Problem
Given a string S
of digits, such as S = "123456579"
, we can split it into a Fibonacci-like sequence [123, 456, 579].
Formally, a Fibonacci-like sequence is a list F
of non-negative integers such that:
0 <= F[i] <= 2^31 - 1
, (that is, each integer fits a 32-bit signed integer type);F.length >= 3
;- and
F[i] + F[i+1] = F[i+2]
for all0 <= i < F.length - 2
.
Also, note that when splitting the string into pieces, each piece must not have extra leading zeroes, except if the piece is the number 0 itself.
Return any Fibonacci-like sequence split from S
, or return []
if it cannot be done.
Example 1:
Input: "123456579" Output: [123,456,579]
Example 2:
Input: "11235813" Output: [1,1,2,3,5,8,13]
Example 3:
Input: "112358130" Output: [] Explanation: The task is impossible.
Example 4:
Input: "0123" Output: [] Explanation: Leading zeroes are not allowed, so "01", "2", "3" is not valid.
Example 5:
Input: "1101111" Output: [110, 1, 111] Explanation: The output [11, 0, 11, 11] would also be accepted.
Note:
1 <= S.length <= 200
S
contains only digits.
Solution: DFS
Time complexity: O(2^n)
Space complexity: O(n)
C++
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// Author: Huahua // Running time: 0 ms class Solution { public: vector<int> splitIntoFibonacci(string s) { const int n = s.length(); vector<int> nums; function<bool(int)> dfs = [&](int pos) { if (pos == n) return nums.size() >= 3; int max_len = s[pos] == '0' ? 1 : 10; long num = 0; for (int i = pos; i < min(pos + max_len, n); ++i) { num = num * 10 + (s[i] - '0'); if (num > INT_MAX) break; if (nums.size() >= 2) { long sum = nums.rbegin()[0]; sum += nums.rbegin()[1]; if (num > sum) break; else if (num < sum) continue; // num must equaals to sum. } nums.push_back(num); if (dfs(i + 1)) return true; nums.pop_back(); } return false; }; dfs(0); return nums; } }; |
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