Is Most Expensive Item That Can Not Be Bought easy or hard?

The problem is rated Medium on LeetCode but becomes very easy if you recognize the Chicken McNugget theorem. Without that insight, many candidates attempt dynamic programming or brute-force enumeration, which is significantly less efficient.

Most Expensive Item That Can Not Be Bought Python/Java solution

The implementation is identical across languages: return a*b - a - b. In Python, Java, C++, Go, or TypeScript, compute the product of the two inputs and subtract both numbers to obtain the largest unreachable value.

How to solve Most Expensive Item That Can Not Be Bought in O(1)?

Use the Chicken McNugget theorem. If two item prices are a and b and gcd(a, b) = 1, the largest unreachable value is a*b - a - b. The implementation simply returns that expression, which eliminates the need for loops or dynamic programming.

What is the best approach for Most Expensive Item That Can Not Be Bought?

The optimal approach uses the Chicken McNugget theorem from number theory. For two coprime integers a and b, the largest value that cannot be formed using a*x + b*y is a*b - a - b. Since the problem guarantees prime numbers, they are coprime, so the answer can be computed in O(1) time with a simple formula.

Is Most Expensive Item That Can Not Be Bought asked at Google/Amazon/Meta?

Problems based on the Frobenius coin problem and number theory formulas appear in interviews at companies like Google and Amazon, especially for candidates expected to recognize mathematical patterns. The exact LeetCode problem may vary, but the concept is commonly tested.

What data structure is used in Most Expensive Item That Can Not Be Bought?

The optimal solution does not require any data structures because it relies on a mathematical formula. A learning-oriented approach may use a boolean array or set to track reachable sums, which resembles dynamic programming state tracking.

What is the time complexity of Most Expensive Item That Can Not Be Bought?

The optimal solution runs in O(1) time and O(1) space because it directly computes a*b - a - b using a mathematical formula. A brute-force or dynamic programming approach that checks reachable sums would take O(a*b) time and space.

Description Hints 4 Solution Video 1:06

2979. Most Expensive Item That Can Not Be Bought

Medium80.2% acceptance1 companyPremium elsewhere, free here

You are given two distinct prime numbers primeOne and primeTwo.

Alice and Bob are visiting a market. The market has an infinite number of items, for any positive integer x there exists an item whose price is x. Alice wants to buy some items from the market to gift to Bob. She has an infinite number of coins in the denomination primeOne and primeTwo. She wants to know the most expensive item she can not buy to gift to Bob.

Return the price of the most expensive item which Alice can not gift to Bob.

Example 1:

Input: primeOne = 2, primeTwo = 5
Output: 3
Explanation: The prices of items which cannot be bought are [1,3]. It can be shown that all items with a price greater than 3 can be bought using a combination of coins of denominations 2 and 5.

Example 2:

Input: primeOne = 5, primeTwo = 7
Output: 23
Explanation: The prices of items which cannot be bought are [1,2,3,4,6,8,9,11,13,16,18,23]. It can be shown that all items with a price greater than 23 can be bought.

Constraints:

1 < primeOne, primeTwo < 10⁴
primeOne, primeTwo are prime numbers.
primeOne * primeTwo < 10⁵

Asked at 1 company

Amazon

Topics

Hints open one at a time

Hint 1

Write out a few cases. It can be seen that all items greater than primeOne * primeTwo can always be bought.

Hint 2

If we can buy items with cost i, we can also buy items with price i + primeOne and i + primeTwo.

Hint 3

Use dynamic programming.

Hint 4

There is an O(1) solution: Use the Chicken McNugget Theorem.

1:06

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