给定一个包含整数的数组A ，任务是找到通过从数组中仅删除一个元素形成的最长斐波纳契子数组的长度。
例子：
Input: arr[] = { 2, 8, 5, 7, 3, 5, 7 }
Output: 5
Explanation:
If we remove the number 7 at index 3, then the remaining array contains a Fibonacci subarray {2, 8, 5, 3, 5} of length 5, which is maximum.
Input: arr[] = { 2, 3, 6, 1 }
Output: 3
Explanation:
If we remove the number 6 at index 2, then the remaining array contains a Fibonacci subarray {2, 3, 1} of length 3, which is maximum.
方法：可以通过在每个索引之前和每个索引之后计算连续的斐波那契数来解决上述问题。
- 现在再次遍历数组，并找到一个索引，该索引前后的斐波纳契数最大。
- 为了检查斐波那契数，我们将构建一个哈希表，其中包含所有小于或等于数组中最大值的斐波那契数，以测试O(1)时间中的数字。
下面是上述方法的实现：
CPP
// C++ program to find length of the longest
// subarray with all fibonacci numbers
#include
using namespace std;
#define N 100000
// Function to create hash table
// to check for Fibonacci numbers
void createHash(set& hash,
int maxElement)
{
// Insert first two fibnonacci numbers
int prev = 0, curr = 1;
hash.insert(prev);
hash.insert(curr);
while (curr <= maxElement) {
// Summation of last two numbers
int temp = curr + prev;
hash.insert(temp);
// Update the variable each time
prev = curr;
curr = temp;
}
}
// Function to find the
// longest fibonacci subarray
int longestFibSubarray(
int arr[], int n)
{
// Find maximum value in the array
int max_val
= *max_element(arr, arr + n);
// Creating a set
// containing Fibonacci numbers
set hash;
createHash(hash, max_val);
int left[n], right[n];
int fibcount = 0, res = -1;
// Left array is used to count number of
// continuous fibonacci numbers starting
// from left of current element
for (int i = 0; i < n; i++) {
left[i] = fibcount;
// Check if current element
// is a fibonacci number
if (hash.find(arr[i])
!= hash.end()) {
fibcount++;
}
else
fibcount = 0;
}
// Right array is used to count number of
// continuous fibonacci numbers starting
// from right of current element
fibcount = 0;
for (int i = n - 1; i >= 0; i--) {
right[i] = fibcount;
// Check if current element
// is a fibonacci number
if (hash.find(arr[i])
!= hash.end()) {
fibcount++;
}
else
fibcount = 0;
}
for (int i = 0; i < n; i++)
res = max(
res,
left[i] + right[i]);
return res;
}
// Driver code
int main()
{
int arr[] = { 2, 8, 5, 7, 3, 5, 7 };
int n = sizeof(arr) / sizeof(arr[0]);
cout << longestFibSubarray(arr, n)
<< endl;
return 0;
} Java
// Java program to find length of the longest
// subarray with all fibonacci numbers
import java.util.*;
class GFG{
static final int N = 100000;
// Function to create hash table
// to check for Fibonacci numbers
static void createHash(HashSet hash,
int maxElement)
{
// Insert first two fibnonacci numbers
int prev = 0, curr = 1;
hash.add(prev);
hash.add(curr);
while (curr <= maxElement) {
// Summation of last two numbers
int temp = curr + prev;
hash.add(temp);
// Update the variable each time
prev = curr;
curr = temp;
}
}
// Function to find the
// longest fibonacci subarray
static int longestFibSubarray(
int arr[], int n)
{
// Find maximum value in the array
int max_val = Arrays.stream(arr).max().getAsInt();
// Creating a set
// containing Fibonacci numbers
HashSet hash = new HashSet();
createHash(hash, max_val);
int []left = new int[n];
int []right = new int[n];
int fibcount = 0, res = -1;
// Left array is used to count number of
// continuous fibonacci numbers starting
// from left of current element
for (int i = 0; i < n; i++) {
left[i] = fibcount;
// Check if current element
// is a fibonacci number
if (hash.contains(arr[i])) {
fibcount++;
}
else
fibcount = 0;
}
// Right array is used to count number of
// continuous fibonacci numbers starting
// from right of current element
fibcount = 0;
for (int i = n - 1; i >= 0; i--) {
right[i] = fibcount;
// Check if current element
