查找范围内缺少的元素

给定一个由不同元素组成的数组arr [0..n-1]和一个范围[low，high]，找到所有在范围内但不在数组中的数字。缺少的元素应按排序顺序打印。

例子：

Input: arr[] = {10, 12, 11, 15}, 
       low = 10, hight = 15
Output: 13, 14

Input: arr[] = {1, 14, 11, 51, 15}, 
       low = 50, hight = 55
Output: 50, 52, 53, 54

可以采用以下两种方法来解决该问题。

使用排序：对数组进行排序，然后对“低”进行二进制搜索。一旦找到低位，请从该位置开始遍历数组，并继续打印所有遗漏的数字。

C++

// A sorting based C++ program to find missing
// elements from an array
#include 
using namespace std;
 
// Print all elements of range [low, high] that
// are not present in arr[0..n-1]
void printMissing(int arr[], int n, int low,
                  int high)
{
    // Sort the array
    sort(arr, arr + n);
 
    // Do binary search for 'low' in sorted
    // array and find index of first element
    // which either equal to or greater than
    // low.
    int* ptr = lower_bound(arr, arr + n, low);
    int index = ptr - arr;
 
    // Start from the found index and linearly
    // search every range element x after this
    // index in arr[]
    int i = index, x = low;
    while (i < n && x <= high) {
        // If x doesn't math with current element
        // print it
        if (arr[i] != x)
            cout << x << " ";
 
        // If x matches, move to next element in arr[]
        else
            i++;
 
        // Move to next element in range [low, high]
        x++;
    }
 
    // Print range elements thar are greater than the
    // last element of sorted array.
    while (x <= high)
        cout << x++ << " ";
}
 
// Driver program
int main()
{
    int arr[] = { 1, 3, 5, 4 };
    int n = sizeof(arr) / sizeof(arr[0]);
    int low = 1, high = 10;
    printMissing(arr, n, low, high);
    return 0;
}

Java

// A sorting based Java program to find missing
// elements from an array
 
import java.util.Arrays;
 
public class PrintMissing {
    // Print all elements of range [low, high] that
    // are not present in arr[0..n-1]
    static void printMissing(int ar[], int low, int high)
    {
        Arrays.sort(ar);
        // Do binary search for 'low' in sorted
        // array and find index of first element
        // which either equal to or greater than
        // low.
        int index = ceilindex(ar, low, 0, ar.length - 1);
        int x = low;
 
        // Start from the found index and linearly
        // search every range element x after this
        // index in arr[]
        while (index < ar.length && x <= high) {
            // If x doesn't math with current element
            // print it
            if (ar[index] != x) {
                System.out.print(x + " ");
            }
 
            // If x matches, move to next element in arr[]
            else
                index++;
            // Move to next element in range [low, high]
            x++;
        }
 
        // Print range elements thar are greater than the
        // last element of sorted array.
        while (x <= high) {
            System.out.print(x + " ");
            x++;
        }
    }
 
    // Utility function to find ceil index of given element
    static int ceilindex(int ar[], int val, int low, int high)
    {
 
        if (val < ar[0])
            return 0;
        if (val > ar[ar.length - 1])
            return ar.length;
 
        int mid = (low + high) / 2;
        if (ar[mid] == val)
            return mid;
        if (ar[mid] < val) {
            if (mid + 1 < high && ar[mid + 1] >= val)
                return mid + 1;
            return ceilindex(ar, val, mid + 1, high);
        }
        else {
            if (mid - 1 >= low && ar[mid - 1] < val)
                return mid;
            return ceilindex(ar, val, low, mid - 1);
        }
    }
 
    // Driver program to test above function
    public static void main(String[] args)
    {
        int arr[] = { 1, 3, 5, 4 };
        int low = 1, high = 10;
        printMissing(arr, low, high);
    }
}
 
// This code is contributed by Rishabh Mahrsee

Python

# Python library for binary search
from bisect import bisect_left
 
# A sorting based C++ program to find missing
# elements from an array
 
# Print all elements of range [low, high] that
# are not present in arr[0..n-1]
 
def printMissing(arr, n, low, high):
     
