Array Range Queries
Last Updated :
23 Aug, 2024
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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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