Decrease Elements To Make Array Zigzag

Decrease Elements To Make Array Zigzag

What is this problem about?

The Decrease Elements To Make Array Zigzag interview question asks you to find the minimum number of operations to transform an array into a "zigzag" pattern. An array is zigzag if every even-indexed element is strictly greater than its neighbors, OR if every odd-indexed element is strictly greater than its neighbors. An operation consists of decreasing an element by 1. This Decrease Elements To Make Array Zigzag coding problem is a greedy optimization task.

Why is this asked in interviews?

Google uses this to test a candidate's ability to evaluate multiple scenarios independently. The problem explicitly states you can only decrease elements, which simplifies the logic but requires you to decide which elements to "sink" to satisfy the zigzag condition. It’s a great test of clean code and avoiding redundant calculations.

Algorithmic pattern used

This follows the Array, Greedy interview pattern.

1. Scenario A (Even indices are peaks): You must decrease all elements at odd indices until they are smaller than their adjacent even-indexed neighbors.
2. Scenario B (Odd indices are peaks): You must decrease all elements at even indices until they are smaller than their adjacent odd-indexed neighbors.
3. Calculation: For each scenario, iterate through the target "valley" indices and calculate the required reduction: max(0, nums[i] - min(left_neighbor, right_neighbor) + 1).
4. Result: The answer is the minimum of the total operations for Scenario A and Scenario B.

Example explanation

Input: [9, 6, 1, 6, 2]

• Valleys at Odd Indices (1, 3):
  • Index 1 (6): Neighbors are 9 and 1. Min neighbor is 1. To be smaller than 1, 6 must become 0. Ops: 6.
  • Index 3 (6): Neighbors are 1 and 2. Min neighbor is 1. To be smaller than 1, 6 must become 0. Ops: 6.
  • Total A: 12.
• Valleys at Even Indices (0, 2, 4):
  • Index 0 (9): Neighbor is 6. Must become 5. Ops: 3.
  • Index 2 (1): Neighbors are 6 and 6. Already smaller. Ops: 0.
  • Index 4 (2): Neighbor is 6. Already smaller. Ops: 0.
  • Total B: 3. The minimum is 3.

Common mistakes candidates make

• Trying to Increase: Forgetting that operations only allow decreasing elements.
• Dependency confusion: Trying to adjust peak elements instead of valley elements. It is always more efficient to decrease the valley to be smaller than its neighbors than to decrease the neighbors.
• Edge cases: Not correctly handling the first and last elements, which only have one neighbor.

Interview preparation tip

When a problem presents two distinct valid final states (like Peak-Even or Peak-Odd), calculate the cost for each independently and take the minimum. Don't try to solve them in a single pass with complex branching.