给定一个包含N个元素的数组arr [] ，任务是查找具有频率计数(即该数组中的斐波那契数)的元素的GCD。
例子：
Input: arr[] = { 5, 3, 6, 5, 6, 6, 5, 5 }
Output: 3
Explanation :
Elements 5, 3, 6 appears 4, 1, 3 times respectively.
Hence, 3 and 6 have Fibonacci frequencies.
So, gcd(3, 6) = 1
Input: arr[] = {4, 2, 3, 3, 3, 3}
Output: 2
Explanation :
Elements 4, 2, 3 appears 1, 1, 4 times respectively.
Hence, 4 and 2 have Fibonacci frequencies.
So, gcd(4, 2) = 2
方法：想法是使用散列来预先计算和存储Fibonacci节点到最大值，以使检查变得容易和高效(在O(1)时间内)。
在预计算哈希之后：
- 遍历数组并将所有元素的频率存储在地图中。
- 使用映射和哈希，使用预先计算的哈希计算具有斐波那契频率的元素的gcd。
下面是上述方法的实现：
C++
// C++ program to find the GCD of
// elements which occur Fibonacci
// number of times
#include
using namespace std;
// Function to create hash table
// to check Fibonacci numbers
void createHash(set& hash,
int maxElement)
{
// Inserting the first two
// numbers into the hash
int prev = 0, curr = 1;
hash.insert(prev);
hash.insert(curr);
// Adding the remaining Fibonacci
// numbers using the previously
// added elements
while (curr <= maxElement) {
int temp = curr + prev;
hash.insert(temp);
prev = curr;
curr = temp;
}
}
// Function to return the GCD of elements
// in an array having fibonacci frequency
int gcdFibonacciFreq(int arr[], int n)
{
set hash;
// Creating the hash
createHash(hash,
*max_element(arr,
arr + n));
int i, j;
// Map is used to store the
// frequencies of the elements
unordered_map m;
// Iterating through the array
for (i = 0; i < n; i++)
m[arr[i]]++;
int gcd = 0;
// Traverse the map using iterators
for (auto it = m.begin();
it != m.end(); it++) {
// Calculate the gcd of elements
// having fibonacci frequencies
if (hash.find(it->second)
!= hash.end()) {
gcd = __gcd(gcd,
it->first);
}
}
return gcd;
}
// Driver code
int main()
{
int arr[] = { 5, 3, 6, 5,
6, 6, 5, 5 };
int n = sizeof(arr) / sizeof(arr[0]);
cout << gcdFibonacciFreq(arr, n);
return 0;
} Java
// Java program to find the GCD of
// elements which occur Fibonacci
// number of times
import java.util.*;
class GFG{
// Function to create hash table
// to check Fibonacci numbers
static void createHash(HashSet hash,
int maxElement)
{
// Inserting the first two
// numbers into the hash
int prev = 0, curr = 1;
hash.add(prev);
hash.add(curr);
// Adding the remaining Fibonacci
// numbers using the previously
// added elements
while (curr <= maxElement) {
int temp = curr + prev;
hash.add(temp);
prev = curr;
curr = temp;
}
}
// Function to return the GCD of elements
// in an array having fibonacci frequency
static int gcdFibonacciFreq(int arr[], int n)
{
HashSet hash = new HashSet();
// Creating the hash
createHash(hash,Arrays.stream(arr).max().getAsInt());
int i;
// Map is used to store the
// frequencies of the elements
HashMap m = new HashMap();
// Iterating through the array
for (i = 0; i < n; i++) {
if(m.containsKey(arr[i])){
m.put(arr[i], m.get(arr[i])+1);
}
else{
m.put(arr[i], 1);
}
}
int gcd = 0;
// Traverse the map using iterators
for (Map.Entry it : m.entrySet()) {
// Calculate the gcd of elements
// having fibonacci frequencies
if (hash.contains(it.getValue())) {
gcd = __gcd(gcd,
it.getKey());
}
}
return gcd;
}
static int __gcd(int a, int b)
{
return b == 0? a:__gcd(b, a % b);
}
// Driver code
public static void main(String[] args)
{
int arr[] = { 5, 3, 6, 5,
6, 6, 5, 5 };
int n = arr.length;
System.out.print(gcdFibonacciFreq(arr, n));
}
}
// This code is contributed by Princi Singh Python3
# Python 3 program to find the GCD of
# elements which occur Fibonacci
# number of times
from collections import defaultdict
import math
# Function to create hash table
# to check Fibonacci numbers
def createHash(hash1,maxElement):
# Inserting the first two
# numbers into the hash
prev , curr = 0, 1
hash1.add(prev)
hash1.add(curr)
# Adding the remaining Fibonacci
# numbers using the previously
# added elements
while (curr <= maxElement):
temp = curr + prev
if temp <= maxElement:
hash1.add(temp)
prev = curr
curr = temp
# Function to return the GCD of elements
# in an array having fibonacci frequency
def gcdFibonacciFreq(arr, n):
hash1 = set()
# Creating the hash
createHash(hash1,max(arr))
# Map is used to store the
# frequencies of the elements
m = defaultdict(int)
# Iterating through the array
for i in range(n):
m[arr[i]] += 1
gcd = 0
# Traverse the map using iterators
for it in m.keys():
# Calculate the gcd of elements
# having fibonacci frequencies
if (m[it] in hash1):
gcd = math.gcd(gcd,it)
return gcd
# Driver code
if __name__ == "__main__":
arr = [ 5, 3, 6, 5,
6, 6, 5, 5 ]
n = len(arr)
print(gcdFibonacciFreq(arr, n))
# This code is contributed by chitranayalC#
// C# program to find the GCD of
// elements which occur Fibonacci
// number of times
using System;
using System.Linq;
using System.Collections.Generic;
class GFG{
// Function to create hash table
// to check Fibonacci numbers
static void createHash(HashSet hash,
int maxElement)
{
// Inserting the first two
// numbers into the hash
int prev = 0, curr = 1;
hash.Add(prev);
hash.Add(curr);
// Adding the remaining Fibonacci
// numbers using the previously
// added elements
while (curr <= maxElement) {
int temp = curr + prev;
hash.Add(temp);
prev = curr;
curr = temp;
}
}
// Function to return the GCD of elements
// in an array having fibonacci frequency
static int gcdFibonacciFreq(int []arr, int n)
{
HashSet hash = new HashSet();
// Creating the hash
createHash(hash, hash.Count > 0 ? hash.Max():0);
int i;
// Map is used to store the
// frequencies of the elements
Dictionary m = new Dictionary();
// Iterating through the array
for (i = 0; i < n; i++) {
if(m.ContainsKey(arr[i])){
m[arr[i]] = m[arr[i]] + 1;
}
else{
m.Add(arr[i], 1);
}
}
int gcd = 0;
// Traverse the map using iterators
foreach(KeyValuePair it in m) {
// Calculate the gcd of elements
// having fibonacci frequencies
if (hash.Contains(it.Value)) {
gcd = __gcd(gcd,
it.Key);
}
}
return gcd;
}
static int __gcd(int a, int b)
{
return b == 0? a:__gcd(b, a % b);
}
// Driver code
public static void Main(String[] args)
{
int []arr = { 5, 3, 6, 5,
6, 6, 5, 5 };
int n = arr.Length;
Console.Write(gcdFibonacciFreq(arr, n));
}
}
// This code is contributed by 29AjayKumar 输出：
3