    # Sort the array
    arr.sort()
     
    # Do binary search for 'low' in sorted
    # array and find index of first element
    # which either equal to or greater than
    # low.
    ptr = bisect_left(arr, low)
    index = ptr
     
    # Start from the found index and linearly
    # search every range element x after this
    # index in arr[]
    i = index
    x = low
    while (i < n and x <= high):
    # If x doesn't math with current element
    # print it
        if(arr[i] != x):
            print(x, end =" ")
 
    # If x matches, move to next element in arr[]
        else:
            i = i + 1
    # Move to next element in range [low, high]
        x = x + 1
 
    # Print range elements thar are greater than the
    # last element of sorted array.
    while (x <= high):
        print(x, end =" ")
        x = x + 1
 
 
# Driver code
 
arr = [1, 3, 5, 4]
n = len(arr)
low = 1
high = 10
printMissing(arr, n, low, high);
 
# This code is contributed by YatinGupta

C#

// A sorting based Java program to
// find missing elements from an array
using System;
 
class GFG {
 
    // Print all elements of range
    // [low, high] that are not
    // present in arr[0..n-1]
    static void printMissing(int[] ar,
                             int low, int high)
    {
        Array.Sort(ar);
 
        // Do binary search for 'low' in sorted
        // array and find index of first element
        // which either equal to or greater than
        // low.
        int index = ceilindex(ar, low, 0,
                              ar.Length - 1);
        int x = low;
 
        // Start from the found index and linearly
        // search every range element x after this
        // index in arr[]
        while (index < ar.Length && x <= high) {
            // If x doesn't math with current
            // element print it
            if (ar[index] != x) {
                Console.Write(x + " ");
            }
 
            // If x matches, move to next
            // element in arr[]
            else
                index++;
 
            // Move to next element in
            // range [low, high]
            x++;
        }
 
        // Print range elements thar
        // are greater than the
        // last element of sorted array.
        while (x <= high) {
            Console.Write(x + " ");
            x++;
        }
    }
 
    // Utility function to find
    // ceil index of given element
    static int ceilindex(int[] ar, int val,
                         int low, int high)
    {
        if (val < ar[0])
            return 0;
        if (val > ar[ar.Length - 1])
            return ar.Length;
 
        int mid = (low + high) / 2;
        if (ar[mid] == val)
            return mid;
        if (ar[mid] < val) {
            if (mid + 1 < high && ar[mid + 1] >= val)
                return mid + 1;
            return ceilindex(ar, val, mid + 1, high);
        }
        else {
            if (mid - 1 >= low && ar[mid - 1] < val)
                return mid;
            return ceilindex(ar, val, low, mid - 1);
        }
    }
 
    // Driver Code
    static public void Main()
    {
        int[] arr = { 1, 3, 5, 4 };
        int low = 1, high = 10;
        printMissing(arr, low, high);
    }
}
 
// This code is contributed
// by Sach_Code

输出：

2 6 7 8 9 10

使用数组：创建一个布尔数组，其中每个索引将表示数组中是否存在第(i + low)个元素。标记所有在给定范围内并且存在于数组中的元素。一旦在给定范围内存在的所有数组项都在数组中标记为true，我们将遍历布尔数组并打印所有值为false的元素。

C++ 14

// An array based C++ program
// to find missing elements from
// an array
#include 
using namespace std;
 
// Print all elements of range
// [low, high] that are not present
// in arr[0..n-1]
void printMissing(
    int arr[], int n,
    int low, int high)
{
    // Create boolean array of size
    // high-low+1, each index i representing
    // wether (i+low)th element found or not.
    bool points_of_range[high - low + 1] = { false };
 
    for (int i = 0; i < n; i++) {
        // if ith element of arr is in
        // range low to high then mark
        // corresponding index as true in array
        if (low <= arr[i] && arr[i] <= high)
            points_of_range[arr[i] - low] = true;
    }
 
    // Traverse through the range and
    // print all elements  whose value
    // is false
    for (int x = 0; x <= high - low; x++) {
        if (points_of_range[x] == false)
            cout << low + x << " ";
    }
}
 
