Linear Search in Array

1. Given an unsoorted array of integers nums and an integer target.

Design an algorithm that perform search for the target in the array using linear search.

Return the index of the first occurence of target if found, otherwise return -1.

Binary Search Implementation

2. Given a sorted array of integers nums in ascending order and an integer target.

Design an algorithm that perform binary search to find the index of target. If the target exists in the array return its index. Otherwise, return -1.

first and last Occurrence

3. Given a Sorted array of integers nums in ascending order and an integer target.

Design an algorithm to find the first and last positions (indices) of target in nums.

• If the target exists in the array, return a two-element array [firstIndex, lastIndex].
• If the target is not present, return [-1, -1].

Rotated Array Search

4. Given a sorted array of unique integers nums that has been rotated at an unknown pivot index.

For exampe, [0, 1, 2, 4, 5, 6, 7] might become [4, 5, 6, 7, 0, 1, 2].

Given an integer target. Design an algorithm to search for target in the array.

If target is found, return its index. Otherwise return -1.

A rotated array is formed by taking a sorted array and moving a prefix (one or more elements from the front) to the end, while keeping the relative order of elements unchanged.

Frequency in Array

5. Given a sorted array of integers nums and an integer target.

Design an algorithm that returns the total number of times target appears in the array.

Adaptive Search in any Array

6. Given an array of integers nums and an integer target. Design an algorithm that determines whether target exists in the array.

If the array is sorted in ascending order, use Binary Search. Otherwise, use linear search.

Return true if target exists in nums, otherwise return false.

Rotated Sorted Array Minimum

7. Given a rotated sorted array of unique integers nums (original sorted in strictly increasing order).

Design an algorithm that find and return the minimum element in the array.

Rotated Search Array 2

1. Given a rotated sorted array nums of integers, which may contain duplicate values and an integer target. Design an algorithm that determines if target exists in nums.

The array was sorted in ascending order, but then rotated at an unknown pivot index.

For example, [0,1,2,4,4,4,5,6,6,7] might become [4,5,6,6,7,0,1,2,4,4].

Return true if target exists in the array, otherwise return false.

Peak Element in an Array

2. Given an array of integers nums. A peak element that is strictly greater than its immediate neighbors.

The array may contain multiple peaks . Design an algorithm that return the index of any one of them.

You may assume that nums[i] != nums[i+1] for all valid i.

You can assume that nums[-1] = nums[n] = -∞ (i.e., elements outside the array are smaller than any element inside the array).

A peak element is an index i such that: nums[i] > nums[i - 1] and nums[i] > nums[i + 1]

Search in 2D Matrix

3. Given an m * n 2D matrix matrix where:

• Each row is sorted in ascending order (left to right).
• Each Column is also sorted in ascending order (top to bottom).

Given an integer target. Desing an algorithm the determine whether target exists in the matrix.

Return true if target is found, otherwise return false.

Matrix Property:

• Entire matrix behaves like a 1D sorted array.
• Can be flattened into a single sorted list.

Next Greater Letter

4. Given a sorted array of lowercase letters called letters and a target letter target.

The array is circular — meaning if the target is equal to or greater than the last character, the search wraps around to the start.

Design an algorithm to find and return the smallest letter in the array that is strictly greater than target.

Integer Square Root

5. Given a non-negative integer x. Design an algorithm that computes and returns the integer part of its square root.

In other words, return the floor value of √x, i.e., the largest integer r such that r * r ≤ x.

K Closest Elements

6. Given a sorted array of integers arr, an integer k, and a target value x. Design an algorithm that returns the k closest integers to x in the array.

If multiple values are equally close, prefer the smaller one.

    Input: arr = [1,2,3,4,5], k = 4, x = 3  
    Output: [1,2,3,4]
    
    Input: arr = [1,2,3,4,5], k = 4, x = -1  
    Output: [1,2,3,4]
    
    Input: arr = [1,3,5,7,9], k = 3, x = 6  
    Output: [3,5,7]
 
 

Median of two Sorted Arrays

7. Given two sorted arrays of integers, nums1 and nums2, of sizes m and n respectively.

Design an algorithms that find the median of the combined array formed by merging the two arrays.

Return the median as a floating point number.