在排序的数组中搜索，插入和删除

在此后搜索中，讨论了排序数组中的插入和删除操作。

搜索操作

在排序的数组中，可以通过使用二进制搜索来执行搜索操作。

C++

// C++ program to implement binary search in sorted array
#include 
using namespace std;
 
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 code */
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;
 
    cout << "Index: " << binarySearch(arr, 0, n - 1, key)
         << endl;
    return 0;
}
 
// This code is contributed by NamrataSrivastava1

C

// C program to implement binary search in sorted array
#include 
 
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 Code */
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-1, 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 Code*/
    public static void main(String[] args)
    {
        int arr[] = { 5, 6, 7, 8, 9, 10 };
        int n, key;
        n = arr.length - 1;
        key = 10;
 
        System.out.println("Index: " + binarySearch(arr, 0, n, key));
    }
}

Python3

# python 3  program to implement
# binary search in sorted array
 
def binarySearch(arr, low, high, key):
 
    if (high < low):
        return -1
    # low + (high - low)/2
    mid = (low + high)/2
 
    if (key == arr[int(mid)]):
        return mid
 
    if (key > arr[int(mid)]):
        return binarySearch(arr,
           (mid + 1), high, key)
 
    return (binarySearch(arr, low,
           (mid -1), key))
 
# Driver program to check above functions
# Let us search 3 in below array
arr = [5, 6, 7, 8, 9, 10]
n = len(arr)
key = 10
print("Index:", int(binarySearch(arr, 0, n-1, key) ))
 
# This code is contributed by
# Smitha Dinesh Semwal

C#

// C# program to implement binary
// search in a sorted array
 
using System;
 
public class GFG {
    // function to implement
    // binary search
    public 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 Code */
    public static void Main(string[] args)
    {
        int[] arr = new int[] { 5, 6, 7, 8, 9, 10 };
        int n, key;
        n = arr.Length;
        key = 10;
 
        Console.WriteLine("Index: "
                          + binarySearch(arr, 0, n-1, key));
    }
}
 
// This code is contributed by Shrikant13

PHP

// PHP program to implement
// binary search in sorted array
 $arr[(int)$mid])
        return binarySearch($arr, ($mid + 1),
                            $high, $key);
     
    return (binarySearch($arr, $low,
                        ($mid -1), $key));
}
 
// Driver Code
 
// Let us search 3 in below array
$arr = array(5, 6, 7, 8, 9, 10);
$n = count($arr);
$key = 10;
echo "Index: ", (int)binarySearch($arr, 0,
                                  $n-1, $key);
 
// This code is contributed by
// Srathore
?>

Javascript

 
 
// Javascript program to implement
// binary search in sorted array
 
function binarySearch( arr, low, high, key)
{
    if (high < low)
        return -1;
        /*low + (high - low)/2;*/
    let mid = Math.trunc((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
     
    // Let us search 3 in below array
    let arr = [ 5, 6, 7, 8, 9, 10 ];
    let n, key;
 
    n = arr.length;
    key = 10;
 
    document.write( "Index: " + binarySearch(arr, 0, n - 1, key)
    + "</br>");
     
     

输出

Index: 5

搜索操作的时间复杂度： O(Log n)[使用二进制搜索]

插入操作

在未排序的数组中，插入操作比已排序的数组要快，因为我们不必关心要放置元素的位置。

C++

// C++ program to implement insert operation in
// an sorted array.
#include 
using namespace std;
 
// 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 code */
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;
 
    cout<< "\nBefore Insertion: ";
    for (i = 0; i < n; i++)
        cout << arr[i] << " ";
 
    // Inserting key
    n = insertSorted(arr, n, key, capacity);
 
    cout << "\nAfter Insertion: ";
    for (i = 0; i < n; i++)
        cout << arr[i]<< " ";
 
    return 0;
}
 
// This code is contributed by SHUBHAMSINGH10

C

// C program to implement insert operation in
// an sorted array.
#include 
 
// 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; (i >= 0 && arr[i] > key); 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] + " ");
    }
}

Python3

# Python3 program to implement insert
# operation in an sorted array.
 
# 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.
def insertSorted(arr, n, key, capacity):
     
    # Cannot insert more elements if n is
    # already more than or equal to capcity
    if (n >= capacity):
        return n
 
    i = n - 1
    while i >= 0 and arr[i] > key:
        arr[i + 1] = arr[i]
        i -= 1
 
    arr[i + 1] = key
 
    return (n + 1)
 
