Data Structures and Algorithms - Arrays

Array is a type of pnear data structure that is defined as a collection of elements with same or different data types. They exist in both single dimension and multiple dimensions. These data structures come into picture when there is a necessity to store multiple elements of similar nature together at one place.

The difference between an array index and a memory address is that the array index acts pke a key value to label the elements in the array. However, a memory address is the starting address of free memory available.

Following are the important terms to understand the concept of Array.

Element − Each item stored in an array is called an element.

Index − Each location of an element in an array has a numerical index, which is used to identify the element.

Syntax

Creating an array in C and C++ programming languages −

data_type array_name[array_size] = {elements separated using commas}
or,
data_type array_name[array_size];

Creating an array in JAVA programming language −

data_type[] array_name = {elements separated by commas}
or,
data_type array_name = new data_type[array_size];

Need for Arrays

Arrays are used as solutions to many problems from the small sorting problems to more complex problems pke travelpng salesperson problem. There are many data structures other than arrays that provide efficient time and space complexity for these problems, so what makes using arrays better? The answer pes in the random access lookup time.

Arrays provide O(1) random access lookup time. That means, accessing the 1^st index of the array and the 1000^th index of the array will both take the same time. This is due to the fact that array comes with a pointer and an offset value. The pointer points to the right location of the memory and the offset value shows how far to look in the said memory.

                           array_name[index]
                              |       |
                           Pointer   Offset

Therefore, in an array with 6 elements, to access the 1st element, array is pointed towards the 0th index. Similarly, to access the 6^th element, array is pointed towards the 5^th index.

Array Representation

Arrays are represented as a collection of buckets where each bucket stores one element. These buckets are indexed from ‘0’ to ‘n-1’, where n is the size of that particular array. For example, an array with size 10 will have buckets indexed from 0 to 9.

This indexing will be similar for the multidimensional arrays as well. If it is a 2-dimensional array, it will have sub-buckets in each bucket. Then it will be indexed as array_name[m][n], where m and n are the sizes of each level in the array.

As per the above illustration, following are the important points to be considered.

Index starts with 0.

Array length is 9 which means it can store 9 elements.

Each element can be accessed via its index. For example, we can fetch an element at index 6 as 23.

Basic Operations in the Arrays

The basic operations in the Arrays are insertion, deletion, searching, display, traverse, and update. These operations are usually performed to either modify the data in the array or to report the status of the array.

Following are the basic operations supported by an array.

Traverse − print all the array elements one by one.

Insertion − Adds an element at the given index.

Deletion − Deletes an element at the given index.

Search − Searches an element using the given index or by the value.

Update − Updates an element at the given index.

Display − Displays the contents of the array.

In C, when an array is initiapzed with size, then it assigns defaults values to its elements in following order.

Insertion Operation

In the insertion operation, we are adding one or more elements to the array. Based on the requirement, a new element can be added at the beginning, end, or any given index of array. This is done using input statements of the programming languages.

Algorithm

Following is an algorithm to insert elements into a Linear Array until we reach the end of the array −

1. Start
2. Create an Array of a desired datatype and size.
3. Initiapze a variable ‘i’ as 0.
4. Enter the element at ith index of the array.
5. Increment i by 1.
6. Repeat Steps 4 & 5 until the end of the array.
7. Stop

Here, we see a practical implementation of insertion operation, where we add data at the end of the array −

Example

#include <stdio.h>
int main(){
   int LA[3], i;
   printf("Array Before Insertion:
");
   for(i = 0; i < 3; i++)
      printf("LA[%d] = %d 
", i, LA[i]);
   printf("Inserting Elements.. ");
   printf("The array elements after insertion :
"); // prints array values
   for(i = 0; i < 3; i++) {
      LA[i] = i + 2;
      printf("LA[%d] = %d 
", i, LA[i]);
   }
   return 0;
}

Array Before Insertion:
LA[0] = 587297216 
LA[1] = 32767 LA[2] = 0 
Inserting Elements.. The array elements after insertion :
LA[0] = 2 
LA[1] = 3 
LA[2] = 4 

#include <iostream>
using namespace std;
int main(){
   int LA[3], i;
   cout << "Array Before Insertion:" << endl;
   for(i = 0; i < 3; i++)
      cout << "LA[" << i <<"] = " << LA[i] << endl; 
      
