Search, insert and delete in a sorted array

In this post search, insert and delete operation in a sorted array is discussed.

Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

Search Operation

In a sorted array, the search operation can be performed by using binary search.

C

```// C program to implement binary search in sorted array
#include<stdio.h>

int binarySearch(int arr[], int low, int high, int key)
{
if (high < low)
return -1;
int mid = (low + high)/2;  /*low + (high - low)/2;*/
if (key == arr[mid])
return mid;
if (key > arr[mid])
return binarySearch(arr, (mid + 1), high, key);
return binarySearch(arr, low, (mid -1), key);
}

/* Driver program to check above functions */
int main()
{
// Let us search 3 in below array
int arr[] = {5, 6, 7, 8, 9, 10};
int n,key;

n = sizeof(arr)/sizeof(arr[0]);
key =10;

printf("Index: %d\n", binarySearch(arr,0, n, key) );
return 0;
}
```

Java

```// Java program to implement binary
// search in a sorted array

class Main
{
// function to implement
// binary search
static int binarySearch(int arr[], int low, int high, int key)
{
if (high < low)
return -1;

/*low + (high - low)/2;*/
int mid = (low + high)/2;
if (key == arr[mid])
return mid;
if (key > arr[mid])
return binarySearch(arr, (mid + 1), high, key);
return binarySearch(arr, low, (mid -1), key);
}

/* Driver program to test above function */
public static void main (String[] args)
{
int arr[] = {5, 6, 7, 8, 9, 10};
int n,key;
n = arr.length;
key =10;

System.out.println("Index: " +
binarySearch(arr,0, n, key) );
}
}
```

Output:

```Index: 5
```

Insert Operation

In an unsorted array, the insert operation is faster as compared to sorted array because we don’t have to care about the position at which the element to be placed.

C

```// C program to implement insert operation in
// an sorted array.
#include<stdio.h>

// Inserts a key in arr[] of given capacity.  n is current
// size of arr[]. This function returns n+1 if insertion
// is successful, else n.
int insertSorted(int arr[], int n, int key, int capacity)
{
// Cannot insert more elements if n is already
// more than or equal to capcity
if (n >= capacity)
return n;

int i;
for (i=n-1; ( i >= 0  && arr[i] > key); i--)
arr[i+1] = arr[i];

arr[i+1] = key;

return (n+1);
}

/* Driver program to test above function */
int main()
{
int arr[20] = {12, 16, 20, 40, 50, 70};
int capacity = sizeof(arr)/sizeof(arr[0]);
int n = 6;
int i, key = 26;

printf("\nBefore Insertion: ");
for (i=0; i<n; i++)
printf("%d  ", arr[i]);

// Inserting key
n = insertSorted(arr, n, key, capacity);

printf("\nAfter Insertion: ");
for (i=0; i<n; i++)
printf("%d  ",arr[i]);

return 0;
}
```

Java

```// Java program to insert an
// element in a sorted array

class Main
{
// Inserts a key in arr[] of given
// capacity.  n is current size of arr[].
// This function returns n+1 if insertion
// is successful, else n.
static int insertSorted(int arr[], int n, int key, int capacity)
{
// Cannot insert more elements if n is already
// more than or equal to capcity
if (n >= capacity)
return n;

int i;
for (i=n-1; (arr[i] > key && i >= 0); i--)
arr[i+1] = arr[i];

arr[i+1] = key;

return (n+1);
}

/* Driver program to test above function */
public static void main (String[] args)
{
int arr[] = new int[20];
arr[0] = 12;
arr[1] = 16;
arr[2] = 20;
arr[3] = 40;
arr[4] = 50;
arr[5] = 70;
int capacity = arr.length;
int n = 6;
int key = 26;

System.out.print("\nBefore Insertion: ");
for (int i=0; i<n; i++)
System.out.print(arr[i] + " ");

// Inserting key
n = insertSorted(arr, n, key, capacity);

System.out.print("\nAfter Insertion: ");
for (int i=0; i<n; i++)
System.out.print(arr[i] + " ");
}
}
```

Output:

```Before Insertion: 12 16 20 40 50 70
After Insertion: 12 16 20 26 40 50 70
```

Delete Operation

In delete operation, the element to be deleted is searched using binary search and then delete operation is performed followed by shifting the elements.

C

```// C program to implement delete operation in a
// sorted array
#include<stdio.h>

// To search a ley to be deleted
int binarySearch(int arr[], int low, int high, int key);

/* Function to delete an element */
int deleteElement(int arr[], int n, int key)
{
// Find position of element to be deleted
int pos = binarySearch(arr, 0, n-1, key);

if (pos==-1)
{
return n;
}

// Deleting element
int i;
for (i=pos; i<n; i++)
arr[i] = arr[i+1];

return n-1;
}

int binarySearch(int arr[], int low, int high, int key)
{
if (high < low)
return -1;
int mid = (low + high)/2;
if (key == arr[mid])
return mid;
if (key > arr[mid])
return binarySearch(arr, (mid + 1), high, key);
return binarySearch(arr, low, (mid -1), key);
}

// Driver code
int main()
{
int i;
int arr[] = {10, 20, 30, 40, 50};

int n = sizeof(arr)/sizeof(arr[0]);
int key = 30;

printf("Array before deletion\n");
for (i=0; i<n; i++)
printf("%d  ", arr[i]);

n = deleteElement(arr, n, key);

printf("\n\nArray after deletion\n");
for (i=0; i<n; i++)
printf("%d  ", arr[i]);
}
```

Java

```// Java program to delete an
// element from a sorted array

class Main
{
// binary search
static int binarySearch(int arr[], int low, int high, int key)
{
if (high < low)
return -1;
int mid = (low + high)/2;
if (key == arr[mid])
return mid;
if (key > arr[mid])
return binarySearch(arr, (mid + 1), high, key);
return binarySearch(arr, low, (mid -1), key);
}

/* Function to delete an element */
static int deleteElement(int arr[], int n, int key)
{
// Find position of element to be deleted
int pos = binarySearch(arr, 0, n-1, key);

if (pos==-1)
{
return n;
}

// Deleting element
int i;
for (i=pos; i<n-1; i++)
arr[i] = arr[i+1];

return n-1;
}

/* Driver program to test above function */
public static void main (String[] args)
{

int i;
int arr[] = {10, 20, 30, 40, 50};

int n = arr.length;
int key = 30;

System.out.print("Array before deletion:\n");
for (i=0; i<n; i++)
System.out.print(arr[i] + " ");

n = deleteElement(arr, n, key);

System.out.print("\n\nArray after deletion:\n");
for (i=0; i<n; i++)
System.out.print(arr[i] + " ");
}
}
```

Output:

```Array before deletion
10 20 30 40 50

Array after deletion
10 20 40 50
```

Search: O(Log n) [Using Binary Search]
Insert: O(n) [In worst case all elements may have to be moved]
Delete: O(n) [In worst case all elements may have to be moved]

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