Javascript:

Given an array of N numbers within the range $[1..$N$],$ find the minimum number of increments and decrements of a single element required to make the array a permutation.

Task description

You are given an array A consisting of N integers within the range $[1..$N$].$ In one move, you can increase or decrease the value of any element by $1.$ After each move, all numbers should remain within the range $[1..$N$].$

Your task is to find the smallest required number of moves to make all elements in the array pairwise distinct $($in other words, no value can appear in the array more than once$).$

Write a function:

function solution$($A$)$;

that, given an array A consisting of N integers, returns the smallest number of moves required to make all elements in the array pairwise distinct. If the result is greater than $1,000,000,000,$ the function should return $-1.$

Examples:

$1.$ Given A $=[1,2,1],$ the function should return $2,$ because you can increase A$[2]$ twice: $[1,2,1]>[1,2,2]>[1,2,3].$ In this example, you could also change the array to the following values in two moves: $[3,2,1],[1,3,2],[2,3,1].$

$2.$ Given A $=[2,1,4,4],$ the function should return $1,$ as it is sufficient to decrease A$[2]$ or A$[3]$ by $1,$ resulting in $[2,1,3,4]$ or $[2,1,4,3].$

$3.$ Given A $=[6,2,3,5,6,3],$ the function should return $4,$ because you can achieve the following array in four moves: $[6,2,1,5,4,3].$

Write an efficient algorithm for the following assumptions:

$$ N is an integer within the range $[1.\mathrm{.}200,000]$;

$$ each element of array A is an integer within the range $[1..$N$].$