Codility: Perm Check

Check whether array A is a permutation.

Question

A non-empty zero-indexed array A consisting of N integers is given.

A permutation is a sequence containing each element from 1 to N once, and only once.

For example, array A such that:

    A[0] = 4
    A[1] = 1
    A[2] = 3
    A[3] = 2

is a permutation, but array A such that:

    A[0] = 4
    A[1] = 1
    A[2] = 3

is not a permutation, because value 2 is missing.

The goal is to check whether array A is a permutation.

Write a function:

int solution(int A[], int N);

that, given a zero-indexed array A, returns 1 if array A is a permutation and 0 if it is not.

For example, given array A such that:

    A[0] = 4
    A[1] = 1
    A[2] = 3
    A[3] = 2

the function should return 1.

Given array A such that:

    A[0] = 4
    A[1] = 1
    A[2] = 3

the function should return 0.

Assume that:

  • N is an integer within the range [1..100,000];
  • each element of array A is an integer within the range [1..1,000,000,000].

Complexity:

  • expected worst-case time complexity is O(N);
  • expected worst-case space complexity is O(N), beyond input storage (not counting the storage required for input arguments).

Elements of input arrays can be modified.

Solution

#import <Foundation/NSDictionary.h>  
//Remember to import or else you cannot use NSMutableDictionary
//TESTCASE
//Perm: (1, 4, 1)  expected 0
//Perm: (1, 1)  expected 0
//Perm: (2, 2, 2)  expected 0
int solution(NSMutableArray *A) {
    int sumArray = 0;
    int sumPerm = 0;
    NSMutableDictionary *numbers = [[NSMutableDictionary alloc] initWithCapacity:A.count];

    for(int i= 0; i < A.count; i++){
        int index = [A[i] intValue];
        
        if(index < 1||index > A.count) //check out of bounds
            return 0;
        else if([numbers objectForKey:[NSString stringWithFormat:@"%d", index]]) //check for duplicates
            return 0;
        else
            [numbers setValue:[NSNumber numberWithInt:1]
                                   forKey:[NSString stringWithFormat:@"%d", index]];
        
        sumArray += index;
        sumPerm += (i+1);
    }

    
    if(sumPerm != sumArray) return 0;
    else return 1;
}

Detected time complexity:
O(N) or O(N * log(N))

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