Array Data Structure

Recent articles on Arrays

An array is a collection of items stored at contiguous memory locations. The idea is to store multiple items of the same type together. This makes it easier to calculate the position of each element by simply adding an offset to a base value, i.e., the memory location of the first element of the array (generally denoted by the name of the array).

The above image can be looked as a top-level view of a staircase where you are at the base of the staircase. Each element can be uniquely identified by their index in the array (in a similar way as you could identify your friends by the step on which they were on in the above example).

Topics :

Array Introduction :

  1. Introduction to Arrays
  2. Arrays in C/C++
  3. Arrays in Java
  4. Arrays in Python

Array Rotations :



  1. Program for array rotation
  2. Reversal algorithm for array rotation
  3. Block swap algorithm for array rotation
  4. Program to cyclically rotate an array by one
  5. Search an element in a sorted and rotated array
  6. Given a sorted and rotated array, find if there is a pair with a given sum
  7. Find maximum value of Sum( i*arr[i]) with only rotations on given array allowed
  8. Maximum sum of i*arr[i] among all rotations of a given array
  9. Find the Rotation Count in Rotated Sorted array
  10. Quickly find multiple left rotations of an array
  11. Find the minimum element in a sorted and rotated array
  12. Reversal algorithm for right rotation of an array
  13. Find a rotation with maximum hamming distance
  14. Queries on Left and Right Circular shift on array
  15. Print left rotation of array in O(n) time and O(1) space
  16. Find element at given index after a number of rotations
  17. Split the array and add the first part to the end

More >>

Arrangement Rearrangement :

  1. Rearrange an array such that arr[i] = i
  2. Write a program to reverse an array or string
  3. Rearrange array such that arr[i] >= arr[j] if i is even and arr[i]<=arr[j] if i is odd and j < i
  4. Rearrange positive and negative numbers in O(n) time and O(1) extra space
  5. Rearrange array in alternating positive & negative items with O(1) extra space | Set 1
  6. Move all zeroes to end of array
  7. Move all zeroes to end of array | Set-2 (Using single traversal)
  8. Minimum swaps required to bring all elements less than or equal to k together
  9. Rearrange positive and negative numbers using inbuilt sort function
  10. Rearrange array such that even positioned are greater than odd
  11. Rearrange an array in order – smallest, largest, 2nd smallest, 2nd largest, ..
  12. Double the first element and move zero to end
  13. Reorder an array according to given indexes
  14. Rearrange positive and negative numbers with constant extra space
  15. Arrange given numbers to form the biggest number
  16. Rearrange an array such that ‘arr[j]’ becomes ‘i’ if ‘arr[i]’ is ‘j’
  17. Rearrange an array in maximum minimum form | Set 1
  18. Rearrange an array in maximum minimum form | Set 2 (O(1) extra space)
  19. Move all negative numbers to beginning and positive to end with constant extra space
  20. Move all negative elements to end in order with extra space allowed
  21. Rearrange array such that even index elements are smaller and odd index elements are greater
  22. Positive elements at even and negative at odd positions
  23. Replace every array element by multiplication of previous and next
  24. Shuffle a given array
  25. Segregate even and odd numbers

More >>

Order Statistics :

  1. K’th Smallest/Largest Element in Unsorted Array | Set 1
  2. K’th Smallest/Largest Element in Unsorted Array | Set 2 (Expected Linear Time)
  3. K’th Smallest/Largest Element in Unsorted Array | Set 3 (Worst Case Linear Time)
  4. K’th Smallest/Largest Element using STL
  5. k largest(or smallest) elements in an array | added Min Heap method
  6. Kth smallest element in a row-wise and column-wise sorted 2D array | Set 1
  7. Program to find largest element in an array
  8. Find the largest three elements in an array
  9. Find all elements in array which have at-least two greater elements
  10. Program for Mean and median of an unsorted array
  11. Median of Stream of Running Integers using STL
  12. Minimum product of k integers in an array of positive Integers
  13. K-th Largest Sum Contiguous Subarray
  14. K maximum sum combinations from two arrays
  15. K maximum sums of overlapping contiguous sub-arrays
  16. K maximum sums of non-overlapping contiguous sub-arrays
  17. k smallest elements in same order using O(1) extra space
  18. Find k pairs with smallest sums in two arrays
  19. k-th smallest absolute difference of two elements in an array
  20. Find Second largest element in an array
  21. Find k numbers with most occurrences in the given array
  22. Find the smallest and second smallest elements in an array
  23. Find the smallest missing number
  24. Maximum sum such that no two elements are adjacent
  25. Maximum and minimum of an array using minimum number of comparisons

More >>

Range Queries :

  1. MO’s Algorithm
  2. Sqrt (or Square Root) Decomposition Technique | Set 1 (Introduction)
  3. Sparse Table
  4. Range sum query using Sparse Table
  5. Range Minimum Query (Square Root Decomposition and Sparse Table)
  6. Range Queries for Frequencies of array elements
  7. Constant time range add operation on an array
  8. Range LCM Queries
  9. GCDs of given index ranges in an array
  10. Queries for GCD of all numbers of an array except elements in a given range
  11. Number of elements less than or equal to a given number in a given subarray
  12. Number of elements less than or equal to a given number in a given subarray | Set 2 (Including Updates)
  13. Queries for counts of array elements with values in given range
  14. Queries for decimal values of subarrays of a binary array
  15. Count elements which divide all numbers in range L-R
  16. Number whose sum of XOR with given array range is maximum
  17. XOR of numbers that appeared even number of times in given Range
  18. Array range queries over range queries
  19. Array range queries for searching an element
  20. Array range queries for elements with frequency same as value
  21. Maximum Occurrence in a Given Range
  22. Number of indexes with equal elements in given range
  23. Merge Sort Tree for Range Order Statistics
  24. Total numbers with no repeated digits in a range
  25. Difference Array | Range update query in O(1)

