842. Split Array into Fibonacci Sequence

Description

You are given a string of digits num, such as "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] < 231, (that is, each integer fits in 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.

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 num, or return [] if it cannot be done.

 

Example 1:

Input: num = "1101111"
Output: [11,0,11,11]
Explanation: The output [110, 1, 111] would also be accepted.

Example 2:

Input: num = "112358130"
Output: []
Explanation: The task is impossible.

Example 3:

Input: num = "0123"
Output: []
Explanation: Leading zeroes are not allowed, so "01", "2", "3" is not valid.

 

Constraints:

  • 1 <= num.length <= 200
  • num contains only digits.

Solutions

Solution 1

Python Code
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class Solution:
    def splitIntoFibonacci(self, num: str) -> List[int]:
        def dfs(i):
            if i == n:
                return len(ans) > 2
            x = 0
            for j in range(i, n):
                if j > i and num[i] == '0':
                    break
                x = x * 10 + int(num[j])
                if x > 2**31 - 1 or (len(ans) > 2 and x > ans[-2] + ans[-1]):
                    break
                if len(ans) < 2 or ans[-2] + ans[-1] == x:
                    ans.append(x)
                    if dfs(j + 1):
                        return True
                    ans.pop()
            return False

        n = len(num)
        ans = []
        dfs(0)
        return ans

Java Code
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class Solution {
    private List<Integer> ans = new ArrayList<>();
    private String num;

    public List<Integer> splitIntoFibonacci(String num) {
        this.num = num;
        dfs(0);
        return ans;
    }

    private boolean dfs(int i) {
        if (i == num.length()) {
            return ans.size() >= 3;
        }
        long x = 0;
        for (int j = i; j < num.length(); ++j) {
            if (j > i && num.charAt(i) == '0') {
                break;
            }
            x = x * 10 + num.charAt(j) - '0';
            if (x > Integer.MAX_VALUE
                || (ans.size() >= 2 && x > ans.get(ans.size() - 1) + ans.get(ans.size() - 2))) {
                break;
            }
            if (ans.size() < 2 || x == ans.get(ans.size() - 1) + ans.get(ans.size() - 2)) {
                ans.add((int) x);
                if (dfs(j + 1)) {
                    return true;
                }
                ans.remove(ans.size() - 1);
            }
        }
        return false;
    }
}

C++ Code
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class Solution {
public:
    vector<int> splitIntoFibonacci(string num) {
        int n = num.size();
        vector<int> ans;
        function<bool(int)> dfs = [&](int i) -> bool {
            if (i == n) {
                return ans.size() > 2;
            }
            long long x = 0;
            for (int j = i; j < n; ++j) {
                if (j > i && num[i] == '0') {
                    break;
                }
                x = x * 10 + num[j] - '0';
                if (x > INT_MAX || (ans.size() > 1 && x > (long long) ans[ans.size() - 1] + ans[ans.size() - 2])) {
                    break;
                }
                if (ans.size() < 2 || x == (long long) ans[ans.size() - 1] + ans[ans.size() - 2]) {
                    ans.push_back(x);
                    if (dfs(j + 1)) {
                        return true;
                    }
                    ans.pop_back();
                }
            }
            return false;
        };
        dfs(0);
        return ans;
    }
};

Go Code
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func splitIntoFibonacci(num string) []int {
	n := len(num)
	ans := []int{}
	var dfs func(int) bool
	dfs = func(i int) bool {
		if i == n {
			return len(ans) > 2
		}
		x := 0
		for j := i; j < n; j++ {
			if j > i && num[i] == '0' {
				break
			}
			x = x*10 + int(num[j]-'0')
			if x > math.MaxInt32 || (len(ans) > 1 && x > ans[len(ans)-1]+ans[len(ans)-2]) {
				break
			}
			if len(ans) < 2 || x == ans[len(ans)-1]+ans[len(ans)-2] {
				ans = append(ans, x)
				if dfs(j + 1) {
					return true
				}
				ans = ans[:len(ans)-1]
			}
		}
		return false
	}
	dfs(0)
	return ans
}