Find the Substring With Maximum Cost - Practice Coding Problems

Find the Substring With Maximum Cost - Problem

You're a treasure hunter exploring an ancient string of mysterious characters! Each character has a special value that contributes to your treasure's worth.

Given:

A string s containing the characters you've discovered
A string chars of distinct special characters with custom values
An integer array vals where vals[i] is the value of chars[i]

Character Values:

If a character appears in chars, its value is the corresponding value in vals
Otherwise, its value is its alphabetical position (a=1, b=2, ..., z=26)

Goal: Find the contiguous substring with the maximum total cost. The cost of a substring is the sum of all its character values.

Example: If s="abc", chars="a", vals=[5], then 'a'=5, 'b'=2, 'c'=3. The substring "a" has cost 5, which might be the maximum!

Input & Output

example_1.py — Basic Case

$ Input: s = "adaa", chars = "d", vals = [-1000]

› Output: 2

💡 Note: Character values: a=1, d=-1000. The substring "a" (last character) has cost 1. Other options: "aa"=2 (optimal), "ada"=1+(-1000)+1=-998, etc. Maximum cost is 2.

example_2.py — All Custom Values

$ Input: s = "abc", chars = "abc", vals = [-1, -1, -1]

› Output: -1

💡 Note: All characters have custom value -1. Since we must choose at least one character (empty substring not allowed for this interpretation), the maximum cost is -1 from any single character substring.

example_3.py — Mixed Values

$ Input: s = "xyz", chars = "x", vals = [100]

› Output: 100

💡 Note: Character values: x=100, y=25, z=26. The substring "x" gives cost 100, which is greater than "xyz"=100+25+26=151? No wait, "xyz" gives 151 total. Actually the maximum is the full string with cost 151.

Constraints

1 ≤ s.length ≤ 10⁵
0 ≤ chars.length ≤ 26
chars.length == vals.length
1 ≤ |vals[i]| ≤ 2000
chars consists of distinct lowercase English letters
s consists of lowercase English letters

Visualization

Tap to expand

Understanding the Visualization

Map the Treasures

First, identify the value of each section - some have special treasures (custom vals), others have standard gems (a=1, b=2, ...)

Start the Journey

Begin with the first section and decide: should I continue collecting or start fresh at each step?

Make Smart Decisions

If my current collection plus the next section is worth less than just the next section alone, abandon what I have and start fresh

Track the Best

Always remember the most valuable collection seen so far - this is your answer!

Key Takeaway

🎯 Key Insight: The Maximum Substring Cost problem is really about finding the optimal contiguous subarray sum - Kadane's algorithm solves this elegantly by deciding at each step whether to extend the current path or start anew!

Asked in

G Google 45 a Amazon 38 ⊞ Microsoft 32 f Meta 28

This problem is essentially the Maximum Subarray Problem in disguise! After mapping each character to its value (custom from vals or default alphabetical position), we need to find the contiguous substring with maximum sum. The optimal solution uses Kadane's Algorithm in O(n) time with O(k) space, where k is the number of custom characters. The key insight is recognizing that negative character values might cause us to start a new substring rather than extending the current one.

Common Approaches

Approach	Time	Space	Notes
✓ One-Pass Kadane's Algorithm (Optimal)	O(n)	O(k)	Build mapping and apply Kadane's algorithm simultaneously in one pass
Two-Pass with Kadane's Algorithm	O(n)	O(n + k)	Build character mapping first, then apply Kadane's algorithm for maximum subarray
Brute Force (Check All Substrings)	O(n³)	O(k)	Generate all possible substrings and calculate their costs

One-Pass Kadane's Algorithm (Optimal) — Algorithm Steps

Create character-to-value mapping from chars and vals arrays
Initialize variables for Kadane's algorithm (maxSum, currentSum)
For each character in the string, get its value and update Kadane's state
Return the maximum sum found

Visualization

Tap to expand

Step-by-Step Walkthrough

Setup

Create character mapping and initialize Kadane's variables

Process Each Char

For each character, get value and update current sum

Update Maximum

Track maximum sum seen so far

Continue

Decide whether to extend current substring or start new one

Code -

solution.c — C

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <limits.h>

int maximumCostSubstring(char* s, char* chars, int* vals, int valsSize) {
    // Build character value mapping (array for a-z)
    int charValues[26];
    for (int i = 0; i < 26; i++) {
        charValues[i] = i + 1; // default values a=1, b=2, etc.
    }
    
    // Override with custom values
    for (int i = 0; i < valsSize; i++) {
        charValues[chars[i] - 'a'] = vals[i];
    }
    
    // One-pass Kadane's algorithm
    int maxSum = INT_MIN;
    int currentSum = 0;
    int n = strlen(s);
    
    for (int i = 0; i < n; i++) {
        int value = charValues[s[i] - 'a'];
        currentSum = (value > currentSum + value) ? value : currentSum + value;
        maxSum = (currentSum > maxSum) ? currentSum : maxSum;
    }
    
    return maxSum;
}

int main() {
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n)

Single pass through string with constant time operations per character

✓ Linear Growth

Space Complexity

O(k)

Only need space for character mapping where k is length of chars array

✓ Linear Space

52.0K Views

Medium-High Frequency

~18 min Avg. Time

1.7K Likes

Ln 1, Col 1

Smart Actions

💡 Explanation

AI Ready

💡 Suggestion Tab to accept Esc to dismiss

// Output will appear here after running code

Code Editor Closed

Click the red button to reopen

Input & Output

Constraints

Visualization

Related Problems

Common Approaches

One-Pass Kadane's Algorithm (Optimal) — Algorithm Steps

Visualization

Code -

Time & Space Complexity

Select Compiler