Aang’s Airbending Journey - codepath/compsci_guides GitHub Wiki

Unit 12 Session 1 Advanced (Click for link to problem statements)

Problem Highlights

  • 💡 Difficulty: Medium
  • ⏰ Time to complete: 20 mins
  • 🛠️ Topics: Greedy Algorithms

1: U-nderstand

Understand what the interviewer is asking for by using test cases and questions about the problem.

  • Established a set (2-3) of test cases to verify their own solution later.
  • Established a set (1-2) of edge cases to verify their solution handles complexities.
  • Have fully understood the problem and have no clarifying questions.
  • Have you verified any Time/Space Constraints for this problem?
  • What is the goal of the problem?
    • The goal is to determine if Aang can reach the last platform given the jump distances at each platform.
  • What does each element in the array represent?
    • Each element represents the maximum jump Aang can perform from that platform.
HAPPY CASE
Input: 
    platforms = [2, 3, 1, 1, 4]
Output: 
    True
Explanation:
    Aang can jump from platform 0 to 1, then directly to the last platform.

EDGE CASE
Input: 
    platforms = [3, 2, 1, 0, 4]
Output: 
    False
Explanation:
    Aang is stuck at platform 3 because its maximum jump is 0, so he can't reach the last platform.

2: M-atch

Match what this problem looks like to known categories of problems, e.g. Arrays or Dynamic Programming, and strategies or patterns in those categories.

For Aang’s Airbending Journey, we want to consider the following approaches:

  • Greedy Algorithm: The problem can be solved by keeping track of the farthest platform Aang can reach as he jumps from each platform. If at any point Aang can't move forward, he gets stuck, and the answer is False.

3: P-lan

Plan the solution with appropriate visualizations and pseudocode.

General Idea: Start at the first platform and update the farthest point Aang can reach based on the maximum jump distance from each platform. If at any point Aang gets stuck (i.e., can't reach the next platform), return False. If he can reach or exceed the last platform, return True.

Steps:

  1. Initialize variables:

    • farthest: Keeps track of the farthest point Aang can reach, starting at 0.

  2. Iterate over each platform:

    • For each platform i, check if Aang can reach it (i.e., i <= farthest).
    • Update farthest to be the maximum of the current farthest point and i + platforms[i].
    • If farthest exceeds or reaches the last platform, return True.

  3. Final check:

    • If the loop completes without Aang getting stuck, return False.

4: I-mplement

Implement the code to solve the algorithm.

def aang_journey(platforms):
    n = len(platforms)
    farthest = 0  # The farthest point Aang can reach
    
    for i in range(n):
        # If Aang can't reach this platform, he is stuck
        if i > farthest:
            return False
        
        # Update the farthest point Aang can reach
        farthest = max(farthest, i + platforms[i])
        
        # If Aang can already reach the last platform, return True
        if farthest >= n - 1:
            return True
    
    return False

5: R-eview

Review the code by running specific example(s) and recording values (watchlist) of your code's variables along the way.

Example 1:

  • Input: platforms = [2, 3, 1, 1, 4]
  • Expected Output: True

Example 2:

  • Input: platforms = [3, 2, 1, 0, 4]
  • Expected Output: False

6: E-valuate

Evaluate the performance of your algorithm and state any strong/weak or future potential work.

Assume n is the length of the input list platforms.

  • Time Complexity: O(n) because we iterate through the list once.
  • Space Complexity: O(1) since we only use a few variables.