Here is a detailed markdown blog post for the GeeksforGeeks problem:

Fascinating Number

702881

Summary

The fascinating number problem involves identifying a specific pattern in an array of integers. The given array contains a sequence of numbers where each number is either equal to its previous number plus one or minus one. The goal is to find the first index at which this pattern breaks.

Detailed Explanation

Problem Description

Given an array arr of size n, we need to find the first index i such that arr[i] does not satisfy the condition: either arr[i-1] + 1 == arr[i] or arr[i-1] - 1 == arr[i]. In other words, we are looking for the first index where the difference between two consecutive elements is not equal to 1.

Algorithmic Approach

To solve this problem, we can use a simple iteration over the array. We start by initializing an index i to 0 and a variable prev to the first element of the array (arr[0]). Then, we iterate through the array starting from the second element (index 1). For each element, we check if it satisfies the condition: either it's equal to the previous element plus one or minus one. If not, we return the current index as the result.

Step-by-Step Breakdown

Here is a step-by-step breakdown of the solution:

1. Initialize i to 0 and prev to arr[0].
2. Iterate through the array starting from index 1.
3. For each element at index j, check if it satisfies the condition: either prev + 1 == arr[j] or prev - 1 == arr[j].
4. If the condition is not satisfied, return j as the result.
5. Otherwise, update prev to the current element and increment i.

Time and Space Complexity Analysis

The time complexity of this algorithm is O(n), where n is the size of the input array. This is because we are iterating through the array once.

The space complexity is O(1), as we only use a constant amount of space to store the variables i and prev.

Optimized Solutions

Java