How do you solve Pyramid Transition Matrix on LeetCode?

Pyramid Transition Matrix (LeetCode #756) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Understanding the structure of the pyramid is crucial.

What is the brute force solution for Pyramid Transition Matrix?

The brute force approach for Pyramid Transition Matrix is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach tries all possible combinations to build the pyramid from the bottom row up. It checks if each combination of blocks can form a valid triangle using the allowed patterns. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Pyramid Transition Matrix?

Pyramid Transition Matrix uses the following concepts: Hash Table, String, Backtracking, Bit Manipulation. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Pyramid Transition Matrix?

Explain your thought process clearly while coding. Discuss edge cases and how your solution handles them. Be prepared to optimize your solution if asked.

What are common mistakes when solving Pyramid Transition Matrix?

Failing to consider all possible combinations of top blocks. Not using memoization effectively, leading to repeated calculations.

#756

Pyramid Transition Matrix

Medium

Hash TableStringBacktrackingBit ManipulationHash MapArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

💡

Intuition

Time O(n)Space O(n)

The optimal solution uses backtracking with memoization to efficiently explore valid configurations. It avoids redundant calculations by storing results of previously computed states.

⚙️

Algorithm

3 steps

1Step 1: Create a set of allowed patterns for quick access.
2Step 2: Use a recursive function to build the pyramid from the bottom row, checking if each combination can form a valid triangle.
3Step 3: Use memoization to store results of previously computed states to avoid repeated calculations.

solution.py22 lines

1def pyramidTransition(bottom, allowed):
2    allowed_set = set(allowed)
3    memo = {}
4    def can_build(current):
5        if len(current) == 1:
6            return True
7        if current in memo:
8            return memo[current]
9        next_row = []
10        for i in range(len(current) - 1):
11            found = False
12            for c in 'ABCDEFGHIJKLMNOPQRSTUVWXYZ':
13                if current[i:i+2] in allowed_set:
14                    next_row.append(c)
15                    found = True
16            if not found:
17                memo[current] = False
18                return False
19        result = can_build(''.join(next_row))
20        memo[current] = result
21        return result
22    return can_build(bottom)

ℹ

Complexity note: The time complexity is O(n) due to memoization, which allows us to avoid redundant calculations by storing results of previously computed states. The space complexity is O(n) for storing the memoization map.

1Understanding the structure of the pyramid is crucial.
2Using memoization can significantly reduce computation time.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.