在形成几何级数的排序数组中查找所有三元组

给定一个由不同的正整数组成的排序数组，打印所有三元组，这些三元组构成具有整数公比的几何级数。
几何级数是一系列数字，其中第一项之后的每一项都是通过将前一项乘以一个称为共同比率的固定非零数来找到的。例如，序列 2, 6, 18, 54,… 是公比为 3 的几何级数。
例子：

Input: 
arr = [1, 2, 6, 10, 18, 54]
Output: 
2 6 18
6 18 54

Input: 
arr = [2, 8, 10, 15, 16, 30, 32, 64]
Output: 
2 8 32
8 16 32
16 32 64

Input: 
arr = [ 1, 2, 6, 18, 36, 54]
Output: 
2 6 18
1 6 36
6 18 54

这个想法是从第二个元素开始，将每个元素固定为中间元素，并在三元组中搜索其他两个元素（一个较小，一个较大）。要使元素 arr[j] 处于几何级数的中间，必须存在元素 arr[i] 和 arr[k] 使得 –

arr[j] / arr[i] = r and arr[k] / arr[j] = r
where r is an positive integer and 0 <= i < j and j < k <= n - 1

下面是上述想法的实现——

C++

// C++ program to find if there exist three elements in
// Geometric Progression or not
#include 
using namespace std;
 
// The function prints three elements in GP if exists
// Assumption: arr[0..n-1] is sorted.
void findGeometricTriplets(int arr[], int n)
{
    // One by fix every element as middle element
    for (int j = 1; j < n - 1; j++)
    {
        // Initialize i and k for the current j
        int i = j - 1, k = j + 1;
 
        // Find all i and k such that (i, j, k)
        // forms a triplet of GP
        while (i >= 0 && k <= n - 1)
        {
            // if arr[j]/arr[i] = r and arr[k]/arr[j] = r
            // and r is an integer (i, j, k) forms Geometric
            // Progression
            while (arr[j] % arr[i] == 0 &&
                    arr[k] % arr[j] == 0 &&
                    arr[j] / arr[i] == arr[k] / arr[j])
            {
                // print the triplet
                cout << arr[i] << " " << arr[j]
                     << " " << arr[k] << endl;
 
                // Since the array is sorted and elements
                // are distinct.
                k++ , i--;
            }
 
            // if arr[j] is multiple of arr[i] and arr[k] is
            // multiple of arr[j], then arr[j] / arr[i] !=
            // arr[k] / arr[j]. We compare their values to
            // move to next k or previous i.
            if(arr[j] % arr[i] == 0 &&
                    arr[k] % arr[j] == 0)
            {
                if(arr[j] / arr[i] < arr[k] / arr[j])
                    i--;
                else k++;
            }
 
            // else if arr[j] is multiple of arr[i], then
            // try next k. Else, try previous i.
            else if (arr[j] % arr[i] == 0)
                k++;
            else i--;
        }
    }
}
 
// Driver code
int main()
{
    // int arr[] = {1, 2, 6, 10, 18, 54};
    // int arr[] = {2, 8, 10, 15, 16, 30, 32, 64};
    // int arr[] = {1, 2, 6, 18, 36, 54};
    int arr[] = {1, 2, 4, 16};
    // int arr[] = {1, 2, 3, 6, 18, 22};
    int n = sizeof(arr) / sizeof(arr[0]);
 
    findGeometricTriplets(arr, n);
 
    return 0;
}

Java

// Java program to find if there exist three elements in
// Geometric Progression or not
import java.util.*;
 
class GFG
{
 
// The function prints three elements in GP if exists
// Assumption: arr[0..n-1] is sorted.
static void findGeometricTriplets(int arr[], int n)
{
    // One by fix every element as middle element
    for (int j = 1; j < n - 1; j++)
    {
        // Initialize i and k for the current j
        int i = j - 1, k = j + 1;
 
