数组中三元组的计数，使得 A[i] * A[j] = A[k] 并且 i < j < k

给定一个由N 个正整数组成的数组A[ ] ，任务是在数组中找到三元组A[i]、A[j] 和 A[k]的数量，使得i < j < k和A[i] * A[j] = A[k] 。

例子：

Input: N = 5, A[ ] = {2, 3, 4, 6, 12} 
Output: 3 
Explanation: 
The valid triplets from the given array are: 
(A[0], A[1], A[3]) = (2, 3, 6) where (2*3 = 6) 
(A[0], A[3], A[4]) = (2, 6, 12) where (2*6 = 12) 
(A[1], A[2], A[4]) = (3, 4, 12) where (3*4 = 12) 
Hence, a total of 3 triplets exists which satisfies the given condition.
Input: N = 3, A[ ] = {1, 1, 1} 
Output: 1 
Explanation: 
The only valid triplet is (A[0], A[1], A[2]) = (1, 1, 1) 
 

天真的方法：
解决问题的最简单方法是生成所有可能的三元组，并针对每个三元组检查它是否满足所需条件。如果发现是真的，增加三胞胎的数量。在完整遍历数组并生成所有可能的三元组后，打印最终计数。
时间复杂度： O(N ³ )
辅助空间： O(1)
有效的方法：
上述方法可以使用两个指针和 HashMap 进行优化。
请按照以下步骤解决问题：

• 初始化 Map 以存储数组元素的频率。
• 反向迭代数组，即使用范围[N – 2, 1] 中的变量j进行循环。
• 对于每个j ，增加地图中A[j + 1]的计数。使用变量i在范围[0, j – 1] 上迭代并检查A[i] * A[j]是否存在于地图中。
• 如果A [1] * A [j]的在地图中发现，通过存储在地图A的频率[I] * A [j]的增加三胞胎的计数。
• 完成数组遍历后，打印最终计数。

下面是上述方法的实现：

C++

// C++ Program to implement
// the above approach
#include 
using namespace std;
 
// Returns total number of
// valid triplets possible
int countTriplets(int A[], int N)
{
    // Stores the count
    int ans = 0;
 
    // Map to store frequency
    // of array elements
    map map;
 
    for (int j = N - 2; j >= 1; j--) {
 
        // Increment the frequency
        // of A[j+1] as it can be
        // a valid A[k]
        map[A[j + 1]]++;
 
        for (int i = 0; i < j; i++) {
 
            int target = A[i] * A[j];
 
            // If target exists in the map
            if (map.find(target)
                != map.end())
                ans += map[target];
        }
    }
 
    // Return the final count
    return ans;
}
 
// Driver Code
int main()
{
    int N = 5;
    int A[] = { 2, 3, 4, 6, 12 };
 
    cout << countTriplets(A, N);
 
    return 0;
}

Java

// Java program to implement
// the above approach
import java.util.*;
 
class GFG{
 
// Returns total number of
// valid triplets possible
static int countTriplets(int A[], int N)
{
     
    // Stores the count
    int ans = 0;
 
    // Map to store frequency
    // of array elements
    HashMap map = new HashMap();
                                        
    for(int j = N - 2; j >= 1; j--)
    {
 
        // Increment the frequency
        // of A[j+1] as it can be
        // a valid A[k]
        if(map.containsKey(A[j + 1]))
            map.put(A[j + 1], map.get(A[j + 1]) + 1);
        else
            map.put(A[j + 1], 1);
 
        for(int i = 0; i < j; i++)
        {
            int target = A[i] * A[j];
 
            // If target exists in the map
            if (map.containsKey(target))
                ans += map.get(target);
        }
    }
 
    // Return the final count
    return ans;
}
 
// Driver Code
public static void main(String[] args)
{
    int N = 5;
    int A[] = { 2, 3, 4, 6, 12 };
 
    System.out.print(countTriplets(A, N));
}
}
 
// This code is contributed by sapnasingh4991

Python3

# Python3 program for the above approach
from collections import defaultdict
 
# Returns total number of
# valid triplets possible
def countTriplets(A, N):
 
    # Stores the count
    ans = 0
 
    # Map to store frequency
    # of array elements
    map = defaultdict(lambda: 0)
 
    for j in range(N - 2, 0, -1):
 
        # Increment the frequency
        # of A[j+1] as it can be
        # a valid A[k]
        map[A[j + 1]] += 1
 
        for i in range(j):
            target = A[i] * A[j]
 
            # If target exists in the map
            if(target in map.keys()):
                ans += map[target]
 
    # Return the final count
    return ans
 
# Driver code
if __name__ == '__main__':
 
    N = 5
    A = [ 2, 3, 4, 6, 12 ]
 
    print(countTriplets(A, N))
 
# This code is contributed by Shivam Singh

C#

// C# program to implement
// the above approach
using System;
using System.Collections.Generic;
class GFG{
 
// Returns total number of
// valid triplets possible
static int countTriplets(int []A, int N)
{
     
    // Stores the count
    int ans = 0;
 
    // Map to store frequency
    // of array elements
    Dictionary map = new Dictionary();
                                        
    for(int j = N - 2; j >= 1; j--)
    {
 
        // Increment the frequency
        // of A[j+1] as it can be
        // a valid A[k]
        if(map.ContainsKey(A[j + 1]))
            map[A[j + 1]] = map[A[j + 1]] + 1;
        else
            map.Add(A[j + 1], 1);
 
        for(int i = 0; i < j; i++)
        {
            int target = A[i] * A[j];
 
            // If target exists in the map
            if (map.ContainsKey(target))
                ans += map[target];
        }
    }
 
    // Return the readonly count
    return ans;
}
 
// Driver Code
public static void Main(String[] args)
{
    int N = 5;
    int []A = { 2, 3, 4, 6, 12 };
 
    Console.Write(countTriplets(A, N));
}
}
 
// This code is contributed by sapnasingh4991

Javascript

 
// Javascript program to implement
// the above approach
  
// Returns total number of
// valid triplets possible
function countTriplets(A, N)
{
      
    // Stores the count
    let ans = 0;
  
    // Map to store frequency
    // of array elements
    let map = new Map();
                                         
    for(let j = N - 2; j >= 1; j--)
    {
  
        // Increment the frequency
        // of A[j+1] as it can be
        // a valid A[k]
        if(map.has(A[j + 1]))
            map.set(A[j + 1], map.get(A[j + 1]) + 1);
        else
            map.set(A[j + 1], 1);
  
        for(let i = 0; i < j; i++)
        {
            let target = A[i] * A[j];
  
            // If target exists in the map
            if (map.has(target))
                ans += map.get(target);
        }
    }
  
    // Return the final count
    return ans;
}
  
// Driver code
    let N = 5;
    let A = [ 2, 3, 4, 6, 12 ];
  
    document.write(countTriplets(A, N));
 
// This code is contributed by souravghosh0416.

输出：

3

时间复杂度： O(N ² )
辅助空间： O(N)

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