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Richest Customer Wealth

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Arrays

You are given an m x n integer grid accounts where accounts[i][j] is the amount of money the i^th customer has in the j^th bank. Return the wealth that the richest customer has.

A customer's wealth is the amount of money they have in all their bank accounts. The richest customer is the customer that has the maximum wealth.

Example 1:

Input: accounts = [[1,2,3],[3,2,1]]
Output: 6
Explanation:
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
Explanation: 
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

Constraints:

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

Try coding it in LeetCode

Richest Customer Wealth

Easy

Asked by:

25 views

Topics:

Arrays

You are given an m x n integer grid accounts where accounts[i][j] is the amount of money the i^th customer has in the j^th bank. Return the wealth that the richest customer has.

A customer's wealth is the amount of money they have in all their bank accounts. The richest customer is the customer that has the maximum wealth.

Example 1:

Input: accounts = [[1,2,3],[3,2,1]]
Output: 6
Explanation:
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
Explanation: 
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

Constraints:

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

Try coding it in LeetCode

Solution

Clarifying Questions

When you get asked this question in a real-life environment, it will often be ambiguous (especially at FAANG). Make sure to ask these questions in that case:

What are the dimensions of the `accounts` array, and what are the upper bounds on the number of accounts and the number of banks per account?
Can the wealth in any account (i.e., the value at `accounts[i][j]`) be negative, zero, or a very large number that might cause integer overflow?
Is the `accounts` array ever empty or null? What about the inner arrays representing each account?
What should I return if the `accounts` array is empty?
Is the input array guaranteed to be well-formed (e.g., no rows with different numbers of columns)?

Brute Force Solution

Approach

Imagine each customer has a set of bank accounts with different amounts of money. To find the richest customer using a brute-force approach, we will go through each customer, add up all the money they have, and then compare those totals to find the largest one.

Here's how the algorithm would work step-by-step:

Start with the first customer.
Add up the money from all of their bank accounts to find their total wealth.
Remember this total amount as the current 'richest' amount.
Move to the next customer.
Add up the money from all of their bank accounts to find their total wealth.
Compare this customer's total wealth to the current 'richest' amount.
If this customer's total is bigger than the current 'richest' amount, replace the current 'richest' amount with this new larger amount.
Repeat the process for all the remaining customers, comparing each customer's wealth to the current 'richest' amount and updating it when necessary.
After going through all the customers, the 'richest' amount you have remembered is the wealth of the richest customer.

Code Implementation

def richest_customer_wealth(
    accounts
):
    richest_wealth_so_far = 0

    for customer_accounts in accounts:
        # Calculate wealth for current customer

        customer_wealth = 0

        for account_balance in customer_accounts:
            customer_wealth += account_balance

        #Compare to current max
        if customer_wealth > richest_wealth_so_far:

            richest_wealth_so_far = customer_wealth
            #Update wealth if it is larger

    return richest_wealth_so_far

Big(O) Analysis

Time Complexity

O(m*n) – The input is a 2D array where 'm' is the number of customers (rows) and 'n' is the number of bank accounts per customer (columns). For each customer, we iterate through their bank accounts to calculate their total wealth. Thus, we perform 'n' operations (addition) for each of the 'm' customers. This leads to a total of m * n operations, resulting in a time complexity of O(m*n).

Space Complexity

O(1) – The algorithm described uses only a constant amount of extra space. It stores the current 'richest' amount, which is a single number, and possibly a temporary variable to hold the wealth of the current customer being processed. Neither of these scale with the input size, which is the number of customers and their accounts. Therefore, the auxiliary space used is constant, resulting in O(1) space complexity.

Optimal Solution

Approach

To find the richest customer, we need to calculate each customer's total wealth. Then, we just need to keep track of the highest wealth we've seen so far, updating it whenever we find a customer with more money.

