从给定的排序数组中查找所有缺失的数字

给定一个由N 个整数组成的排序数组arr[] ，任务是在[arr[0], arr[N-1]]范围之间找到数组中的多个缺失元素。

例子：

Input: arr[] = {6, 7, 10, 11, 13}
Output: 8 9 12 
Explanation: 
The elements of the array are present in the range of the maximum and minimum array element [6, 13]. Therefore, the total values will be {6, 7, 8, 9, 10, 11, 12, 13}. 
The elements from the above range which are missing from the array are {8, 9, 12}. 
 

Input: arr[] = {1, 2, 4, 6}
Output: 3 5

朴素的方法：朴素的想法是迭代连续元素对之间的差异，如果差异不为零，则打印此范围内的所有数字。以下是步骤：

1. 初始化等于arr[0] – 0的变量diff 。
2. 现在遍历数组，看看arr[i] – i和diff之间的差异是否为零。
3. 如果上述步骤中的差值不为零，则找到丢失的元素。
4. 要找到多个丢失的元素，请在其中运行一个循环，看看diff是否小于arr[i] – i然后打印丢失的元素，即i + diff 。
5. 现在递增DIFF方面的差异正在增加。
6. 从第 2 步开始重复，直到找不到所有丢失的数字。

下面是上述方法的实现：

C++

// C++ program for the above approach
#include 
using namespace std;
 
// Function to find the missing elements
void printMissingElements(int arr[], int N)
{
 
    // Initialize diff
    int diff = arr[0] - 0;
 
    for (int i = 0; i < N; i++) {
 
        // Check if diff and arr[i]-i
        // both are equal or not
        if (arr[i] - i != diff) {
 
            // Loop for consecutive
            // missing elements
            while (diff < arr[i] - i) {
                cout << i + diff << " ";
                diff++;
            }
        }
    }
}
 
// Driver Code
int main()
{
    // Given array arr[]
    int arr[] = { 6, 7, 10, 11, 13 };
 
    int N = sizeof(arr) / sizeof(int);
 
    // Function Call
    printMissingElements(arr, N);
    return 0;
}

Java

// Java program for the above approach
import java.util.*;
 
class GFG{
     
// Function to find the missing elements
static void printMissingElements(int arr[],
                                 int N)
{
 
    // Initialize diff
    int diff = arr[0] - 0;
 
    for(int i = 0; i < N; i++)
    {
 
        // Check if diff and arr[i]-i
        // both are equal or not
        if (arr[i] - i != diff)
        {
 
            // Loop for consecutive
            // missing elements
            while (diff < arr[i] - i)
            {
                System.out.print((i + diff) + " ");
                diff++;
            }
        }
    }
}
 
// Driver Code
public static void main (String[] args)
{
     
    // Given array arr[]
    int arr[] = { 6, 7, 10, 11, 13 };
     
    int N = arr.length;
     
    // Function call
    printMissingElements(arr, N);
}
}
 
// This code is contributed by offbeat

Python3

# Python3 program for the above approach
 
# Function to find the missing elements
def printMissingElements(arr, N):
 
    # Initialize diff
    diff = arr[0]
 
    for i in range(N):
 
        # Check if diff and arr[i]-i
        # both are equal or not
        if(arr[i] - i != diff):
 
            # Loop for consecutive
            # missing elements
            while(diff < arr[i] - i):
                print(i + diff, end = " ")
                diff += 1
 
# Driver Code
 
# Given array arr[]
arr = [ 6, 7, 10, 11, 13 ]
 
N = len(arr)
 
# Function call
printMissingElements(arr, N)
 
# This code is contributed by Shivam Singh

C#

// C# program for the above approach
using System;
 
class GFG{
     
// Function to find the missing elements
static void printMissingElements(int[] arr,
                                 int N)
{
     
    // Initialize diff
    int diff = arr[0] - 0;
 
    for(int i = 0; i < N; i++)
    {
         
        // Check if diff and arr[i]-i
        // both are equal or not
        if (arr[i] - i != diff)
        {
             
            // Loop for consecutive
            // missing elements
            while (diff < arr[i] - i)
            {
                Console.Write(i + diff + " ");
                diff++;
            }
        }
    }
}
 
// Driver code
static void Main()
{
     
    // Given array arr[]
    int[] arr = { 6, 7, 10, 11, 13 };
     
    int N = arr.Length;
     
    // Function call
    printMissingElements(arr, N);
}
}
 
// This code is contributed by divyeshrabadiya07

Javascript

 
// Javascript program to gather characters
// of a string in minimum cost
  
// Function to find the missing elements
function prletMissingElements(arr, N)
{
  
    // Initialize diff
    let diff = arr[0] - 0;
  
    for(let i = 0; i < N; i++)
    {
  
        // Check if diff and arr[i]-i
        // both are equal or not
        if (arr[i] - i != diff)
        {
  
            // Loop for consecutive
            // missing elements
            while (diff < arr[i] - i)
            {
                document.write((i + diff) + " ");
                diff++;
            }
        }
    }
}
 
// Driver Code
 
     // Given array arr[]
    let arr = [ 6, 7, 10, 11, 13 ];
      
    let N = arr.length;
      
    // Function call
    prletMissingElements(arr, N);
      

输出：

8 9 12

时间复杂度： O(N ² )
辅助空间： O(1)