// is a fibonacci number
if (hash.contains(arr[i])) {
fibcount++;
}
else
fibcount = 0;
}
for (int i = 0; i < n; i++)
res = Math.max(
res,
left[i] + right[i]);
return res;
}
// Driver code
public static void main(String[] args)
{
int arr[] = { 2, 8, 5, 7, 3, 5, 7 };
int n = arr.length;
System.out.print(longestFibSubarray(arr, n)
+"\n");
}
}
// This code is contributed by PrinciRaj1992 Python3
# Python3 program to find length of the longest
# subarray with all fibonacci numbers
N = 100000
# Function to create hash table
# to check for Fibonacci numbers
def createHash(hash, maxElement) :
# Insert first two fibnonacci numbers
prev = 0
curr = 1
hash.add(prev)
hash.add(curr)
while (curr <= maxElement) :
# Summation of last two numbers
temp = curr + prev
hash.add(temp)
# Update the variable each time
prev = curr
curr = temp
# Function to find the
# longest fibonacci subarray
def longestFibSubarray(arr, n) :
# Find maximum value in the array
max_val = max(arr)
# Creating a set
# containing Fibonacci numbers
hash = {int}
createHash(hash, max_val)
left = [ 0 for i in range(n)]
right = [ 0 for i in range(n)]
fibcount = 0
res = -1
# Left array is used to count number of
# continuous fibonacci numbers starting
# from left of current element
for i in range(n) :
left[i] = fibcount
# Check if current element
# is a fibonacci number
if (arr[i] in hash) :
fibcount += 1
else:
fibcount = 0
# Right array is used to count number of
# continuous fibonacci numbers starting
# from right of current element
fibcount = 0
for i in range(n-1,-1,-1) :
right[i] = fibcount
# Check if current element
# is a fibonacci number
if (arr[i] in hash) :
fibcount += 1
else:
fibcount = 0
for i in range(0,n) :
res = max(res, left[i] + right[i])
return res
# Driver code
arr = [ 2, 8, 5, 7, 3, 5, 7 ]
n = len(arr)
print(longestFibSubarray(arr, n))
# This code is contributed by Sanjit_PrasadC#
// C# program to find length of the longest
// subarray with all fibonacci numbers
using System;
using System.Linq;
using System.Collections.Generic;
class GFG{
static readonly int N = 100000;
// Function to create hash table
// to check for Fibonacci numbers
static void createHash(HashSet hash,
int maxElement)
{
// Insert first two fibnonacci numbers
int prev = 0, curr = 1;
hash.Add(prev);
hash.Add(curr);
while (curr <= maxElement) {
// Summation of last two numbers
int temp = curr + prev;
hash.Add(temp);
// Update the variable each time
prev = curr;
curr = temp;
}
}
// Function to find the
// longest fibonacci subarray
static int longestFibSubarray(
int []arr, int n)
{
// Find maximum value in the array
int max_val = arr.Max();
// Creating a set
// containing Fibonacci numbers
HashSet hash = new HashSet();
createHash(hash, max_val);
int []left = new int[n];
int []right = new int[n];
int fibcount = 0, res = -1;
// Left array is used to count number of
// continuous fibonacci numbers starting
// from left of current element
for (int i = 0; i < n; i++) {
left[i] = fibcount;
// Check if current element
// is a fibonacci number
if (hash.Contains(arr[i])) {
fibcount++;
}
else
fibcount = 0;
}
// Right array is used to count number of
// continuous fibonacci numbers starting
// from right of current element
fibcount = 0;
for (int i = n - 1; i >= 0; i--) {
right[i] = fibcount;
// Check if current element
// is a fibonacci number
if (hash.Contains(arr[i])) {
fibcount++;
}
else
fibcount = 0;
}
for (int i = 0; i < n; i++)
res = Math.Max(
res,
left[i] + right[i]);
return res;
}
// Driver code
public static void Main(String[] args)
{
int []arr = { 2, 8, 5, 7, 3, 5, 7 };
int n = arr.Length;
Console.Write(longestFibSubarray(arr, n)
+"\n");
}
}
// This code is contributed by sapnasingh4991 输出：
5