多集等价问题

与集合不同，多重集合可能包含多次出现的相同数字。多重集等价问题声明检查两个给定的多重集是否相等。例如让A = {1, 2, 3} 和B = {1, 1, 2, 3}。这里A已设置但B未设置（1 在 B 中出现两次），而A和B都是多重集。更正式地说，“对的集合是否定义为$\(A' = \{ (a, frequency(a)) | a \in \mathbf{A} \}\)$两个给定的多重集相等吗？”
给定两个多重集 A 和 B，编写一个程序来检查这两个多重集是否相等。
注意：多重集中的元素可以是 10 ⁹的阶数
例子：

Input : A = {1, 1, 3, 4},  
        B = {1, 1, 3, 4}
Output : Yes

Input : A = {1, 3},  
        B = {1, 1}
Output : No

由于元素大到 10^9 我们不能使用直接索引表。
一种解决方案是对两个多重集进行排序并一一比较。

C++

// C++ program to check if two given multisets
// are equivalent
#include 
using namespace std;
 
bool areSame(vector& a, vector& b)
{
    // sort the elements of both multisets
    sort(a.begin(), a.end());
    sort(b.begin(), b.end());
 
    // Return true if both multisets are same.
    return (a == b);
}
 
int main()
{
    vector a({ 7, 7, 5 }), b({ 7, 5, 5 });
    if (areSame(a, b))
        cout << "Yes\n";
    else
        cout << "No\n";
    return 0;
}

Java

// Java program to check if two given multisets
// are equivalent
import java.util.*;
class GFG {
 
 
static boolean areSame(Vectora, Vectorb)
{
    // sort the elements of both multisets
    Collections.sort(a);
    Collections.sort(b);
 
    // Return true if both multisets are same.
    return (a == b);
}
 public static void main(String[] args) {
       Vector a = new Vector(Arrays.asList( 7, 7, 5 ));
       Vector b = new Vector(Arrays.asList( 7, 5, 5));
    if (areSame(a, b))
        System.out.print("Yes\n");
    else
        System.out.print("No\n");
    }
}
// This code is contributed by PrinciRaj1992

Python3

# Python3 program to check if
# two given multisets are equivalent
 
def areSame(a, b):
     
    # sort the elements of both multisets
    a.sort();
    b.sort();
 
    # Return true if both multisets are same.
    return (a == b);
 
# Driver Code
a = [ 7, 7, 5 ];
b = [ 7, 5, 5 ];
if (areSame(a, b)):
    print("Yes");
else:
    print("No");
 
# This code is contributed by Princi Singh

C#

// C# program to check if two given multisets
// are equivalent
using System;
using System.Collections.Generic;
 
class GFG
{
 
static bool areSame(Lista, Listb)
{
    // sort the elements of both multisets
    a.Sort();
    b.Sort();
 
    // Return true if both multisets are same.
    return (a == b);
}
 
// Driver code
public static void Main()
{
    List a = new List { 7, 7, 5 };
    List b = new List { 7, 5, 5 };
    if (areSame(a, b))
        Console.WriteLine("Yes\n");
    else
        Console.WriteLine("No\n");
}
}
 
// This code is contributed by Rajput-Ji

Javascript

 
// JavaScript program to check if two given multisets
// are equivalent
 
 
function areSame(a, b) {
    // sort the elements of both multisets
    a.sort((a, b) => a - b);
    b.sort((a, b) => a - b);
 
    // Return true if both multisets are same.
    return (a == b);
}
 
 
let a = [7, 7, 5], b = [7, 5, 5];
if (areSame(a, b))
    document.write("Yes<br>");
else
    document.write("No<br>");
     

输出：

No

更好的解决方案是使用散列。我们创建了两个空的哈希表（在 C++ 中使用 unordered_map 实现）。我们首先在第一个表中插入第一个多重映射的所有项目，在第二个表中插入第二个多重集的所有项目。现在我们检查两个哈希表是否包含相同的项目和频率。

C++

// C++ program to check if two given multisets
// are equivalent
#include 
using namespace std;
 
bool areSame(vector& a, vector& b)
{
    if (a.size() != b.size())
        return false;
 
    // Create two unordered maps m1 and m2
    // and insert values of both vectors.
    unordered_map m1, m2;
    for (int i = 0; i < a.size(); i++) {
        m1[a[i]]++;
        m2[b[i]]++;
    }
 
