#1672

Easy

LeetCode Problem Workspace

Richest Customer Wealth

Calculate the richest customer's wealth by summing the amounts in each customer's bank accounts in a matrix.

Problem Statement

You are given an m x n integer grid called 'accounts', where each element accounts[i][j] represents the amount of money the i-th customer has in the j-th bank account. The goal is to return the wealth of the richest customer.

A customer's wealth is calculated by summing the amounts of money they hold across all their bank accounts. The richest customer is the one with the maximum wealth. Your task is to identify and return this maximum wealth value.

Examples

Example 1

Input: accounts = [[1,2,3],[3,2,1]]

Output: 6

1st customer has wealth = 1 + 2 + 3 = 6 2nd customer has wealth = 3 + 2 + 1 = 6 Both customers are considered the richest with a wealth of 6 each, so return 6.

Example 2

Input: accounts = [[1,5],[7,3],[3,5]]

Output: 10

1st customer has wealth = 6 2nd customer has wealth = 10 3rd customer has wealth = 8 The 2nd customer is the richest with a wealth of 10.

Example 3

Input: accounts = [[2,8,7],[7,1,3],[1,9,5]]

Output: 17

Example details omitted.

Constraints

m == accounts.length
n == accounts[i].length
1 <= m, n <= 50
1 <= accounts[i][j] <= 100

Solution Approach

Iterating Through the Accounts

The most straightforward approach involves iterating through the 2D array. For each customer (row), sum the values (columns) representing the wealth across their accounts. Keep track of the maximum sum encountered during the iteration.

Optimizing Space Complexity

Instead of creating additional data structures, optimize space by maintaining a simple variable to store the current maximum wealth during the iteration. This prevents unnecessary overhead.

Edge Case Consideration

Handle cases where all customers have the same wealth, or where the grid has the smallest size. Make sure to account for these edge cases in the implementation to ensure the solution is robust.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

The time complexity is O(m * n), where m is the number of customers (rows) and n is the number of bank accounts (columns). Space complexity is O(1) since we are only tracking the current maximum wealth without using extra space.

What Interviewers Usually Probe

Can the candidate optimize the solution for space while maintaining efficiency?
Does the candidate consider edge cases, such as multiple customers with the same wealth?
Is the candidate able to articulate the reasoning behind the iterative approach?

Common Pitfalls or Variants

Common pitfalls

Forgetting to sum the accounts for each customer before comparing with the current maximum.
Inefficient use of space, such as creating unnecessary data structures to hold intermediate sums.
Not handling edge cases where all customers have the same wealth or where the input size is minimal.

Follow-up variants

Consider scenarios where the grid size grows larger, requiring more efficient solutions for both time and space.
Extend this problem by adding constraints where the values in the accounts array vary dynamically.
Modify the problem to calculate the wealth of the least wealthy customer instead of the richest.

FAQ

What is the best approach to solve the 'Richest Customer Wealth' problem?

The best approach is to iterate through the matrix, summing each customer's wealth and tracking the maximum wealth encountered.

How can I optimize my solution for space in the 'Richest Customer Wealth' problem?

You can optimize space by only maintaining a variable to store the current maximum wealth, avoiding additional data structures.

Are there any edge cases I should consider for this problem?

Yes, edge cases include scenarios where all customers have the same wealth or when the grid has the smallest possible size.

How do I handle large inputs efficiently in this problem?

Focus on optimizing the solution by ensuring both time and space complexities remain manageable. The current solution's O(m * n) time complexity is optimal for typical input sizes.

What is the main pattern used in the 'Richest Customer Wealth' problem?

The primary pattern used in this problem is array plus matrix, where you perform operations over a 2D matrix (grid) to calculate the result.

terminal

Solution

Solution 1: Summation

We traverse `accounts` and find the maximum sum of each row.

1

2

3

class Solution:
    def maximumWealth(self, accounts: List[List[int]]) -> int:
        return max(sum(v) for v in accounts)

Continue Practicing

#1706 where will the ball fall #1632 rank transform of a matrix #1631 path with minimum effort