Formatted question description: https://leetcode.ca/all/842.html

842. Split Array into Fibonacci Sequence

Level

Medium

Description

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. 1 <= S.length <= 200
  2. S contains only digits.

Solution

First check the maximum end index of the first number and the second number. Suppose the string contains only three numbers that form a Fibonacci-like sequence, then the third number can’t be shorter than either the first number of the second number. Suppose the length of string S is length, then the maximum end index of the first number is length / 2 - 1 and the maximum end index of the second number is length * 2 / 3 - 1.

For each possible choice of the first number and the second number, try to form a Fibonacci-like sequence starting from the first number and the second number. If one choice can lead to a Fibonacci-like sequence that equals S, return a list containing all the numbers in the sequence. Otherwise, return an empty list.

  • class Solution {
        public List<Integer> splitIntoFibonacci(String S) {
            List<Integer> list = new ArrayList<Integer>();
            if (S == null || S.length() == 0)
                return list;
            int length = S.length();
            int firstMax = Math.min(length / 2, 10), secondMax = Math.min(length * 2 / 3, 20);
            for (int i = 1; i <= firstMax; i++) {
                if (i > 1 && S.charAt(0) == '0' || Long.parseLong(S.substring(0, i)) > Integer.MAX_VALUE)
                    break;
                int secondMaxUpper = Math.min(secondMax, i + 11);
                for (int j = i + 1; j <= secondMaxUpper; j++) {
                    List<Integer> splitIndices = new ArrayList<Integer>();
                    String firstNumStr = S.substring(0, i);
                    String secondNumStr = S.substring(i, j);
                    splitIndices.add(i);
                    splitIndices.add(j);
                    if (secondNumStr.length() > 1 && secondNumStr.charAt(0) == '0')
                        break;
                    StringBuffer sb = new StringBuffer(firstNumStr + secondNumStr);
                    int prevIndex = j;
                    while (sb.length() < length) {
                        long firstNum = Long.parseLong(firstNumStr);
                        long secondNum = Long.parseLong(secondNumStr);
                        long sum = firstNum + secondNum;
                        if (sum > Integer.MAX_VALUE)
                            break;
                        String sumStr = String.valueOf(sum);
                        sb.append(sumStr);
                        int index = prevIndex + sumStr.length();
                        if (index < length)
                            splitIndices.add(index);
                        prevIndex = index;
                        firstNumStr = secondNumStr;
                        secondNumStr = sumStr;
                    }
                    if (sb.toString().equals(S)) {
                        int size = splitIndices.size();
                        for (int k = size - 1; k >= 0; k--) {
                            int splitIndex = splitIndices.get(k);
                            sb.insert(splitIndex, ',');
                        }
                        String[] array = sb.toString().split(",");
                        int sequenceLength = array.length;
                        for (int k = 0; k < sequenceLength; k++)
                            list.add(Integer.parseInt(array[k]));
                        return list;
                    }
                }
            }
            return list;
        }
    }
    
  • // OJ: https://leetcode.com/problems/split-array-into-fibonacci-sequence/
    // Time: O(N!)
    // Space: O(N)
    class Solution {
        vector<int> ans;
        bool dfs(string &s, int i) {
            if (i == s.size()) return ans.size() >= 3;
            for (int j = i; j < s.size(); ++j) {
                long n = stol(s.substr(i, j - i + 1));
                if (n > INT_MAX) return false;
                if (ans.size() >= 2) {
                    long target = (long)ans.back() + ans[ans.size() - 2];
                    if (target > INT_MAX) return false;
                    if (n == target) {
                        ans.push_back(n);
                        if (dfs(s, j + 1)) return true;
                        ans.pop_back();
                        break;
                    }
                    if (n > target) break;
                } else {
                    ans.push_back(n);
                    if (dfs(s, j + 1)) return true;
                    ans.pop_back();
                }
                if (s[i] == '0') return false;
            }
            return false;
        }
    public:
        vector<int> splitIntoFibonacci(string s) {
            dfs(s, 0);
            return ans;
        }
    };
    
  • class Solution(object):
        def splitIntoFibonacci(self, S):
            """
            :type S: str
            :rtype: List[int]
            """
            res = []
            self.dfs(S, [], res)
            return res
            
        def dfs(self, num_str, path, res):
            if len(path) >= 3 and  path[-1] != path[-2] + path[-3]:
                return False
            if not num_str and len(path) >= 3:
                res.extend(path)
                return True
            for i in range(len(num_str)):
                curr = num_str[:i+1]
                if (curr[0] == '0' and len(curr) != 1) or int(curr) >= 2**31:
                    continue
                if self.dfs(num_str[i+1:], path + [int(curr)], res):
                    return True
            return False
    

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