How do you solve Find the Substring With Maximum Cost on LeetCode?

Find the Substring With Maximum Cost (LeetCode #2606) 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 character values is crucial to solving the problem efficiently.

What is the brute force solution for Find the Substring With Maximum Cost?

The brute force approach for Find the Substring With Maximum Cost is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach involves checking all possible substrings of the string `s` and calculating their costs. This is straightforward but inefficient for larger strings due to its quadratic time complexity. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Find the Substring With Maximum Cost?

Find the Substring With Maximum Cost uses the following concepts: Array, Hash Table, String, Dynamic Programming. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Find the Substring With Maximum Cost?

Always clarify the problem requirements and constraints before jumping into coding. Think about edge cases, such as all negative values or empty strings. Practice implementing Kadane’s algorithm, as it’s a common pattern in substring problems.

What are common mistakes when solving Find the Substring With Maximum Cost?

Not correctly handling the case of negative values, leading to incorrect maximum costs. Forgetting to check for the empty substring case.

#2606

Find the Substring With Maximum Cost

Medium

ArrayHash TableStringDynamic ProgrammingHash 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 approach uses a modified version of Kadane’s algorithm to find the maximum sum of a contiguous subarray, which in this case corresponds to the maximum cost of a substring. This is efficient and avoids the need to check all substrings explicitly.

⚙️

Algorithm

4 steps

1Step 1: Create an array to store the values of each character in `s` based on `chars` and `vals`.
2Step 2: Initialize variables to track the current cost and maximum cost found.
3Step 3: Iterate through the value array and apply Kadane’s algorithm to find the maximum contiguous sum.
4Step 4: Return the maximum cost found, ensuring it is not negative.

solution.py20 lines

1# Full working Python code
2
3def calculate_cost(c, chars, vals):
4    if c in chars:
5        return vals[chars.index(c)]
6    return ord(c) - ord('a') + 1
7
8def max_cost_substring(s, chars, vals):
9    n = len(s)
10    values = [calculate_cost(s[i], chars, vals) for i in range(n)]
11    max_cost = 0
12    current_cost = 0
13    for value in values:
14        current_cost = max(value, current_cost + value)
15        max_cost = max(max_cost, current_cost)
16    return max_cost
17
18# Example usage:
19print(max_cost_substring("adaa", "d", [-1000]))  # Output: 2
20

ℹ

Complexity note: This complexity is due to the single pass through the string to calculate values and another pass to apply Kadane’s algorithm, making it linear in relation to the input size.

1Understanding character values is crucial to solving the problem efficiently.
2Kadane's algorithm is a powerful tool for finding maximum subarray sums.

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