1608. 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.

Example 1:

Input: nums = [3,5]
Output: 2
Explanation: There are 2 values (3 and 5) that are greater than or equal to 2.

Example 2:

Input: nums = [0,0]
Output: -1
Explanation: No numbers fit the criteria for x.
If x = 0, there should be 0 numbers >= x, but there are 2.
If x = 1, there should be 1 number >= x, but there are 0.
If x = 2, there should be 2 numbers >= x, but there are 0.
x cannot be greater since there are only 2 numbers in nums.

Example 3:

Input: nums = [0,4,3,0,4]
Output: 3
Explanation: There are 3 values that are greater than or equal to 3.

Example 4:

Input: nums = [3,6,7,7,0]
Output: -1

Constraints:

• 1 <= nums.length <= 100
• 0 <= nums[i] <= 1000

Problem Summary #

You are given a non-negative integer array nums. If there exists a number x such that exactly x elements in nums are greater than or equal to x, then nums is called a special array, and x is the characteristic value of the array. (Note: x does not have to be an element in nums.) If the array nums is a special array, return its characteristic value x. Otherwise, return -1. It can be proven that if nums is a special array, then its characteristic value x is unique.

Solution Approach #

• Easy problem. Use the proof given in the statement: the characteristic value is unique. First sort the array in ascending order; then the meaning of the index becomes equivalent to the characteristic value. Index i means there are len(nums) - i elements greater than or equal to nums[i]. Starting from the element at index 0, if this element is greater than len(nums), then the following len(nums) elements are also greater than or equal to it, so the characteristic value has been found. If, after subtracting one from the characteristic value, nums[i] >= x still holds, it means there are multiple values satisfying the condition, which violates the uniqueness of the characteristic value, so return -1 directly. Continue moving the index to the right and decrementing the characteristic value. If no characteristic value is found by the end of the loop, return -1.

Code #

package leetcode

import "sort"

func specialArray(nums []int) int {
	sort.Ints(nums)
	x := len(nums)
	for _, num := range nums {
		if num >= x {
			return x
		}
		x--
		if num >= x {
			return -1
		}
	}
	return -1
}