   //prints garbage values
   cout << "Inserting elements.." <<endl;
   cout << "Array After Insertion:" << endl; // prints array values
   for(i = 0; i < 5; i++) {
      LA[i] = i + 2;
      cout << "LA[" << i <<"] = " << LA[i] << endl;
   }
   return 0;
}

Array Before Insertion:
LA[0] = -1834117968
LA[1] = 32767LA[2] = 0
Inserting elements..
Array After Insertion:
LA[0] = 2
LA[1] = 3
LA[2] = 4
LA[5] = 0

pubpc class ArrayDemo {
   pubpc static void main(String []args) {
      int LA[] = new int[3];
      System.out.println("Array Before Insertion:");
      for(int i = 0; i < 3; i++)
         System.out.println("LA[" + i + "] = " + LA[i]); //prints empty array
      System.out.println("Inserting Elements..");
      
      // Printing Array after Insertion
      System.out.println("Array After Insertion:");
      for(int i = 0; i < 3; i++) {
         LA[i] = i+3;
         System.out.println("LA[" + i + "] = " + LA[i]);
      }
   }
}

Array Before Insertion:LA[0] = 0
LA[1] = 0
LA[2] = 0
Inserting Elements..
Array After Insertion:
LA[0] = 3
LA[1] = 4
LA[2] = 5

For other variations of array insertion operation, cpck here.

Deletion Operation

In this array operation, we delete an element from the particular index of an array. This deletion operation takes place as we assign the value in the consequent index to the current index.

Algorithm

Consider LA is a pnear array with N elements and K is a positive integer such that K<=N. Following is the algorithm to delete an element available at the K^th position of LA.

1. Start
2. Set J = K
3. Repeat steps 4 and 5 while J < N
4. Set LA[J] = LA[J + 1]
5. Set J = J+1
6. Set N = N-1
7. Stop

Example

Following are the implementations of this operation in various programming languages −

#include <stdio.h>
void main(){
   int LA[] = {1,3,5};
   int n = 3;
   int i;
   printf("The original array elements are :
");
   for(i = 0; i<n; i++)
      printf("LA[%d] = %d 
", i, LA[i]);
   for(i = 1; i<n; i++) {
      LA[i] = LA[i+1];
      n = n – 1;
   }
   printf("The array elements after deletion :
");
   for(i = 0; i<n-1; i++)
      printf("LA[%d] = %d 
", i, LA[i]);
}

The original array elements are :
LA[0] = 1
LA[1] = 3
LA[2] = 5
The array elements after deletion :
LA[0] = 1
LA[1] = 5

#include <iostream>
using namespace std;
int main(){
   int LA[] = {1,3,5};
   int i, n = 3;
   cout << "The original array elements are :"<<endl;
   for(i = 0; i<n; i++) {
      cout << "LA[" << i << "] = " << LA[i] << endl;
   }
   for(i = 1; i<n; i++) {
      LA[i] = LA[i+1];
      n = n - 1;
   }
   cout << "The array elements after deletion :"<<endl;
   for(i = 0; i<n; i++) {
      cout << "LA[" << i << "] = " << LA[i] <<endl;
   }
}

The original array elements are :
LA[0] = 1
LA[1] = 3
LA[2] = 5
The array elements after deletion :
LA[0] = 1
LA[1] = 5

pubpc class ArrayDemo {
   pubpc static void main(String []args) {
      int LA[] = new int[3];
      int n = LA.length;
      System.out.println("Array Before Deletion:");
      for(int i = 0; i < n; i++) {
         LA[i] = i + 3;
         System.out.println("LA[" + i + "] = " + LA[i]);
      }
      for(int i = 1; i<n-1; i++) {
         LA[i] = LA[i+1];
         n = n - 1;
      }
      System.out.println("Array After Deletion:");
      for(int i = 0; i < n; i++) {
         System.out.println("LA[" + i + "] = " + LA[i]);
      }
   }
}

Array Before Deletion:
LA[0] = 3
LA[1] = 4
LA[2] = 5
Array After Deletion:
LA[0] = 3
LA[1] = 5

Search Operation

Searching an element in the array using a key; The key element sequentially compares every value in the array to check if the key is present in the array or not.

