 # FLV - Editorial

Contest

Practice

Author: Sahil Rajput

Tester: Sahil Rajput

Editorialist: Sahil Rajput

Difficulty

EASY

Prerequisites

Maths

Problem

Given an array of N size with K elements in the array. Task is to find the Minimum and Maximum number of possible good places in the array, A place is called good place when at least one value is already present adjacent to it.

Explanation

The approach for this question is simple calculation with some exceptions. The exceptions are cases in which K = 0 and K = N, in these cases both minimum and maximum number of good places is 0 since there is no inhabitant or vacant index in the array. Calculate the number of places with indices 2, 5, 8 and so on excluding the one with index N if it exists. Number of that places is equal to x = (floor)(N/3) , and if K ≤ x you can occupy some of these places to reach maximum number of good places equal to 2·K. Otherwise, if K> x, assume that place with indices 2, 5, 8 and so on are occupied, so any place has at least one inhabited place adjacent to it. Therefore number of good places for the value is equal to number of vacant places and is equal to n - k.

Time complexity

O(1).