Making Array Beautiful - Problem Statement

Make array alternating: even indices have even values, odd indices have odd values. Minimum changes. Split into two problems: even indices should be even, odd indices should be odd.

Rounding to nearest valid value. Cost: for even index with value $v$, cost to make even is $v \mod 2$. For odd index, cost to make odd is $(v + 1) \mod 2$. This is a simpler structure. Slope Trick applies if we generalize to 'make non-decreasing with parity constraints'.