# Driver Code
arr = [12, 16, 20, 40, 50, 70]
 
for i in range(20):
    arr.append(0)
 
capacity = len(arr)
n = 6
key = 26
 
print("Before Insertion: ", end = " ");
for i in range(n):
    print(arr[i], end = " ")
     
# Inserting key
n = insertSorted(arr, n, key, capacity)
 
print("\nAfter Insertion: ", end = "")
for i in range(n):
    print(arr[i], end = " ")
 
# This code is contributed by Mohit Kumar

C＃

using System;
 
// C# program to insert an
// element in a sorted array
 
public class GFG {
    // 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.
    public 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; (i >= 0 && arr[i] > key); 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;
 
        Console.Write("\nBefore Insertion: ");
        for (int i = 0; i < n; i++) {
            Console.Write(arr[i] + " ");
        }
 
        // Inserting key
        n = insertSorted(arr, n, key, capacity);
 
        Console.Write("\nAfter Insertion: ");
        for (int i = 0; i < n; i++) {
            Console.Write(arr[i] + " ");
        }
    }
}
 
// This code is contributed by Shrikant13

输出

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

插入操作的时间复杂度： O(n)[在最坏的情况下，所有元素都可能需要移动]

删除操作

在删除操作中，使用二进制搜索来搜索要删除的元素，然后执行删除操作，然后移动这些元素。

C++

// C++ program to implement delete operation in a
// sorted array
#include 
using namespace std;
 
// 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)
    {
        cout << "Element not found";
        return n;
    }
 
    // Deleting element
    int i;
    for (i = pos; i < n - 1; 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;
 
    cout << "Array before deletion\n";
    for (i = 0; i < n; i++)
        cout << arr[i] << " ";
 
    n = deleteElement(arr, n, key);
 
    cout << "\n\nArray after deletion\n";
    for (i = 0; i < n; i++)
        cout << arr[i] << " ";
}
 
// This code is contributed by shubhamsingh10

C

// C program to implement delete operation in a
// sorted array
#include 
 
// 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) {
        printf("Element not found");
        return n;
    }
 
    // Deleting element
    int i;
    for (i = pos; i < n - 1; 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) {
            System.out.println("Element not found");
            return n;
        }
 
        // Deleting element
        int i;
        for (i = pos; i < n - 1; i++)
            arr[i] = arr[i + 1];
 
        return n - 1;
    }
 
    /* Driver Code */
    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] + " ");
    }
}

Python3

# Python program to implement delete operation in a
# sorted array
 
#/* Function to delete an element */
def deleteElement(arr, n, key):
     
    # Find position of element to be deleted
    pos = binarySearch(arr, 0, n - 1, key)
     
    if (pos == -1):
        print("Element not found")
        return n
         
    # Deleting element
    for i in range(pos,n - 1):
        arr[i] = arr[i + 1]
     
    return n - 1
     
# To search a ley to be deleted
def binarySearch(arr, low, high, key):
     
    if (high < low):
        return -1
    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
arr = [10, 20, 30, 40, 50 ]
 
n = len(arr)
key = 30
 
print("Array before deletion")
 
for i in range(n):
    print(arr[i],end=" ")
     
n = deleteElement(arr, n, key)
print("\n\nArray after deletion")
for i in range(n):
    print(arr[i],end=" ")
 
# This code is contributed by shubhamsingh10

C＃

// C# program to delete an
// element from a sorted array
using System;
public class GFG {
    // 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) {
            Console.WriteLine("Element not found");
            return n;
        }
 
        // Deleting element
        int i;
        for (i = pos; i < n - 1; i++)
            arr[i] = arr[i + 1];
 
        return n - 1;
    }
 
    /* Driver Code */
    public static void Main()
    {
 
        int i;
        int[] arr = { 10, 20, 30, 40, 50 };
 
        int n = arr.Length;
        int key = 30;
 
        Console.Write("Array before deletion:\n");
        for (i = 0; i < n; i++)
            Console.Write(arr[i] + " ");
 
        n = deleteElement(arr, n, key);
 
        Console.Write("\n\nArray after deletion:\n");
        for (i = 0; i < n; i++)
            Console.Write(arr[i] + " ");
    }
}
 
// This code is contributed by Rajput-Ji

输出

Array before deletion
10 20 30 40 50 

Array after deletion
10 20 40 50 

删除操作的时间复杂度： O(n)[在最坏的情况下，所有元素都可能必须移动]

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