高效的方法：想法是使用Hashing来优化上述方法。创建一个大小等于数组中最大元素的布尔数组（比如b[] ），并仅标记数组 b[] 中存在于给定数组中的那些位置。打印数组b[]中所有未标记的索引。
以下是步骤：

1. 初始化一个布尔数组b[] ，其大小为零，等于数组的最大元素。
2. 迭代给定数组并标记给定数组中的每个元素，在数组b[]中将该索引标记为真。
3. 现在从索引arr[0]遍历给定数组b[]并打印那些值为 false 的索引，因为它们是给定数组中缺少的元素。

下面是上述方法的实现：

C++

// C++ program for the above approach
 
#include 
using namespace std;
 
// Function to find the missing elements
void printMissingElements(int arr[], int N)
{
    // Initialize an array with zero
    // of size equals to the maximum
    // element in the array
    int b[arr[N - 1] + 1] = { 0 };
 
    // Make b[i]=1 if i is present
    // in the array
    for (int i = 0; i < N; i++) {
 
        // If the element is present
        // make b[arr[i]]=1
        b[arr[i]] = 1;
    }
 
    // Print the indices where b[i]=0
    for (int i = arr[0]; i <= arr[N - 1]; i++) {
 
        if (b[i] == 0) {
            cout << i << " ";
        }
    }
}
 
// Driver Code
int main()
{
    // Given array arr[]
    int arr[] = { 6, 7, 10, 11, 13 };
 
    int N = sizeof(arr) / sizeof(int);
 
    // Function Call
    printMissingElements(arr, N);
 
    return 0;
}

Java

// Java program for the above approach
import java.util.*;
 
class GFG{
     
// Function to find the missing elements
static void printMissingElements(int arr[],
                                int N)
{
     
    // Initialize an array with zero
    // of size equals to the maximum
    // element in the array
    int[] b = new int[arr[N - 1] + 1];
 
    // Make b[i]=1 if i is present
    // in the array
    for(int i = 0; i < N; i++)
    {
         
        // If the element is present
        // make b[arr[i]]=1
        b[arr[i]] = 1;
    }
 
    // Print the indices where b[i]=0
    for(int i = arr[0]; i <= arr[N - 1]; i++)
    {
        if (b[i] == 0)
        {
            System.out.print(i + " ");
        }
    }
}
 
// Driver Code
public static void main (String[] args)
{
     
    // Given array arr[]
    int arr[] = { 6, 7, 10, 11, 13 };
     
    int N = arr.length;
     
    // Function call
    printMissingElements(arr, N);
}
}
 
// This code is contributed by offbeat

蟒蛇3

# Python3 program to implement
# the above approach
 
# Function to find the missing elements
def printMissingElements(arr, N):
 
    # Initialize an array with zero
    # of size equals to the maximum
    # element in the array
    b = [0] * (arr[N - 1] + 1)
 
    # Make b[i]=1 if i is present
    # in the array
    for i in range(N):
 
        # If the element is present
        # make b[arr[i]]=1
        b[arr[i]] = 1
 
    # Print the indices where b[i]=0
    for i in range(arr[0], arr[N - 1] + 1):
        if(b[i] == 0):
            print(i, end = " ")
 
# Driver Code
 
# Given array arr[]
arr = [ 6, 7, 10, 11, 13 ]
 
N = len(arr)
 
# Function call
printMissingElements(arr, N)
 
# This code is contributed by Shivam Singh

C＃

// C# program for
// the above approach
using System;
class GFG{
     
// Function to find the missing elements
static void printMissingElements(int []arr,
                                 int N)
{    
  // Initialize an array with zero
  // of size equals to the maximum
  // element in the array
  int[] b = new int[arr[N - 1] + 1];
 
  // Make b[i]=1 if i is present
  // in the array
  for(int i = 0; i < N; i++)
  {
    // If the element is present
    // make b[arr[i]]=1
    b[arr[i]] = 1;
  }
 
  // Print the indices where b[i]=0
  for(int i = arr[0]; i <= arr[N - 1];
          i++)
  {
    if (b[i] == 0)
    {
      Console.Write(i + " ");
    }
  }
}
 
// Driver Code
public static void Main(String[] args)
{
  // Given array []arr
  int []arr = {6, 7, 10, 11, 13};
 
  int N = arr.Length;
 
  // Function call
  printMissingElements(arr, N);
}
}
 
// This code is contributed by Princi Singh

Javascript

 
// JavaScript program for the above approach
 
// Function to find the missing elements
function printMissingElements(arr, N)
{
    // Initialize an array with zero
    // of size equals to the maximum
    // element in the array
    let b  = new Uint8Array(arr[N - 1] + 1);
 
    // Make b[i]=1 if i is present
    // in the array
    for (let i = 0; i < N; i++) {
 
        // If the element is present
        // make b[arr[i]]=1
        b[arr[i]] = 1;
    }
 
    // Print the indices where b[i]=0
    for (let i = arr[0]; i <= arr[N - 1]; i++) {
 
        if (b[i] == 0) {
            document.write( i + " ");
        }
    }
}
 
// Driver Code
 
    // Given array arr[]
    let arr = [ 6, 7, 10, 11, 13 ];
 
    let N = arr.length;
 
    // Function Call
    printMissingElements(arr, N);
 
     
//This code is contributed by Mayank Tyagi

输出：

8 9 12

时间复杂度： O(M)，其中 M 是数组的最大元素。
辅助空间： O(M)

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