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Classic problem #3191MediumArrayBit ManipulationQueueSliding WindowPrefix Sum

Minimum Operations to Make Binary Array Elements Equal to One I

Real-world version: Raising Every Flag With Triple Flips
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The statement here is our own: the same inputs, outputs and technique.

A row of flags holds only the values 0 and 1. One move picks any three neighbouring flags and flips each of them: a 0 becomes a 1 and a 1 becomes a 0.

Return the fewest moves needed to leave every flag showing 1, or -1 when no number of moves can do it.

Examples

Example 1

Input
flags = [0, 0, 0]
Output
1

One move over all three flags raises the whole row.

Example 2

Input
flags = [0, 0, 1, 0, 0]
Output
2

Flipping the first three flags leaves 1, 1, 0, 0, 0 and flipping the last three finishes the row.

Example 3

Input
flags = [1, 1, 1, 0, 1]
Output
-1

The single 0 sits second from the end. Working left to right nothing needs flipping, and the two trailing flags start no window, so that 0 can never be raised.

Constraints

  • 3 <= flags.length <= 10^5
  • 0 <= flags[i] <= 1

The signature

The editor starts with this. It matches the parent problem's shape, so a solution that works here works on a standard judge unchanged.

Python
def min_operations(flags: list[int]) -> int:
Java
public int minOperations(int[] flags)

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