# Longest Geometric Progression

Datetime:2016-08-23 03:13:31         Topic: Dynamic Programming  C++          Share        Original >>

Given a set of numbers, find the L ength of the L ongest G eometrix P rogression ( LLGP ) in it. The common ratio of GP must be an integer.

Examples:

```set[] = {5, 7, 10, 15, 20, 29}
output = 3
The longest arithmetic progression is {5, 10, 20}

set[] = {3, 9, 27, 81}
output = 4```

This problem is similar to Longest Arithmetic Progression Problem . We can solve this problem using Dynamic Programming.

We first sort the given set. We use an auxiliary table L[n][n] to store results of subproblems. An entry L[i][j] in this table stores LLGP with set[i] and set[j] as first two elements of GP and j > i. The table is filled from bottom right to top left. To fill the table, j (second element in GP) is first fixed. i and k are searched for a fixed j. If i and k are found such that i, j, k form an GP, then the value of L[i][j] is set as L[j][k] + 1. Note that the value of L[j][k] must have been filled before as the loop traverses from right to left columns.

Following is C++ implementation of the Dynamic Programming algorithm.

```// C++ program to find length of the longest geometric
// progression in a given set
#include <iostream>
#include <algorithm>
using namespace std;

// Returns length of the longest GP subset of set[]
int lenOfLongestGP(int set[], int n)
{
// Base cases
if (n < 2)
return n;
if (n == 2)
return (set[1] % set[0] == 0);

// Let us sort the set first
sort(set, set+n);

// An entry L[i][j] in this table stores LLGP with
// set[i] and set[j] as first two elements of GP
// and j > i.
int L[n][n];

// Initialize result (A single element is always a GP)
int llgp = 1;

// Initialize values of last column
for (int i = 0; i < n; ++i)
if (set[n-1] % set[i] == 0)
L[i][n-1] = 2;
else
L[i][n-1] = 1;

// Consider every element as second element of GP
for (int j = n - 2; j >= 1; --j)
{
// Search for i and k for j
int i = j - 1, k = j+1;
while (i>=0 && k <= n-1)
{
// Two cases when i, j and k don't form
// a GP.
if (set[i] * set[k] < set[j]*set[j])
++k;

else if (set[i] * set[k] > set[j]*set[j])
{
if (set[j] % set[i] == 0)
L[i][j] = 2;
else
L[i][j] = 1;
--i;
}

// i, j and k form GP, LLGP with i and j as
// first two elements is equal to LLGP with
// j and k as first two elements plus 1.
// L[j][k] must have been filled before as
// we run the loop from right side
else
{
L[i][j] = L[j][k] + 1;

// Update overall LLGP
if (L[i][j] > llgp)
llgp = L[i][j];

// Change i and k to fill more L[i][j]
// values for current j
--i;
++k;
}
}

// If the loop was stopped due to k becoming
// more than n-1, set the remaining entties
// in column j as 1 or 2 based on divisibility
// of set[j] by set[i]
while (i >= 0)
{
if (set[j] % set[i] == 0)
L[i][j] = 2;
else
L[i][j] = 1;
--i;
}
}

// Return result
return llgp;
}

// Driver code
int main()
{
int set1[] = {1, 3, 9, 27, 81, 243};
int n1 = sizeof(set1)/sizeof(set1[0]);
cout << lenOfLongestGP(set1, n1) << "\n";

int set2[] = {1, 3, 4, 9, 7, 27};
int n2 = sizeof(set2)/sizeof(set2[0]);
cout << lenOfLongestGP(set2, n2) << "\n";

int set3[] = {2, 3, 5, 7, 11, 13};
int n3 = sizeof(set3)/sizeof(set3[0]);
cout << lenOfLongestGP(set3, n3) << "\n";

return 0;
}```

Output:

Time Complexity:O(n 2 )

Auxiliary Space:O(n 2 )

This article is contributed by Vivek Pandya . If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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