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This approach uses backtracking to recursively split the string into all potential combinations of integers and checks if they form a valid Fibonacci sequence.
Time Complexity: O(2^n), since each combination of splitting points is considered recursively.
Space Complexity: O(n), for the recursion stack and the result list.
1def splitIntoFibonacci(S):
2 def backtrack(index):
3 if index == len(S):
4 return len(result) >= 3
5 current_number = 0
6 for i in range(index, len(S)):
7 if i > index and S[index] == '0':
8 break
9 current_number = current_number * 10 + int(S[i])
10 if current_number > 2**31 - 1:
11 break
12 if len(result) < 2 or current_number == result[-1] + result[-2]:
13 result.append(current_number)
14 if backtrack(i + 1):
15 return True
16 result.pop()
17 return False
18
19 result = []
20 return result if backtrack(0) else []This Python code implements a backtracking solution to split the input string into potential Fibonacci sequences.
backtrack is defined to recursively attempt to form a sequence.This approach involves iteratively parsing possible substrings and dynamically checking for valid Fibonacci sequences.
Time Complexity: O(n^3), due to nested loops exploring potential splits and sequence validity.
Space Complexity: O(n), primarily to store intermediate sequence results.
1import java.util.*;
2
This Java code uses an iterative method to find Fibonacci-like sequences.
isValid function checks if extending the sequence remains valid.