More >>



Optimization Problems :

  1. Largest Sum Contiguous Subarray
  2. Maximum profit by buying and selling a share at most twice
  3. Find the subarray with least average
  4. Find the minimum distance between two numbers
  5. Minimize the maximum difference between the heights
  6. Minimum number of jumps to reach end
  7. Dynamic Programming | Set 14 (Maximum Sum Increasing Subsequence)
  8. Smallest subarray with sum greater than a given value
  9. Find maximum average subarray of k length
  10. Count minimum steps to get the given desired array
  11. Number of subsets with product less than k
  12. Find minimum number of merge operations to make an array palindrome
  13. Find the smallest positive integer value that cannot be represented as sum of any subset of a given array
  14. Size of The Subarray With Maximum Sum
  15. Find minimum difference between any two elements
  16. Space optimization using bit manipulations
  17. Longest Span with same Sum in two Binary arrays

Sorting :

  1. Alternative Sorting
  2. Sort a nearly sorted (or K sorted) array
  3. Sort an array according to absolute difference with given value
  4. Sort an array in wave form
  5. Merge an array of size n into another array of size m+n
  6. Sort an array which contain 1 to n values
  7. Sort 1 to N by swapping adjacent elements
  8. Sort an array containing two types of elements
  9. Sort elements by frequency | Set 1
  10. Count Inversions in an array | Set 1 (Using Merge Sort)
  11. Two elements whose sum is closest to zero
  12. Shortest Un-ordered Subarray
  13. Minimum number of swaps required to sort an array
  14. Union and Intersection of two sorted arrays
  15. Find Union and Intersection of two unsorted arrays
  16. Sort an array of 0s, 1s and 2s
  17. Find the Minimum length Unsorted Subarray, sorting which makes the complete array sorted
  18. Median in a stream of integers (running integers)
  19. Count the number of possible triangles
  20. Find number of pairs (x, y) in an array such that x^y > y^x
  21. Count all distinct pairs with difference equal to k
  22. Print All Distinct Elements of a given integer array
  23. Construct an array from its pair-sum array
  24. Merge two sorted arrays with O(1) extra space
  25. Product of maximum in first array and minimum in second

More >>

Searching :

  1. Search, insert and delete in an unsorted array
  2. Search, insert and delete in a sorted array
  3. Given an array A[] and a number x, check for pair in A[] with sum as x
  4. Searching in an array where adjacent differ by at most k
  5. Find common elements in three sorted arrays
  6. Find position of an element in a sorted array of infinite numbers
  7. Find the only repetitive element between 1 to n-1
  8. Find the element that appears once
  9. Maximum Subarray Sum Excluding Certain Elements
  10. Maximum equlibrium sum in an array
  11. Equilibrium index of an array
  12. Leaders in an array
  13. Ceiling in a sorted array
  14. Majority Element
  15. Check for Majority Element in a sorted array
  16. Check if an array has a majority element
  17. Two Pointers Technique
  18. Find a peak element
  19. Find the two repeating elements in a given array
  20. Find a Fixed Point in a given array
  21. Find sub-array with given sum
  22. Maximum triplet sum in array
  23. Smallest Difference Triplet from Three arrays
  24. Find a triplet that sum to a given value
  25. Find all triplets with zero sum

More >>

Matrix :

  1. Rotate Matrix Elements
  2. Inplace rotate square matrix by 90 degrees | Set 1
  3. Rotate a matrix by 90 degree without using any extra space | Set 2
  4. Rotate a Matrix by 180 degree
  5. Turn an image by 90 degree
  6. Rotate each ring of matrix anticlockwise by K elements
  7. Check if all rows of a matrix are circular rotations of each other
  8. Sort the given matrix
  9. Find the row with maximum number of 1s
  10. Find median in row wise sorted matrix
  11. Matrix Multiplication | Recursive
  12. Program to multiply two matrices
  13. Program for scalar multiplication of a matrix
  14. Program to print Lower triangular and Upper triangular matrix of an array
  15. Find distinct elements common to all rows of a matrix
  16. Print a given matrix in spiral form
  17. Find maximum element of each row in a matrix
  18. Find unique elements in a matrix
  19. Shift matrix elements row-wise by k
  20. Different Operations on Matrices
  21. Print a given matrix in counter-clock wise spiral form
  22. Swap major and minor diagonals of a square matrix
  23. Maximum path sum in matrix
  24. Squares of Matrix Diagonal Elements
  25. Move matrix elements in given direction and add elements with same value

More >>

Misc :

  1. Subarray/Substring vs Subsequence and Programs to Generate them
  2. A Product Array Puzzle
  3. Number of subarrays with given product
  4. Linked List vs Array
  5. Check if array elements are consecutive | Added Method 3
  6. Find whether an array is subset of another array | Added Method 3
  7. Implement two stacks in an array
  8. Find relative complement of two sorted arrays
  9. Minimum increment by k operations to make all elements equal
  10. Minimize (max(A[i], B[j], C[k]) – min(A[i], B[j], C[k])) of three different sorted arrays

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