Absolute distinct count in a sorted array?

In this article, we will learn how to count the number of elements whose absolute values are distinct in an array. For example, in the array {5, 5, 6, -5, 8, 2, -2, 1}, there are 8 elements total, but only 5 distinct absolute values: {5, 6, 8, 2, 1}. Note that -5 and 5 are considered the same since their absolute values are identical.

Syntax

int absoluteDistinctCount(int arr[], int n);

Algorithm

To solve this problem, we use a simple approach −

1. Create a boolean array to mark visited absolute values
2. For each element in the array:
   - Calculate its absolute value
   - Mark this absolute value as visited
3. Count the number of marked positions

Example 1: Using Boolean Array Method

This approach uses a boolean array to track which absolute values we have encountered −

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

int absoluteDistinctCount(int arr[], int n) {
    int maxVal = 0;
    
    // Find maximum absolute value to determine array size
    for (int i = 0; i < n; i++) {
        int absVal = abs(arr[i]);
        if (absVal > maxVal) {
            maxVal = absVal;
        }
    }
    
    // Create boolean array to mark visited values
    int *visited = (int*)calloc(maxVal + 1, sizeof(int));
    if (visited == NULL) {
        return -1; // Memory allocation failed
    }
    
    int count = 0;
    for (int i = 0; i < n; i++) {
        int absVal = abs(arr[i]);
        if (!visited[absVal]) {
            visited[absVal] = 1;
            count++;
        }
    }
    
    free(visited);
    return count;
}

int main() {
    int arr[] = {5, 5, 6, -5, 8, 2, -2, 1};
    int n = sizeof(arr) / sizeof(arr[0]);
    
    int result = absoluteDistinctCount(arr, n);
    printf("Array: ");
    for (int i = 0; i < n; i++) {
        printf("%d ", arr[i]);
    }
    printf("\nAbsolute Distinct Count: %d<br>", result);
    
    return 0;
}

Array: 5 5 6 -5 8 2 -2 1 
Absolute Distinct Count: 5

Example 2: Using Sorting Approach

This method first converts all elements to their absolute values and sorts them to count distinct elements −

#include <stdio.h>
#include <stdlib.h>

int compare(const void *a, const void *b) {
    return (*(int*)a - *(int*)b);
}

int absoluteDistinctCountSorted(int arr[], int n) {
    // Create a copy to avoid modifying original array
    int *temp = (int*)malloc(n * sizeof(int));
    if (temp == NULL) {
        return -1;
    }
    
    // Convert to absolute values
    for (int i = 0; i < n; i++) {
        temp[i] = abs(arr[i]);
    }
    
    // Sort the array
    qsort(temp, n, sizeof(int), compare);
    
    // Count distinct elements
    int count = 1;
    for (int i = 1; i < n; i++) {
        if (temp[i] != temp[i-1]) {
            count++;
        }
    }
    
    free(temp);
    return count;
}

int main() {
    int arr[] = {5, 5, 6, -5, 8, 2, -2, 1};
    int n = sizeof(arr) / sizeof(arr[0]);
    
    int result = absoluteDistinctCountSorted(arr, n);
    printf("Array: ");
    for (int i = 0; i < n; i++) {
        printf("%d ", arr[i]);
    }
    printf("\nAbsolute Distinct Count: %d<br>", result);
    
    return 0;
}

Array: 5 5 6 -5 8 2 -2 1 
Absolute Distinct Count: 5

Comparison

Conclusion

Both methods effectively count distinct absolute values in an array. The boolean array method is faster but uses more space, while the sorting method is more space-efficient for arrays with large values.