# A permutation where each element indicates either number of elements before or after it?

In this section we will see one problem. Here n elements are given in an array. We have to check whether there is a permutation of that array exists, such that each element indicates the number of elements present either before or after it.

Suppose the array elements are {2, 1, 3, 3}. The appropriate permutation is like {3, 1, 2, 3}. Here the first 3 is indicating there are three elements next of it, the 1 indicates there is only one element before this. The 2 indicates there are two elements before it and the last 3 indicates that there are three elements before it.

## Algorithm

#### checkPermutation(arr, n)

begin
define a hashmap to hold frequencies. The key and value are of integer type of the map.
for each element e in arr, do
increase map[e] by 1
done
for i := 0 to n-1, do
if map[i] is non-zero, then
decrease map[i] by 1
else if map[n-i-1] is non-zero, then
decrease map[n-i-1] by 1
else
return false
end if
done
return true
end

## Example

Live Demo

#include<iostream>
#include<map>
using namespace std;
bool checkPermutation(int arr[], int n) {
map<int, int> freq_map;
for(int i = 0; i < n; i++){ //get the frequency of each number
freq_map[arr[i]]++;
}
for(int i = 0; i < n; i++){
if(freq_map[i]){ //count number of elements before current element
freq_map[i]--;
} else if(freq_map[n-i-1]){ //count number of elements after current element
freq_map[n-i-1]--;
} else {
return false;
}
}
return true;
}
main() {
int data[] = {3, 2, 3, 1};
int n = sizeof(data)/sizeof(data[0]);
if(checkPermutation(data, n)){
cout << "Permutation is present";
} else {
cout << "Permutation is not present";
}
}

## Output

Permutation is present