Given an array of integers, change it in such a way that it follows a zig-zag pattern. A zig-zag array is one where for each integer, its adjacent integers are both greater than or less than itself. In other words, using L to mean a lower value and H to mean higher, the array follows either the pattern [L, H,L, H...] or [H, L,H, L...]. To make the array a zig-zag array, you can replace any element with any other integer (positive, negative, or zero). What is the minimum number of replacements required to accomplish this

The idea that, for each pair of devices v and w, there’s a strict dichotomy between being “in range” or “out of range” is a simplified abstraction. more accurately, there’s a power decay function f (·) that specifies, for a pair of devices at distance δ, the signal strength f(δ) that they’ll be able to achieve on their wireless connection. (we’ll assume that f (δ) decreases with increasing δ.) we might want to build this into our notion of back-up sets as follows: among the k devices in the back-up set of v, there should be at least one that can be reached with very high signal strength, at least one other that can be reached with moderately high signal strength, and so forth. more concretely, we have values p1 ≥ p2 ≥ . . ≥ pk, so that if the back-up set for v consists of devices at distances d1≤d2≤≤dk,thenweshouldhavef(dj)≥pj foreachj. give an algorithm that determines whether it is possible to choose a back-up set for each device subject to this more detailed condition, still requiring that no device should appear in the back-up set of more than b other devices. again, the algorithm should output the back-up sets themselves, provided they can be found.\