Divide Chocolate

Divide Chocolate

What is this problem about?

The Divide Chocolate interview question is a classic optimization problem. You have a chocolate bar represented as an array of integers, where each integer is the "sweetness" of a piece. You want to share the chocolate with k friends, meaning you must cut the bar into k + 1 contiguous pieces. You are "selfless" and want to maximize the sweetness of the piece you get, which will be the one with the minimum total sweetness among all pieces.

Why is this asked in interviews?

Google frequently asks this coding problem to test a candidate's mastery of the Binary Search on the Answer pattern. It evaluates whether you can identify that the possible "minimum sweetness" value is monotonic—if you can achieve a minimum sweetness of X, you can also achieve any value less than X. It's a "Hard" problem because it requires a greedy validation function inside a binary search loop.

Algorithmic pattern used

This problem uses Binary Search on the Answer.

1. Range: The possible answer (your sweetness) ranges from min(sweetness) to sum(sweetness) / (k + 1).
2. Binary Search: Pick a middle value mid and check if it's possible to cut the bar into at least k + 1 pieces, where each piece has a total sweetness $\ge mid$.
3. Validation (Greedy): Iterate through the chocolate, summing up sweetness until it reaches mid. When it does, "cut" the piece and start a new sum. Count how many pieces you can make.
4. Adjust: If you can make $\ge k + 1$ pieces, mid is a possible answer; try a higher value. Otherwise, try a lower value.

Example explanation

Sweetness: [1, 2, 3, 4, 5, 6, 7, 8, 9], $k = 5$ (need 6 pieces).

• Try mid = 10:
  • [1, 2, 3, 4] (sum 10) - Piece 1
  • [5, 6] (sum 11) - Piece 2
  • [7, 8] (sum 15) - Piece 3
  • [9] (sum 9) - Not enough for Piece 4.
  • Total pieces: 3. Too few. Try smaller mid.
• The binary search will converge on the maximum possible value for the minimum piece.

Common mistakes candidates make

• Binary Search on Indices: Trying to binary search where to cut, which is $O(N^K)$. You must binary search on the result value.
• Off-by-one in friends: Forgetting that $k$ friends plus yourself means $k+1$ pieces.
• Greedy logic error: Not correctly resetting the running sum after a "cut."

Interview preparation tip

Whenever a problem asks to "maximize the minimum" or "minimize the maximum," Binary Search on the Answer should be your first thought. It’s a very consistent pattern across many competitive programming problems.