Is Minimum Cost to Split into Ones easy or hard?

The problem is usually categorized as Medium because many candidates initially model it with dynamic programming. Once the invariant about the number of splits is recognized, the final solution becomes a simple constant-time formula.

Minimum Cost to Split into Ones Python/Java solution

The implementation is extremely short because the answer depends only on n. Return n - 1 using basic arithmetic. The same logic works identically in Python, Java, C++, Go, and TypeScript.

How to solve Minimum Cost to Split into Ones in O(1)?

Observe that converting a single number into n pieces of value 1 requires exactly n-1 splits. Since each split contributes deterministically to the total cost, the minimum cost simplifies to n-1. The implementation only performs a constant-time arithmetic computation.

What is the best approach for Minimum Cost to Split into Ones?

The optimal approach uses a mathematical observation instead of full dynamic programming. Splitting a number into n ones always requires exactly n-1 operations because each split increases the number of pieces by one. Using this invariant, the minimum total cost can be computed directly in O(1) time and O(1) space.

Is Minimum Cost to Split into Ones asked at Google/Amazon/Meta?

Problems based on mathematical observations and dynamic programming reductions frequently appear in interviews at companies like Google, Amazon, and Meta. Interviewers use them to test whether candidates can simplify a DP recurrence into a direct formula.

What data structure is used in Minimum Cost to Split into Ones?

The optimal solution does not require any data structures. It relies on a mathematical invariant about the number of splits. A conceptual dynamic programming formulation may use an array dp[n], but it becomes unnecessary after deriving the closed-form result.

What is the time complexity of Minimum Cost to Split into Ones?

The optimal solution runs in O(1) time and O(1) space because the answer can be derived directly from the value of n. A naive dynamic programming formulation that tests every partition would take O(n^2) time and O(n) space.

Description Hints 2 Solution Video 10:33

3857. Minimum Cost to Split into Ones

Medium82.6% acceptance1 company

You are given an integer n.

In one operation, you may split an integer x into two positive integers a and b such that a + b = x.

The cost of this operation is a * b.

Return an integer denoting the minimum total cost required to split the integer n into n ones.

Example 1:

Input: n = 3

Output: 3

Explanation:

One optimal set of operations is:

`x`	`a`	`b`	`a + b`	`a * b`	Cost
3	1	2	3	2	2
2	1	1	2	1	1

Thus, the minimum total cost is 2 + 1 = 3.

Example 2:

Input: n = 4

Output: 6

Explanation:

One optimal set of operations is:

`x`	`a`	`b`	`a + b`	`a * b`	Cost
4	2	2	4	4	4
2	1	1	2	1	1
2	1	1	2	1	1

Thus, the minimum total cost is 4 + 1 + 1 = 6.

Constraints:

1 <= n <= 500

Asked at 1 company

Amazon

Topics

Dynamic Programming Math

Hints open one at a time

Hint 1

Use dynamic programming or math.

Hint 2

It is always optimal to split the current integer x into 1 and x - 1.

10:33

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