Is Integer Break easy or hard?

Integer Break is generally classified as a Medium difficulty problem. The dynamic programming formulation is straightforward once the recurrence is identified, while the mathematical optimization requires recognizing a pattern about maximizing products using 3s.

Integer Break Python/Java solution

In Python or Java, the dynamic programming solution uses an array of size n+1 and iterates through all split points to compute the maximum product. The mathematical solution calculates the product of powers of 3 with a few conditional checks, resulting in very concise code.

How to solve Integer Break in O(1)?

Use the mathematical observation that the maximum product occurs when the integer is broken into factors of 3. Repeatedly subtract 3 from n and multiply the result until the remaining value is 4 or less. Multiply the remainder with the accumulated product to get the final answer.

What is the best approach for Integer Break?

The mathematical greedy approach is the optimal solution. It relies on the observation that splitting the number into as many 3s as possible maximizes the product. This method runs in O(1) time and O(1) space. In interviews, candidates often start with the dynamic programming solution and then optimize using this mathematical insight.

Is Integer Break asked at Google/Amazon/Meta?

Integer Break appears frequently in coding interview practice sets and has been reported in interviews at companies like Amazon and Google. It tests dynamic programming fundamentals and the ability to derive mathematical optimizations from patterns.

What data structure is used in Integer Break?

The dynamic programming approach uses a simple array dp where dp[i] stores the maximum product obtainable by breaking integer i. The mathematical solution does not require any additional data structure and works with basic arithmetic operations.

What is the time complexity of Integer Break?

The dynamic programming solution runs in O(n^2) time because for every integer i you iterate through all possible splits j from 1 to i-1. The optimized mathematical approach reduces this to O(1) time by directly computing the product using powers of 3.

Description Hints 2 Solution Video 16:38

343. Integer Break

Medium62.6% acceptance6 companies

Given an integer n, break it into the sum of k positive integers, where k >= 2, and maximize the product of those integers.

Return the maximum product you can get.

Example 1:

Input: n = 2
Output: 1
Explanation: 2 = 1 + 1, 1 × 1 = 1.

Example 2:

Input: n = 10
Output: 36
Explanation: 10 = 3 + 3 + 4, 3 × 3 × 4 = 36.

Constraints:

2 <= n <= 58

Asked at 6 companies

Meta Accenture

Google Bloomberg Amazon Microsoft

Topics

Dynamic Programming Math

Hints open one at a time

Hint 1

There is a simple O(n) solution to this problem.

Hint 2

You may check the breaking results of n ranging from 7 to 10 to discover the regularities.

16:38

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