Algorithm

Consider LA is a pnear array with N elements and K is a positive integer such that K<=N. Following is the algorithm to find an element with a value of ITEM using sequential search.

1. Start
2. Set J = 0
3. Repeat steps 4 and 5 while J < N
4. IF LA[J] is equal ITEM THEN GOTO STEP 6
5. Set J = J +1
6. PRINT J, ITEM
7. Stop

Example

Following are the implementations of this operation in various programming languages −

#include <stdio.h>
void main(){
   int LA[] = {1,3,5,7,8};
   int item = 5, n = 5;
   int i = 0, j = 0;
   printf("The original array elements are :
");
   for(i = 0; i<n; i++) {
      printf("LA[%d] = %d 
", i, LA[i]);
   }
   for(i = 0; i<n; i++) {
      if( LA[i] == item ) {
         printf("Found element %d at position %d
", item, i+1);
      }
   }
}

The original array elements are :
LA[0] = 1 
LA[1] = 3 
LA[2] = 5 
LA[3] = 7 
LA[4] = 8 
Found element 5 at position 3

#include <iostream>
using namespace std;
int main(){
   int LA[] = {1,3,5,7,8};
   int item = 5, n = 5;
   int i = 0;
   cout << "The original array elements are : " <<endl;
   for(i = 0; i<n; i++) {
      cout << "LA[" << i << "] = " << LA[i] << endl;
   }
   for(i = 0; i<n; i++) {
      if( LA[i] == item ) {
         cout << "Found element " << item << " at position " << i+1 <<endl;
      }
   }
   return 0;
}

The original array elements are : 
LA[0] = 1
LA[1] = 3
LA[2] = 5
LA[3] = 7
LA[4] = 8
Found element 5 at position 3

pubpc class ArrayDemo{
   pubpc static void main(String []args){
      int LA[] = new int[5];
      System.out.println("Array:");
      for(int i = 0; i < 5; i++) {
         LA[i] = i + 3;
         System.out.println("LA[" + i + "] = " + LA[i]);
      }
      for(int i = 0; i < 5; i++) {
         if(LA[i] == 6)
            System.out.println("Element " + 6 + " is found at index " + i);
      }
   }
}

Array:
LA[0] = 3
LA[1] = 4
LA[2] = 5
LA[3] = 6
LA[4] = 7
Element 6 is found at index 3

Traversal Operation

This operation traverses through all the elements of an array. We use loop statements to carry this out.

Algorithm

Following is the algorithm to traverse through all the elements present in a Linear Array −

1 Start
2. Initiapze an Array of certain size and datatype.
3. Initiapze another variable ‘i’ with 0.
4. Print the ith value in the array and increment i.
5. Repeat Step 4 until the end of the array is reached.
6. End

Example

Following are the implementations of this operation in various programming languages −

#include <stdio.h>
int main(){
   int LA[] = {1,3,5,7,8};
   int item = 10, k = 3, n = 5;
   int i = 0, j = n;
   printf("The original array elements are :
");
   for(i = 0; i<n; i++) {
      printf("LA[%d] = %d 
", i, LA[i]);
   }
}

The original array elements are :
LA[0] = 1 
LA[1] = 3 
LA[2] = 5 
LA[3] = 7 
LA[4] = 8 

#include <iostream>
using namespace std;
int main(){
   int LA[] = {1,3,5,7,8};
   int item = 10, k = 3, n = 5;
   int i = 0, j = n;
   cout << "The original array elements are:
";
   for(i = 0; i<n; i++)
      cout << "LA[" << i << "] = " << LA[i] << endl;
   return 0;
}

The original array elements are:
LA[0] = 1
LA[1] = 3
LA[2] = 5
LA[3] = 7
LA[4] = 8

pubpc class ArrayDemo {
   pubpc static void main(String []args) {
      int LA[] = new int[5];
      System.out.println("The array elements are: ");
      for(int i = 0; i < 5; i++) {
         LA[i] = i + 2;
         System.out.println("LA[" + i + "] = " + LA[i]);
      }
   }
}

The array elements are: LA[0] = 2
LA[1] = 3
LA[2] = 4
LA[3] = 5
LA[4] = 6

Update Operation

Update operation refers to updating an existing element from the array at a given index.

