How do you solve Minimum Cost Tree From Leaf Values on LeetCode?

Minimum Cost Tree From Leaf Values (LeetCode #1130) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n³) time complexity and O(n²) space complexity. Key insight: Dynamic programming can significantly reduce redundant calculations.

What is the brute force solution for Minimum Cost Tree From Leaf Values?

The brute force approach for Minimum Cost Tree From Leaf Values is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves generating all possible binary trees from the given leaf values and calculating the cost for each tree. This is inefficient as it explores all combinations, leading to a high time complexity. The optimal Optimal Solution approach improves this to O(n³).

What algorithm or data structure is used to solve Minimum Cost Tree From Leaf Values?

Minimum Cost Tree From Leaf Values uses the following concepts: Array, Dynamic Programming, Stack, Greedy, Monotonic Stack. The recommended patterns to study are: Dynamic Programming, Divide and Conquer.

What are the interview tips for Minimum Cost Tree From Leaf Values?

Clearly explain your thought process and approach before coding. Consider edge cases and constraints while designing your solution. Practice explaining your code and logic as you write it.

What are common mistakes when solving Minimum Cost Tree From Leaf Values?

Failing to correctly calculate the maximum values for subarrays. Not considering all possible partitions when calculating costs.

#1130

Minimum Cost Tree From Leaf Values

Medium

ArrayDynamic ProgrammingStackGreedyMonotonic StackDynamic ProgrammingDivide and Conquer

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n³)
Space	O(1)	O(n²)

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Intuition

Time O(n³)Space O(n²)

The optimal solution uses dynamic programming to store intermediate results, avoiding redundant calculations. By leveraging the properties of the binary tree structure, we can efficiently compute the minimum cost without generating all possible trees.

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Algorithm

3 steps

1Step 1: Create a DP table where dp[i][j] represents the minimum cost for the subarray arr[i] to arr[j].
2Step 2: Iterate through all possible lengths of subarrays and fill the DP table based on previously computed values.
3Step 3: For each subarray, find the maximum leaf values and compute the cost using the DP table.

solution.py12 lines

1def minCost(arr):
2    n = len(arr)
3    dp = [[0] * n for _ in range(n)]
4    for length in range(2, n + 1):
5        for i in range(n - length + 1):
6            j = i + length - 1
7            max_left = max(arr[i:j + 1])
8            for k in range(i, j):
9                max_right = max(arr[k + 1:j + 1])
10                cost = max_left * max_right + dp[i][k] + dp[k + 1][j]
11                dp[i][j] = min(dp[i][j], cost) if dp[i][j] else cost
12    return dp[0][n - 1]

ℹ

Complexity note: The time complexity is O(n³) due to the nested loops for subarray lengths, starting index, and partition index. The space complexity is O(n²) because we maintain a DP table to store results for subarrays.

1Dynamic programming can significantly reduce redundant calculations.
2Understanding tree structures helps in optimizing the problem-solving approach.

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