The array range query problem can be defined as follows:

Given an array of numbers, the array range query problem is to build a data structure that can efficiently answer queries of a particular type mentioned in terms of an interval of the indices.

The specific query can be of type – maximum element in the given range, most frequent element in the given range or queries like these.

Types of Array Range Queries:

Array range queries can be classified based on the type of input provided and on the type of output:

1. Based on the type of input:

• The value of interest is completely determined by the problem, in this case, the query consists of only a range of indices.
• A single value of interest is provided in the query.
• The query consists of a threshold where all the values above or below the threshold are of interest.
• The query consists of an exact threshold value.

2. Based on the type of output:

• Returns a single value matching the criteria.
• Index of an element that matches the criteria provided in the query.
• A list of all values that satisfy the given criteria.
• Only a response like “yes” or “no” denoting if there is any result matching the criteria of the query.

Easy Problems on Array range Queries:

• Range sum queries without updates
• Range Queries for Frequencies of array elements
• Range LCM Queries
• Count Primes in Ranges
• Queries for number of distinct elements in a subarray
• Mean of range in array
• Check in binary array the number represented by a subarray is odd or even
• Total numbers with no repeated digits in a range
• Queries for counts of array elements with values in given range
• Queries for decimal values of subarrays of a binary array
• GCDs of given index ranges in an array
• Queries on probability of even or odd number in given ranges

Medium Problems on Array range Queries:

• Difference Array | Range update query in O(1)
• Range sum query using Sparse Table
• Number of indexes with equal elements in given range
• Constant time range add operation on an array
• Number whose sum of XOR with given array range is maximum
• Number of primes in a subarray (with updates)
• Print modified array after executing the commands of addition and subtraction
• Sum of Interval and Update with Number of Divisors
• Queries on XOR of greatest odd divisor of the range
• Print modified array after multiple array range increment operations
• Binary array after M range toggle operations

Hard Problems on Array range Queries:

• Sparse Table
• MO’s Algorithm
• Sqrt (or Square Root) Decomposition Technique | Set 1 (Introduction)
• Range Minimum Query (Square Root Decomposition and Sparse Table)
• Number of elements less than or equal to a given number in a given subarray
• Number of elements less than or equal to a given number in a given subarray | Set 2 (Including Updates)
• Array range queries over range queries
• Array range queries for searching an element
• Maximum Occurrence in a Given Range
• Merge Sort Tree for Range Order Statistics
• Count and Toggle Queries on a Binary Array
• Min-Max Range Queries in Array
• Range Query on array whose each element is XOR of index value and previous element
• Count elements which divide all numbers in range L-R
• Queries for GCD of all numbers of an array except elements in a given range
• XOR of numbers that appeared even number of times in given Range

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