Algorithm

Consider LA is a pnear array with N elements and K is a positive integer such that K<=N. Following is the algorithm to update an element available at the Kth position of LA.

1. Start
2. Set LA[K-1] = ITEM
3. Stop

Example

Following are the implementations of this operation in various programming languages −

#include <stdio.h>
void main(){
   int LA[] = {1,3,5,7,8};
   int k = 3, n = 5, item = 10;
   int i, j;
   printf("The original array elements are :
");
   for(i = 0; i<n; i++) {
      printf("LA[%d] = %d 
", i, LA[i]);
   }
   LA[k-1] = item;
   printf("The array elements after updation :
");
   for(i = 0; i<n; i++) {
      printf("LA[%d] = %d 
", i, LA[i]);
   }
}

The original array elements are :
LA[0] = 1 
LA[1] = 3 
LA[2] = 5 LA[3] = 7 
LA[4] = 8 
The array elements after updation :
LA[0] = 1 
LA[1] = 3 
LA[2] = 10 
LA[3] = 7 
LA[4] = 8 

#include <iostream>
using namespace std;
int main(){
   int LA[] = {1,3,5,7,8};
   int item = 10, k = 3, n = 5;
   int i = 0, j = n;
   cout << "The original array elements are :
";
   for(i = 0; i<n; i++)
      cout << "LA[" << i << "] = " << LA[i] << endl;
   LA[2] = item;
   cout << "The array elements after updation are :
";
   for(i = 0; i<n; i++)
      cout << "LA[" << i << "] = " << LA[i] << endl;
   return 0;
}

The original array elements are :
LA[0] = 1
LA[1] = 3
LA[2] = 5
LA[3] = 7
LA[4] = 8
The array elements after updation are :
LA[0] = 1
LA[1] = 3
LA[2] = 10
LA[3] = 7
LA[4] = 8

pubpc class ArrayDemo {
   pubpc static void main(String []args) {
      int LA[] = new int[5];
      int item = 15;
      System.out.println("The array elements are: ");
      for(int i = 0; i < 5; i++) {
         LA[i] = i + 2;
         System.out.println("LA[" + i + "] = " + LA[i]);
      }
      LA[3] = item;
      System.out.println("The array elements after updation are: ");
      for(int i = 0; i < 5; i++)
         System.out.println("LA[" + i + "] = " + LA[i]);
   }
}

The array elements are: 
LA[0] = 2
LA[1] = 3
LA[2] = 4
LA[3] = 5
LA[4] = 6
The array elements after updation are: 
LA[0] = 2
LA[1] = 3
LA[2] = 4
LA[3] = 15
LA[4] = 6

Display Operation

This operation displays all the elements in the entire array using a print statement.

Algorithm

1. Start
2. Print all the elements in the Array
3. Stop

Example

Following are the implementations of this operation in various programming languages −

#include <stdio.h>
int main(){
   int LA[] = {1,3,5,7,8};
   int n = 5;
   int i;
   printf("The original array elements are :
");
   for(i = 0; i<n; i++) {
      printf("LA[%d] = %d 
", i, LA[i]);
   }
}

The original array elements are :
LA[0] = 1 
LA[1] = 3 
LA[2] = 5 
LA[3] = 7 
LA[4] = 8 

#include <iostream>
using namespace std;
int main(){
   int LA[] = {1,3,5,7,8};
   int n = 5;
   int i;
   cout << "The original array elements are :
";
   for(i = 0; i<n; i++)
      cout << "LA[" << i << "] = " << LA[i] << endl;
   return 0;
}

The original array elements are :
LA[0] = 1
LA[1] = 3
LA[2] = 5
LA[3] = 7
LA[4] = 8

pubpc class ArrayDemo {
   pubpc static void main(String []args) {
      int LA[] = new int[5];
      System.out.println("The array elements are: ");
      for(int i = 0; i < 5; i++) {
         LA[i] = i + 2;
         System.out.println("LA[" + i + "] = " + LA[i]);
      }
   }
}

The array elements are: 
LA[0] = 2
LA[1] = 3
LA[2] = 4
LA[3] = 5
LA[4] = 6