Here's how the algorithm would work step-by-step:

Start by assuming the richest customer has zero wealth.
Go through each customer, one at a time.
For each customer, add up all the money they have in their accounts.
Compare that customer's total money to the richest customer we've found so far.
If the current customer has more money, update the richest customer's wealth to that amount.
Once we've checked all the customers, the richest customer's wealth will be the answer.

Code Implementation

def maximum_wealth(accounts):
    richest_customer_wealth = 0

    for customer_accounts in accounts:
        customer_wealth = 0
        # Calculate total wealth for current customer.
        for account_balance in customer_accounts:
            customer_wealth += account_balance

        # Update richest customer's wealth if current exceeds.
        if customer_wealth > richest_customer_wealth:

            richest_customer_wealth = customer_wealth

    return richest_customer_wealth

Big(O) Analysis

Time Complexity

O(m*n) – The outer loop iterates through each of the 'm' customers. For each customer, the inner loop iterates through their 'n' bank accounts to calculate their total wealth. Therefore, the time complexity is proportional to the product of the number of customers and the number of bank accounts per customer, giving us O(m*n).

Space Complexity

O(1) – The algorithm calculates each customer's wealth by summing their account balances. It only uses a variable to store the current customer's wealth and another variable to keep track of the maximum wealth seen so far. These variables occupy a constant amount of space regardless of the number of customers or accounts. Therefore, the auxiliary space complexity is O(1).

Edge Cases

Case	How to Handle
Null or empty accounts array	Return 0 immediately, as no wealth can be calculated.
Empty individual account (inner array)	Treat an empty inner array as a customer with zero wealth.
Accounts with a single bank account	The wealth of that customer is simply the value of that single account.
Very large number of customers	The solution should still perform adequately because the wealth calculation for each customer remains independent.
Accounts with extremely large monetary values leading to integer overflow	Use a data type with a larger range (e.g., long or BigInteger) to prevent overflow during wealth calculation.
All customers have the same wealth	The algorithm correctly identifies the common wealth as the richest.
Accounts with negative values (representing debts)	The algorithm handles negative numbers correctly, since they contribute to reducing a customer's total wealth.
Maximum number of accounts and maximum value for each account	The algorithm should perform efficiently (linear with the total number of banks) up to the limits of the chosen integer type to hold total wealth.

Null or empty accounts array

How to Handle:

Return 0 immediately, as no wealth can be calculated.

Empty individual account (inner array)

How to Handle:

Treat an empty inner array as a customer with zero wealth.

Accounts with a single bank account

How to Handle:

The wealth of that customer is simply the value of that single account.

Very large number of customers

How to Handle:

The solution should still perform adequately because the wealth calculation for each customer remains independent.

Accounts with extremely large monetary values leading to integer overflow

How to Handle:

Use a data type with a larger range (e.g., long or BigInteger) to prevent overflow during wealth calculation.

All customers have the same wealth

How to Handle:

The algorithm correctly identifies the common wealth as the richest.

Accounts with negative values (representing debts)

How to Handle:

The algorithm handles negative numbers correctly, since they contribute to reducing a customer's total wealth.

Maximum number of accounts and maximum value for each account

How to Handle:

The algorithm should perform efficiently (linear with the total number of banks) up to the limits of the chosen integer type to hold total wealth.

Solution

Clarifying Questions

When you get asked this question in a real-life environment, it will often be ambiguous (especially at FAANG). Make sure to ask these questions in that case:

What are the dimensions of the `accounts` array, and what are the upper bounds on the number of accounts and the number of banks per account?
Can the wealth in any account (i.e., the value at `accounts[i][j]`) be negative, zero, or a very large number that might cause integer overflow?
Is the `accounts` array ever empty or null? What about the inner arrays representing each account?
What should I return if the `accounts` array is empty?
Is the input array guaranteed to be well-formed (e.g., no rows with different numbers of columns)?

