Problem Statement: Numbers with No Neighbors

Problem Description

Given a 0-indexed array nums of length n, you are to determine the number of indices i such that there is no other number in the array with the value nums[i] - 1. In other words, find the number of local maxima from the given array.

Constraints

• n == nums.length
• 1 <= n <= 105
• 0 <= nums[i] <= 105

Example 1

Input: nums = [2, 1, 2]

Output: 2

Explanation:

• For index i = 0, nums[0] - 1 = 1, which is present in the array. Hence, it is not a local maxima.
• For index i = 1, nums[1] - 1 = 0, which is not present in the array. Hence, it is a local maxima.
• For index i = 2, nums[2] - 1 = 1, which is present in the array. Hence, it is not a local maxima.

Example 2

Input: nums = [8, 10, 1, 8, 7, 7]

Output: 3

Explanation:

• For index i = 0, nums[0] - 1 = 7, which is present in the array. Hence, it is not a local maxima.
• For index i = 1, nums[1] - 1 = 9, which is not present in the array. Hence, it is a local maxima.
• For index i = 2, nums[2] - 1 = 0, which is not present in the array. Hence, it is a local maxima.
• For index i = 3, nums[3] - 1 = 7, which is present in the array. Hence, it is not a local maxima.
• For index i = 4, nums[4] - 1 = 6, which is not present in the array. Hence, it is a local maxima.
• For index i = 5, nums[5] - 1 = 6, which is not present in the array. Hence, it is a local maxima.

Example 3

Input: nums = [6, 6, 5, 6, 5]

Output: 1

Explanation:

• For index i = 0, nums[0] - 1 = 5, which is present in the array. Hence, it is not a local maxima.
• For index i = 1, nums[1] - 1 = 5, which is present in the array. Hence, it is not a local maxima.
• For index i = 2, nums[2] - 1 = 4, which is not present in the array. Hence, it is a local maxima.
• For index i = 3, nums[3] - 1 = 5, which is present in the array. Hence, it is not a local maxima.
• For index i = 4, nums[4] - 1 = 4, which is not present in the array. Hence, it is a local maxima.

Hints

• Consider the problem as finding local maxima in an array.
• You can use a hash map to keep track of the presence of numbers in the array.
• Iterate through the array and check if nums[i] - 1 is present in the hash map. If not, increment your count.