// Driver program
int main()
{
    int arr[] = { 1, 3, 5, 4 };
    int n = sizeof(arr) / sizeof(arr[0]);
    int low = 1, high = 10;
    printMissing(arr, n, low, high);
    return 0;
}
 
// This code is contributed by Shubh Bansal

Java

// An array based Java program
// to find missing elements from
// an array
 
import java.util.Arrays;
 
public class Print {
    // Print all elements of range
    // [low, high] that are not present
    // in arr[0..n-1]
    static void printMissing(
        int arr[], int low,
        int high)
    {
        // Create boolean array of
        // size high-low+1, each index i
        // representing wether (i+low)th
        // element found or not.
        boolean[] points_of_range = new boolean
            [high - low + 1];
 
        for (int i = 0; i < arr.length; i++) {
            // if ith element of arr is in
            // range low to high then mark
            // corresponding index as true in array
            if (low <= arr[i] && arr[i] <= high)
                points_of_range[arr[i] - low] = true;
        }
 
        // Traverse through the range and print all
        // elements whose value is false
        for (int x = 0; x <= high - low; x++) {
            if (points_of_range[x] == false)
                System.out.print((low + x) + " ");
        }
    }
 
    // Driver program to test above function
    public static void main(String[] args)
    {
        int arr[] = { 1, 3, 5, 4 };
        int low = 1, high = 10;
        printMissing(arr, low, high);
    }
}
 
// This code is contributed by Shubh Bansal

Python3

# An array-based Python3 program to
# find missing elements from an array
 
# Print all elements of range
# [low, high] that are not
# present in arr[0..n-1]
def printMissing(arr, n, low, high):
 
    # Create boolean list of size
    # high-low+1, each index i
    # representing wether (i+low)th
    # element found or not.
    points_of_range = [False] * (high-low+1)
     
    for i in range(n) :
        # if ith element of arr is in range
        # low to high then mark corresponding
        # index as true in array
        if ( low <= arr[i] and arr[i] <= high ) :
            points_of_range[arr[i]-low] = True
 
    # Traverse through the range
    # and print all elements  whose value
    # is false
    for x in range(high-low+1) :
        if (points_of_range[x]==False) :
            print(low+x, end = " ")
 
# Driver Code
arr = [1, 3, 5, 4]
n = len(arr)
low, high = 1, 10
printMissing(arr, n, low, high)
 
# This code is contributed
# by Shubh Bansal

C＃

// An array based C# program
// to find missing elements from
// an array
using System;
 
class GFG{
 
// Print all elements of range
// [low, high] that are not present
// in arr[0..n-1]
static void printMissing(int[] arr, int n,
                         int low, int high)
{
     
    // Create boolean array of size
    // high-low+1, each index i representing
    // wether (i+low)th element found or not.
      bool[] points_of_range = new bool[high - low + 1];
       
      for(int i = 0; i < high - low + 1; i++)
          points_of_range[i] = false;
 
    for(int i = 0; i < n; i++)
    {
         
        // If ith element of arr is in
        // range low to high then mark
        // corresponding index as true in array
        if (low <= arr[i] && arr[i] <= high)
            points_of_range[arr[i] - low] = true;
    }
 
    // Traverse through the range and
    // print all elements  whose value
    // is false
    for(int x = 0; x <= high - low; x++)
    {
        if (points_of_range[x] == false)
            Console.Write("{0} ", low + x);
    }
}
 
// Driver code
public static void Main()
{
    int[] arr = { 1, 3, 5, 4 };
    int n = arr.Length;
    int low = 1, high = 10;
     
    printMissing(arr, n, low, high);
}
}
 
// This code is contributed by subhammahato348

输出：

2 6 7 8 9 10

使用哈希：创建哈希表并将所有数组项插入哈希表。一旦所有项目都在哈希表中，遍历范围并打印所有缺少的元素。

C++

// A hashing based C++ program to find missing
// elements from an array
#include 
using namespace std;
 