Brute Force Solution

Approach

Here's how the algorithm would work step-by-step:

Start with the first customer.
Add up the money from all of their bank accounts to find their total wealth.
Remember this total amount as the current 'richest' amount.
Move to the next customer.
Add up the money from all of their bank accounts to find their total wealth.
Compare this customer's total wealth to the current 'richest' amount.
If this customer's total is bigger than the current 'richest' amount, replace the current 'richest' amount with this new larger amount.
Repeat the process for all the remaining customers, comparing each customer's wealth to the current 'richest' amount and updating it when necessary.
After going through all the customers, the 'richest' amount you have remembered is the wealth of the richest customer.

Code Implementation

def richest_customer_wealth(
    accounts
):
    richest_wealth_so_far = 0

    for customer_accounts in accounts:
        # Calculate wealth for current customer

        customer_wealth = 0

        for account_balance in customer_accounts:
            customer_wealth += account_balance

        #Compare to current max
        if customer_wealth > richest_wealth_so_far:

            richest_wealth_so_far = customer_wealth
            #Update wealth if it is larger

    return richest_wealth_so_far

Big(O) Analysis

Time Complexity

Space Complexity

Optimal Solution

Approach

Here's how the algorithm would work step-by-step:

Start by assuming the richest customer has zero wealth.
Go through each customer, one at a time.
For each customer, add up all the money they have in their accounts.
Compare that customer's total money to the richest customer we've found so far.
If the current customer has more money, update the richest customer's wealth to that amount.
Once we've checked all the customers, the richest customer's wealth will be the answer.

Code Implementation

def maximum_wealth(accounts):
    richest_customer_wealth = 0

    for customer_accounts in accounts:
        customer_wealth = 0
        # Calculate total wealth for current customer.
        for account_balance in customer_accounts:
            customer_wealth += account_balance

        # Update richest customer's wealth if current exceeds.
        if customer_wealth > richest_customer_wealth:

            richest_customer_wealth = customer_wealth

    return richest_customer_wealth

Big(O) Analysis

Time Complexity

Space Complexity

Edge Cases

Case	How to Handle
Null or empty accounts array	Return 0 immediately, as no wealth can be calculated.
Empty individual account (inner array)	Treat an empty inner array as a customer with zero wealth.
Accounts with a single bank account	The wealth of that customer is simply the value of that single account.
Very large number of customers	The solution should still perform adequately because the wealth calculation for each customer remains independent.
Accounts with extremely large monetary values leading to integer overflow	Use a data type with a larger range (e.g., long or BigInteger) to prevent overflow during wealth calculation.
All customers have the same wealth	The algorithm correctly identifies the common wealth as the richest.
Accounts with negative values (representing debts)	The algorithm handles negative numbers correctly, since they contribute to reducing a customer's total wealth.
Maximum number of accounts and maximum value for each account	The algorithm should perform efficiently (linear with the total number of banks) up to the limits of the chosen integer type to hold total wealth.

Null or empty accounts array

How to Handle:

Return 0 immediately, as no wealth can be calculated.

Empty individual account (inner array)

How to Handle:

Treat an empty inner array as a customer with zero wealth.

Accounts with a single bank account

How to Handle:

The wealth of that customer is simply the value of that single account.

Very large number of customers

How to Handle:

The solution should still perform adequately because the wealth calculation for each customer remains independent.

Accounts with extremely large monetary values leading to integer overflow

How to Handle:

Use a data type with a larger range (e.g., long or BigInteger) to prevent overflow during wealth calculation.

All customers have the same wealth

How to Handle:

The algorithm correctly identifies the common wealth as the richest.

Accounts with negative values (representing debts)

How to Handle:

The algorithm handles negative numbers correctly, since they contribute to reducing a customer's total wealth.

Maximum number of accounts and maximum value for each account

How to Handle:

The algorithm should perform efficiently (linear with the total number of banks) up to the limits of the chosen integer type to hold total wealth.