        // Find all i and k such that (i, j, k)
        // forms a triplet of GP
        while (i >= 0 && k <= n - 1)
        {
            // if arr[j]/arr[i] = r and arr[k]/arr[j] = r
            // and r is an integer (i, j, k) forms Geometric
            // Progression
            while (i >= 0 && arr[j] % arr[i] == 0 &&
                    arr[k] % arr[j] == 0 &&
                    arr[j] / arr[i] == arr[k] / arr[j])
            {
                // print the triplet
                System.out.println(arr[i] +" " + arr[j]
                    + " " + arr[k]);
 
                // Since the array is sorted and elements
                // are distinct.
                k++ ; i--;
            }
 
            // if arr[j] is multiple of arr[i] and arr[k] is
            // multiple of arr[j], then arr[j] / arr[i] !=
            // arr[k] / arr[j]. We compare their values to
            // move to next k or previous i.
            if(i >= 0 && arr[j] % arr[i] == 0 &&
                    arr[k] % arr[j] == 0)
            {
                if(i >= 0 && arr[j] / arr[i] < arr[k] / arr[j])
                    i--;
                else k++;
            }
 
            // else if arr[j] is multiple of arr[i], then
            // try next k. Else, try previous i.
            else if (i >= 0 && arr[j] % arr[i] == 0)
                k++;
            else i--;
        }
    }
}
 
// Driver code
public static void main(String[] args)
{
    // int arr[] = {1, 2, 6, 10, 18, 54};
    // int arr[] = {2, 8, 10, 15, 16, 30, 32, 64};
    // int arr[] = {1, 2, 6, 18, 36, 54};
    int arr[] = {1, 2, 4, 16};
    // int arr[] = {1, 2, 3, 6, 18, 22};
    int n = arr.length;
 
    findGeometricTriplets(arr, n);
}
}
 
// This code is contributed by Rajput-Ji

Python 3

# Python 3 program to find if
# there exist three elements in
# Geometric Progression or not
 
# The function prints three elements
# in GP if exists.
# Assumption: arr[0..n-1] is sorted.
def findGeometricTriplets(arr, n):
 
    # One by fix every element
    # as middle element
    for j in range(1, n - 1):
     
        # Initialize i and k for
        # the current j
        i = j - 1
        k = j + 1
 
        # Find all i and k such that
        # (i, j, k) forms a triplet of GP
        while (i >= 0 and k <= n - 1):
         
            # if arr[j]/arr[i] = r and
            # arr[k]/arr[j] = r and r
            # is an integer (i, j, k) forms
            # Geometric Progression
            while (arr[j] % arr[i] == 0 and
                   arr[k] % arr[j] == 0 and
                   arr[j] // arr[i] == arr[k] // arr[j]):
             
                # print the triplet
                print( arr[i] , " " , arr[j],
                                " " , arr[k])
 
                # Since the array is sorted and
                # elements are distinct.
                k += 1
                i -= 1
 
            # if arr[j] is multiple of arr[i]
            # and arr[k] is multiple of arr[j],
            # then arr[j] / arr[i] != arr[k] / arr[j].
            # We compare their values to
            # move to next k or previous i.
            if(arr[j] % arr[i] == 0 and
                        arr[k] % arr[j] == 0):
             
                if(arr[j] // arr[i] < arr[k] // arr[j]):
                    i -= 1
                else:
                    k += 1
 
            # else if arr[j] is multiple of
            # arr[i], then try next k. Else,
            # try previous i.
            elif (arr[j] % arr[i] == 0):
                k += 1
            else:
                i -= 1
 
# Driver code
if __name__ =="__main__":
     
    arr = [1, 2, 4, 16]
    n = len(arr)
 
    findGeometricTriplets(arr, n)
 
# This code is contributed
# by ChitraNayal

C#

// C# program to find if there exist three elements
// in Geometric Progression or not
using System;
 
class GFG
{
     
// The function prints three elements in GP if exists
// Assumption: arr[0..n-1] is sorted.
static void findGeometricTriplets(int []arr, int n)
{
     
    // One by fix every element as middle element
    for (int j = 1; j < n - 1; j++)
    {
        // Initialize i and k for the current j
        int i = j - 1, k = j + 1;
 
