Leetcode -- 842. Split Array into Fibonacci Sequence

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原文链接：https://leetcode.com/problems/split-array-into-fibonacci-sequence/discuss/371574/Backtracking-with-Cpp

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本文介绍了一种算法，用于将给定的数字字符串拆分成满足斐波那契数列特性的子序列。该算法使用深度优先搜索(DFS)策略，确保每个子序列都是有效的32位整数，且不包含前导零。

842. Split Array into Fibonacci Sequence

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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 all 0 <= 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.

dfs

class Solution {
public:
 	vector<int> splitIntoFibonacci(string S) {
		vector<long> res;
		vector<int> int_res;
		if (isFib(res,0,S)) {
			for (long val : res)
				int_res.push_back((int)val);
		}
		
		return int_res;
			
	}
	bool isFib(vector<long>&res,int index, string S) {
		if (index == S.length() && res.size() >= 3)
			return true;

		for (int i = 1; i <= S.size()-index; i++) {
			long num = stol(S.substr(index, i));
			if (num > INT_MAX) break;

			if (S[index] == '0'&&i > 1)break;
			if (res.size() >= 2 && res[res.size() - 1] + res[res.size() - 2] <num) break;
			if (res.size() <= 1|| res[res.size() - 1] + res[res.size() - 2] == num) {
				res.push_back(num);
				if (isFib(res, index + i, S)) {
					return true;
				}
				res.pop_back();
			}

			
		}
		return false;

	}
};