.

Edge Cases

Potential edge cases include:

An empty array of hurdles: The function should return True.
All hurdles having the same height: The function should correctly compare the jumper's height with this uniform height.
Jumper's height being exactly equal to the maximum hurdle height: The function should return True.

Testing

To test the solution comprehensively, we should include a variety of test cases:

Simple cases with a few hurdles.
Cases where the jumper's height is less than, equal to, and greater than the maximum hurdle height.
Edge cases such as an empty array of hurdles.

Thinking and Problem-Solving Tips

When approaching such problems, it's essential to:

Understand the problem requirements and constraints thoroughly.
Consider edge cases and how they should be handled.
Think about the most efficient way to solve the problem, avoiding unnecessary computations.
Practice solving similar problems to improve problem-solving skills and familiarity with common patterns.

Conclusion

In this blog post, we discussed the problem of determining if a jumper can clear all hurdles given their heights. We explored a naive solution and an optimized solution, provided a detailed algorithm, and implemented the solution in Python. We also analyzed the complexity and discussed edge cases and testing strategies. Understanding and solving such problems is crucial for developing strong problem-solving skills and improving algorithmic thinking.

Additional Resources

For further reading and practice, consider the following resources:

LeetCode - A platform for practicing coding problems.
GeeksforGeeks - A website with tutorials and problems on various algorithms and data structures.
HackerRank - Another platform for coding challenges and competitions.

Hurdle Jump in Python (Time Complexity: O(n))