Describe an advanced data structure : Array Problems Involving Modulos

The video tutorial covers the modulo operation, explaining its properties and how it applies to arrays. It introduces a problem of finding the minimum length subarray with a sum mod K equal to zero, demonstrating an efficient implementation using prefix sums and dictionaries. A new problem is introduced, involving removing elements from an array to achieve a sum mod 3 equal to zero.

What is the result of 5 mod 3?

• 0

• 3

• 2

• 1

Which property does not hold for division in modulo operations?

• Associative

• Distributive

• Commutative

• None of the above

What is a perfect sum in the context of the subarray problem?

• The sum of numbers up to a given position in the array

• The sum of numbers in the entire array

• The sum of all numbers in the array

• The sum of numbers after a given position in the array

How can we determine if a subarray sum is zero modulo a given number?

• By checking if the subarray sum is negative

• By checking if the subarray sum is zero

• By checking if the subarray sum is equal to the given number

• By checking if two prefix sums are equal

What is the purpose of the dictionary in the efficient implementation of the subarray problem?

• To store the sum of all elements

• To store the array elements

• To store the last position of each element

• To store the last position of a perfect sum

What is the time complexity of the efficient implementation of the subarray problem?

• O(n log n)

• O(n^2)

• O(n^3)

• O(n)

What should be considered when removing numbers from an array to make the sum modulo 3 equal to zero?

• The largest element in the array

• The number of elements in the array

• The smallest element in the array

• The total sum modulo 3