LeetCode #2606 — MEDIUM

Find the Substring With Maximum Cost

Move from brute-force thinking to an efficient approach using array strategy.

Solve on LeetCode
The Problem

Problem Statement

You are given a string s, a string chars of distinct characters and an integer array vals of the same length as chars.

The cost of the substring is the sum of the values of each character in the substring. The cost of an empty string is considered 0.

The value of the character is defined in the following way:

  • If the character is not in the string chars, then its value is its corresponding position (1-indexed) in the alphabet.
    • For example, the value of 'a' is 1, the value of 'b' is 2, and so on. The value of 'z' is 26.
  • Otherwise, assuming i is the index where the character occurs in the string chars, then its value is vals[i].

Return the maximum cost among all substrings of the string s.

Example 1:

Input: s = "adaa", chars = "d", vals = [-1000]
Output: 2
Explanation: The value of the characters "a" and "d" is 1 and -1000 respectively.
The substring with the maximum cost is "aa" and its cost is 1 + 1 = 2.
It can be proven that 2 is the maximum cost.

Example 2:

Input: s = "abc", chars = "abc", vals = [-1,-1,-1]
Output: 0
Explanation: The value of the characters "a", "b" and "c" is -1, -1, and -1 respectively.
The substring with the maximum cost is the empty substring "" and its cost is 0.
It can be proven that 0 is the maximum cost.

Constraints:

  • 1 <= s.length <= 105
  • s consist of lowercase English letters.
  • 1 <= chars.length <= 26
  • chars consist of distinct lowercase English letters.
  • vals.length == chars.length
  • -1000 <= vals[i] <= 1000
Patterns Used

Roadmap

  1. Brute Force Baseline
  2. Core Insight
  3. Algorithm Walkthrough
  4. Edge Cases
  5. Full Annotated Code
  6. Interactive Study Demo
  7. Complexity Analysis
Step 01

Brute Force Baseline

Problem summary: You are given a string s, a string chars of distinct characters and an integer array vals of the same length as chars. The cost of the substring is the sum of the values of each character in the substring. The cost of an empty string is considered 0. The value of the character is defined in the following way: If the character is not in the string chars, then its value is its corresponding position (1-indexed) in the alphabet. For example, the value of 'a' is 1, the value of 'b' is 2, and so on. The value of 'z' is 26. Otherwise, assuming i is the index where the character occurs in the string chars, then its value is vals[i]. Return the maximum cost among all substrings of the string s.

Baseline thinking

Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.

Pattern signal: Array · Hash Map · Dynamic Programming

Example 1

"adaa"
"d"
[-1000]

Example 2

"abc"
"abc"
[-1,-1,-1]

Related Problems

  • Maximum Subarray (maximum-subarray)
Step 02

Core Insight

What unlocks the optimal approach

  • Create a new integer array where arr[i] denotes the value of character s[i].
  • We can use Kadane’s maximum subarray sum algorithm to find the maximum cost.
Interview move: turn each hint into an invariant you can check after every iteration/recursion step.
Step 03

Algorithm Walkthrough

Iteration Checklist

  1. Define state (indices, window, stack, map, DP cell, or recursion frame).
  2. Apply one transition step and update the invariant.
  3. Record answer candidate when condition is met.
  4. Continue until all input is consumed.
Use the first example testcase as your mental trace to verify each transition.
Step 04

Edge Cases

Minimum Input
Single element / shortest valid input
Validate boundary behavior before entering the main loop or recursion.
Duplicates & Repeats
Repeated values / repeated states
Decide whether duplicates should be merged, skipped, or counted explicitly.
Extreme Constraints
Upper-end input sizes
Re-check complexity target against constraints to avoid time-limit issues.
Invalid / Corner Shape
Empty collections, zeros, or disconnected structures
Handle special-case structure before the core algorithm path.
Step 05

Full Annotated Code

Source-backed implementations are provided below for direct study and interview prep.

// Accepted solution for LeetCode #2606: Find the Substring With Maximum Cost
class Solution {
    public int maximumCostSubstring(String s, String chars, int[] vals) {
        int[] d = new int[26];
        for (int i = 0; i < d.length; ++i) {
            d[i] = i + 1;
        }
        int m = chars.length();
        for (int i = 0; i < m; ++i) {
            d[chars.charAt(i) - 'a'] = vals[i];
        }
        int ans = 0, tot = 0, mi = 0;
        int n = s.length();
        for (int i = 0; i < n; ++i) {
            int v = d[s.charAt(i) - 'a'];
            tot += v;
            ans = Math.max(ans, tot - mi);
            mi = Math.min(mi, tot);
        }
        return ans;
    }
}
Step 06

Interactive Study Demo

Use this to step through a reusable interview workflow for this problem.

Press Step or Run All to begin.
Step 07

Complexity Analysis

Time
O(n)
Space
O(C)

Approach Breakdown

RECURSIVE
O(2ⁿ) time
O(n) space

Pure recursion explores every possible choice at each step. With two choices per state (take or skip), the decision tree has 2ⁿ leaves. The recursion stack uses O(n) space. Many subproblems are recomputed exponentially many times.

DYNAMIC PROGRAMMING
O(n × m) time
O(n × m) space

Each cell in the DP table is computed exactly once from previously solved subproblems. The table dimensions determine both time and space. Look for the state variables — each unique combination of state values is one cell. Often a rolling array can reduce space by one dimension.

Shortcut: Count your DP state dimensions → that’s your time. Can you drop one? That’s your space optimization.
Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Off-by-one on range boundaries

Wrong move: Loop endpoints miss first/last candidate.

Usually fails on: Fails on minimal arrays and exact-boundary answers.

Fix: Re-derive loops from inclusive/exclusive ranges before coding.

Mutating counts without cleanup

Wrong move: Zero-count keys stay in map and break distinct/count constraints.

Usually fails on: Window/map size checks are consistently off by one.

Fix: Delete keys when count reaches zero.

State misses one required dimension

Wrong move: An incomplete state merges distinct subproblems and caches incorrect answers.

Usually fails on: Correctness breaks on cases that differ only in hidden state.

Fix: Define state so each unique subproblem maps to one DP cell.