Special Array With X Elements Greater Than or Equal X

Special Array With X Elements Greater Than or Equal X - Problem

You are given an array nums of non-negative integers. nums is considered special if there exists a number x such that there are exactly x numbers in nums that are greater than or equal to x.

Notice that x does not have to be an element in nums.

Return x if the array is special, otherwise, return -1. It can be proven that if nums is special, the value for x is unique.

Input & Output

Example 1 — Basic Special Array

$ Input: nums = [3,5]

› Output: 2

💡 Note: There are exactly 2 numbers greater than or equal to 2: both 3 and 5. So x = 2 makes this a special array.

Example 2 — Not Special Array

$ Input: nums = [0,0]

› Output: -1

💡 Note: For x=0: 2 elements ≥ 0 (2≠0). For x=1: 0 elements ≥ 1 (0≠1). For x=2: 0 elements ≥ 2 (0≠2). No valid x exists.

Example 3 — Edge Case with Zero

$ Input: nums = [0,4,3,0,4]

› Output: 3

💡 Note: There are exactly 3 numbers greater than or equal to 3: [4,3,4]. So x = 3 makes this a special array.

Constraints

1 ≤ nums.length ≤ 100
0 ≤ nums[i] ≤ 1000

Visualization

Tap to expand

Understanding the Visualization

Input Array

Given array of non-negative integers

Find Special X

Look for x where count(elements ≥ x) = x

Output Result

Return x if found, otherwise -1

Key Takeaway

🎯 Key Insight: The special value x must satisfy the exact balance: x elements are ≥ x

Asked in

G Google 15 a Amazon 12 M Microsoft 8

The key insight is that x must be between 0 and array length, and we need exactly x elements ≥ x. The brute force approach checks every possible x value. The sort-first approach leverages sorting for efficient validation. Best approach depends on array size: brute force for small arrays, sorting for medium, binary search for very large. Time: O(n²) to O(n log n), Space: O(1).

Common Approaches

Approach	Time	Space	Notes
✓ Sort First Approach	O(n log n)	O(1)	Sort array in descending order, then check if nums[i-1] >= i for each position
Brute Force - Check All Possible Values	O(n²)	O(1)	Try every possible value of x from 0 to n and count elements ≥ x
Binary Search on Answer	O(n log n)	O(1)	Binary search on possible x values (0 to n) with efficient counting

Sort First Approach — Algorithm Steps

Sort array in descending order
For each position i from 1 to n, check if nums[i-1] >= i
If true and (i==n or nums[i] < i), return i
If no match found, return -1

Visualization

Tap to expand

Step-by-Step Walkthrough

Sort Descending

Arrange elements in descending order

Check Positions

At position i, first i elements are largest i

Find Match

When nums[i-1] >= i and nums[i] < i

Code -

solution.c — C

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

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

int solution(int* nums, int numsSize) {
    qsort(nums, numsSize, sizeof(int), compare);
    
    // Check x = 0
    if (numsSize == 0 || nums[numsSize-1] < 0) {
        return 0;
    }
    
    // Check x = 1 to numsSize
    for (int i = 1; i <= numsSize; i++) {
        if (nums[i-1] >= i && (i == numsSize || nums[i] < i)) {
            return i;
        }
    }
    
    return -1;
}

int main() {
    char line[1000];
    fgets(line, sizeof(line), stdin);
    
    int nums[1000];
    int numsSize = 0;
    char* token = strtok(line, "[],\n");
    while (token != NULL) {
        if (strlen(token) > 0) {
            nums[numsSize++] = atoi(token);
        }
        token = strtok(NULL, "[],\n");
    }
    
    int result = solution(nums, numsSize);
    printf("%d\n", result);
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n log n)

Sorting takes O(n log n), then single pass through array takes O(n)

⚡ Linearithmic

Space Complexity

O(1)

Only using constant extra space if sorting in-place

✓ Linear Space

25.0K Views

Medium Frequency

~15 min Avg. Time

892 Likes

Ln 1, Col 1

Smart Actions

💡 Explanation

AI Ready

💡 Suggestion Tab to accept Esc to dismiss

// Output will appear here after running code

Code Editor Closed

Click the red button to reopen

Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Sort First Approach — Algorithm Steps

Visualization

Code -

Time & Space Complexity

Select Compiler