// Print all elements of range [low, high] that
// are not present in arr[0..n-1]
void printMissing(int arr[], int n, int low,
                  int high)
{
    // Insert all elements of arr[] in set
    unordered_set s;
    for (int i = 0; i < n; i++)
        s.insert(arr[i]);
 
    // Traverse throught the range an print all
    // missing elements
    for (int x = low; x <= high; x++)
        if (s.find(x) == s.end())
            cout << x << " ";
}
 
// Driver program
int main()
{
    int arr[] = { 1, 3, 5, 4 };
    int n = sizeof(arr) / sizeof(arr[0]);
    int low = 1, high = 10;
    printMissing(arr, n, low, high);
    return 0;
}

Java

// A hashing based Java program to find missing
// elements from an array
 
import java.util.Arrays;
import java.util.HashSet;
 
public class Print {
    // Print all elements of range [low, high] that
    // are not present in arr[0..n-1]
    static void printMissing(int ar[], int low, int high)
    {
        HashSet hs = new HashSet<>();
 
        // Insert all elements of arr[] in set
        for (int i = 0; i < ar.length; i++)
            hs.add(ar[i]);
 
        // Traverse throught the range an print all
        // missing elements
        for (int i = low; i <= high; i++) {
            if (!hs.contains(i)) {
                System.out.print(i + " ");
            }
        }
    }
 
    // Driver program to test above function
    public static void main(String[] args)
    {
        int arr[] = { 1, 3, 5, 4 };
        int low = 1, high = 10;
        printMissing(arr, low, high);
    }
}
 
// This code is contributed by Rishabh Mahrsee

Python3

# A hashing based Python3 program to
# find missing elements from an array
 
# Print all elements of range
# [low, high] that are not
# present in arr[0..n-1]
def printMissing(arr, n, low, high):
 
    # Insert all elements of
    # arr[] in set
    s = set(arr)
 
    # Traverse through the range
    # and print all missing elements
    for x in range(low, high + 1):
        if x not in s:
            print(x, end = ' ')
 
# Driver Code
arr = [1, 3, 5, 4]
n = len(arr)
low, high = 1, 10
printMissing(arr, n, low, high)
 
# This code is contributed
# by SamyuktaSHegde

C＃

// A hashing based C# program to
// find missing elements from an array
using System;
using System.Collections.Generic;
 
class GFG {
 
    // Print all elements of range
    // [low, high] that are not
    // present in arr[0..n-1]
    static void printMissing(int[] arr, int n,
                             int low, int high)
    {
        // Insert all elements of arr[] in set
        HashSet s = new HashSet();
        for (int i = 0; i < n; i++) {
            s.Add(arr[i]);
        }
 
        // Traverse throught the range
        // an print all missing elements
        for (int x = low; x <= high; x++)
            if (!s.Contains(x))
                Console.Write(x + " ");
    }
 
    // Driver Code
    public static void Main()
    {
        int[] arr = { 1, 3, 5, 4 };
        int n = arr.Length;
        int low = 1, high = 10;
        printMissing(arr, n, low, high);
    }
}
 
// This code is contributed by ihritik

输出：

2 6 7 8 9 10

哪种方法更好?
第一种方法的时间复杂度是O(nLogn + k)，其中k是丢失元素的数量(请注意，如果数组较小且范围较大，则k可能大于nLogn)
第二个和第三个解决方案的时间复杂度为O(n +(high-low + 1))。

如果给定的数组几乎具有范围内的元素，即n接近(high-low + 1)的值，则第二和第三种方法肯定更好，因为没有Log n因子。但是，如果n小于范围，则第一种方法会更好，因为它不需要用于散列的额外空间。我们还可以修改第一种方法以将相邻的缺失元素打印为范围，以节省时间。例如，如果缺少50、51、52、53、54、59，我们可以在第一种方法中将它们打印为50-54、59。如果允许以这种方式打印，则第一种方法仅需要O(n Log n)时间。

在第二和第三解决方案之外，第二解决方案更好，因为第二种解决方案在最坏情况下的时间复杂度比第三种更好。