A sequence X1, X2, ..., Xn
is Fibonacci-like if:
n >= 3
Xi + Xi+1 = Xi+2
for alli + 2 <= n
Given a strictly increasing array arr
of positive integers forming a sequence, return the length of the longest Fibonacci-like subsequence of arr
. If one does not exist, return 0
.
A subsequence is derived from another sequence arr
by deleting any number of elements (including none) from arr
, without changing the order of the remaining elements. For example, [3, 5, 8]
is a subsequence of [3, 4, 5, 6, 7, 8]
.
Example 1:
Input: arr = [1,2,3,4,5,6,7,8] Output: 5 Explanation: The longest subsequence that is fibonacci-like: [1,2,3,5,8].
Example 2:
Input: arr = [1,3,7,11,12,14,18] Output: 3 Explanation: The longest subsequence that is fibonacci-like: [1,11,12], [3,11,14] or [7,11,18].
Constraints:
3 <= arr.length <= 1000
1 <= arr[i] < arr[i + 1] <= 109
Dynamic programming.
class Solution:
def lenLongestFibSubseq(self, arr: List[int]) -> int:
mp = {v: i for i, v in enumerate(arr)}
n = len(arr)
dp = [[0] * n for _ in range(n)]
for i in range(n):
for j in range(i):
dp[j][i] = 2
ans = 0
for i in range(n):
for j in range(i):
delta = arr[i] - arr[j]
if delta in mp:
k = mp[delta]
if k < j:
dp[j][i] = dp[k][j] + 1
ans = max(ans, dp[j][i])
return ans
class Solution {
public int lenLongestFibSubseq(int[] arr) {
int n = arr.length;
Map<Integer, Integer> mp = new HashMap<>();
for (int i = 0; i < n; ++i) {
mp.put(arr[i], i);
}
int[][] dp = new int[n][n];
for (int i = 0; i < n; ++i) {
for (int j = 0; j < i; ++j) {
dp[j][i] = 2;
}
}
int ans = 0;
for (int i = 0; i < n; ++i) {
for (int j = 0; j < i; ++j) {
int delta = arr[i] - arr[j];
if (mp.containsKey(delta)) {
int k = mp.get(delta);
if (k < j) {
dp[j][i] = dp[k][j] + 1;
ans = Math.max(ans, dp[j][i]);
}
}
}
}
return ans;
}
}
class Solution {
public:
int lenLongestFibSubseq(vector<int>& arr) {
unordered_map<int, int> mp;
int n = arr.size();
for (int i = 0; i < n; ++i) mp[arr[i]] = i;
vector<vector<int>> dp(n, vector<int>(n));
for (int i = 0; i < n; ++i)
{
for (int j = 0; j < i; ++j)
dp[j][i] = 2;
}
int ans = 0;
for (int i = 0; i < n; ++i)
{
for (int j = 0; j < i; ++j)
{
int delta = arr[i] - arr[j];
if (mp.count(delta))
{
int k = mp[delta];
if (k < j)
{
dp[j][i] = dp[k][j] + 1;
ans = max(ans, dp[j][i]);
}
}
}
}
return ans;
}
};
func lenLongestFibSubseq(arr []int) int {
n := len(arr)
mp := make(map[int]int, n)
for i, v := range arr {
mp[v] = i + 1
}
dp := make([][]int, n)
for i := 0; i < n; i++ {
dp[i] = make([]int, n)
for j := 0; j < i; j++ {
dp[j][i] = 2
}
}
ans := 0
for i := 0; i < n; i++ {
for j := 0; j < i; j++ {
delta := arr[i] - arr[j]
k := mp[delta] - 1
if k >= 0 && k < j {
dp[j][i] = dp[k][j] + 1
ans = max(ans, dp[j][i])
}
}
}
return ans
}
func max(a, b int) int {
if a > b {
return a
}
return b
}