        // Find all i and k such that (i, j, k)
        // forms a triplet of GP
        while (i >= 0 && k <= n - 1)
        {
            // if arr[j]/arr[i] = r and arr[k]/arr[j] = r
            // and r is an integer (i, j, k) forms Geometric
            // Progression
            while (i >= 0 && arr[j] % arr[i] == 0 &&
                             arr[k] % arr[j] == 0 &&
                    arr[j] / arr[i] == arr[k] / arr[j])
            {
                // print the triplet
            Console.WriteLine(arr[i] +" " +
                              arr[j] + " " + arr[k]);
 
                // Since the array is sorted and elements
                // are distinct.
                k++ ; i--;
            }
 
            // if arr[j] is multiple of arr[i] and arr[k] is
            // multiple of arr[j], then arr[j] / arr[i] !=
            // arr[k] / arr[j]. We compare their values to
            // move to next k or previous i.
            if(i >= 0 && arr[j] % arr[i] == 0 &&
                         arr[k] % arr[j] == 0)
            {
                if(i >= 0 && arr[j] / arr[i] <
                             arr[k] / arr[j])
                    i--;
                else k++;
            }
 
            // else if arr[j] is multiple of arr[i], then
            // try next k. Else, try previous i.
            else if (i >= 0 && arr[j] % arr[i] == 0)
                k++;
            else i--;
        }
    }
}
 
// Driver code
static public void Main ()
{
     
    // int arr[] = {1, 2, 6, 10, 18, 54};
    // int arr[] = {2, 8, 10, 15, 16, 30, 32, 64};
    // int arr[] = {1, 2, 6, 18, 36, 54};
    int []arr = {1, 2, 4, 16};
     
    // int arr[] = {1, 2, 3, 6, 18, 22};
    int n = arr.Length;
     
    findGeometricTriplets(arr, n);
}
}
 
// This code is contributed by ajit.

Javascript

// Javascript program to find if there exist three elements in
// Geometric Progression or not
 
    // The function prints three elements in GP if exists
    // Assumption: arr[0..n-1] is sorted.
    function findGeometricTriplets(arr,n)
    {
     
        // One by fix every element as middle element
        for (let j = 1; j < n - 1; j++)
        {
         
            // Initialize i and k for the current j
            let i = j - 1, k = j + 1;
       
            // Find all i and k such that (i, j, k)
            // forms a triplet of GP
            while (i >= 0 && k <= n - 1)
            {
             
                // if arr[j]/arr[i] = r and arr[k]/arr[j] = r
                // and r is an integer (i, j, k) forms Geometric
                // Progression
                while (i >= 0 && arr[j] % arr[i] == 0 &&
                        arr[k] % arr[j] == 0 &&
                        arr[j] / arr[i] == arr[k] / arr[j])
                {
                 
                    // print the triplet
                    document.write(arr[i] +" " + arr[j]
                        + " " + arr[k]+"<br>");
       
                    // Since the array is sorted and elements
                    // are distinct.
                    k++ ; i--;
                }
       
                // if arr[j] is multiple of arr[i] and arr[k] is
                // multiple of arr[j], then arr[j] / arr[i] !=
                // arr[k] / arr[j]. We compare their values to
                // move to next k or previous i.
                if(i >= 0 && arr[j] % arr[i] == 0 &&
                        arr[k] % arr[j] == 0)
                {
                    if(i >= 0 && arr[j] / arr[i] < arr[k] / arr[j])
                        i--;
                    else k++;
                }
       
                // else if arr[j] is multiple of arr[i], then
                // try next k. Else, try previous i.
                else if (i >= 0 && arr[j] % arr[i] == 0)
                    k++;
                else i--;
            }
        }
    }
     
    // Driver code
    // int arr[] = {1, 2, 6, 10, 18, 54};
    // int arr[] = {2, 8, 10, 15, 16, 30, 32, 64};
    // int arr[] = {1, 2, 6, 18, 36, 54};
     
    let arr = [1, 2, 4, 16];
     
    // int arr[] = {1, 2, 3, 6, 18, 22};
    let n = arr.length;
    findGeometricTriplets(arr, n);
     
    // This code is contributed by avanitrachhadiya2155

输出：

1 2 4
1 4 16