    // Now we check if both unordered_maps
    // are same of not.
    for (auto x : m1) {
        if (m2.find(x.first) == m2.end() ||
            m2[x.first] != x.second)
            return false;
    }
 
    return true;
}
 
// Driver code
int main()
{
    vector a({ 7, 7, 5 }), b({ 7, 7, 5 });
    if (areSame(a, b))
        cout << "Yes\n";
    else
        cout << "No\n";
    return 0;
}

Java

// Java program to check if two given multisets
// are equivalent
import java.util.*;
 
class GFG
{
static boolean areSame(int []a, int []b)
{
    if (a.length != b.length)
        return false;
 
    // Create two unordered maps m1 and m2
    // and insert values of both vectors.
    HashMap m1, m2;
    m1 = new HashMap();
    m2 = new HashMap();
    for (int i = 0; i < a.length; i++)
    {
        if(m1.containsKey(a[i]))
        {
            m1.put(a[i], m1.get(a[i]) + 1);
        }
        else
        {
            m1.put(a[i], 1);
        }
        if(m2.containsKey(b[i]))
        {
            m2.put(b[i], m2.get(b[i]) + 1);
        }
        else
        {
            m2.put(b[i], 1);
        }
    }
 
    // Now we check if both unordered_maps
    // are same of not.
    for (Map.Entry x : m1.entrySet())
    {
        if (!m2.containsKey(x.getKey()) ||
             m2.get(x.getKey()) != x.getValue())
            return false;
    }
    return true;
}
 
// Driver code
public static void main(String args[])
{
    int []a = { 7, 7, 5 };
    int []b = { 7, 7, 5 };
    if (areSame(a, b))
        System.out.println("Yes");
    else
        System.out.println("No");
}
}
 
// This code is contributed by 29AjayKumar

C＃

// C# program to check if two given multisets
// are equivalent
using System;
using System.Collections.Generic;
 
class GFG
{
static bool areSame(int []a, int []b)
{
    if (a.Length != b.Length)
        return false;
 
    // Create two unordered maps m1 and m2
    // and insert values of both vectors.
    Dictionary m1, m2;
    m1 = new Dictionary();
    m2 = new Dictionary();
    for (int i = 0; i < a.Length; i++)
    {
        if(m1.ContainsKey(a[i]))
        {
            m1[a[i]] = m1[a[i]] + 1;
        }
        else
        {
            m1.Add(a[i], 1);
        }
        if(m2.ContainsKey(b[i]))
        {
            m2[b[i]] = m2[b[i]] + 1;
        }
        else
        {
            m2.Add(b[i], 1);
        }
    }
 
    // Now we check if both unordered_maps
    // are same of not.
    foreach(KeyValuePair x in m1)
    {
        if (!m2.ContainsKey(x.Key) ||
             m2[x.Key] != x.Value)
            return false;
    }
    return true;
}
 
// Driver code
public static void Main(String []args)
{
    int []a = { 7, 7, 5 };
    int []b = { 7, 7, 5 };
    if (areSame(a, b))
        Console.WriteLine("Yes");
    else
        Console.WriteLine("No");
}
}
 
// This code is contributed by 29AjayKumar

Javascript

      // JavaScript program to check if two given multisets
      // are equivalent
      function areSame(a, b)
      {
        if (a.length != b.length) return false;
 
        // Create two unordered maps m1 and m2
        // and insert values of both vectors.
        var m1, m2;
        m1 = {};
        m2 = {};
        for (var i = 0; i < a.length; i++)
        {
          if (m1.hasOwnProperty(a[i]))
          {
            m1[a[i]] = m1[a[i]] + 1;
          } else {
            m1[a[i]] = 1;
          }
          if (m2.hasOwnProperty(b[i])) {
            m2[b[i]] = m2[b[i]] + 1;
          } else {
            m2[b[i]] = 1;
          }
        }
 
        // Now we check if both unordered_maps
        // are same of not.
        for (const [key, value] of Object.entries(m1)) {
          if (!m2.hasOwnProperty(key) || m2[key] != value) return false;
        }
        return true;
      }
 
      // Driver code
      var a = [7, 7, 5];
      var b = [7, 7, 5];
      if (areSame(a, b)) document.write("Yes");
      else document.write("No");
       
      // This code is contributed by rdtank.
    

输出：

Yes

时间复杂度： O(n) 假设 unordered_map find() 和 insert() 操作在 O(1) 时间内工作。

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