Question

Formatted question description: https://leetcode.ca/all/306.html

An additive number is a string whose digits can form an additive sequence.

A valid additive sequence should contain at least three numbers. Except for the first two numbers, each subsequent number in the sequence must be the sum of the preceding two.

Given a string containing only digits, return true if it is an additive number or false otherwise.

Note: Numbers in the additive sequence cannot have leading zeros, so sequence 1, 2, 03 or 1, 02, 3 is invalid.

Example 1:

Input: "112358"
Output: true
Explanation: 
The digits can form an additive sequence: 1, 1, 2, 3, 5, 8. 
1 + 1 = 2, 1 + 2 = 3, 2 + 3 = 5, 3 + 5 = 8

Example 2:

Input: "199100199"
Output: true
Explanation: 
The additive sequence is: 1, 99, 100, 199. 
1 + 99 = 100, 99 + 100 = 199

Constraints:

1 <= num.length <= 35
num consists only of digits.

Follow up: How would you handle overflow for very large input integers?

Algorithm

Let the first digit start with one digit, and the second digit will be searched for higher digits. The first two digits are confirmed, and the third digit is obtained by adding them.

The three arrays are arranged to form a string, which is the same length as the original string if it is less than the original length, then take out the second and third numbers from the previous calculation, and use the same method to get the third number, then add the current string, and then sum Compared to the original string length.

Code

import java.util.ArrayList;

public class Additive_Number {

    public static void main(String[] args) {
        Additive_Number out = new Additive_Number();
        Solution s = out.new Solution();

        System.out.println(s.isAdditiveNumber("112358"));
    }


    // very good follow up analysis
    class Solution {

        boolean isFound = false;

        public boolean isAdditiveNumber(String num) {
            if (num == null || num.length() == 0) {
                return false;
            }

            dfs(num, 0, new ArrayList<Long>());

            return isFound;
        }

        private void dfs(String num, int startIndex, ArrayList<Long> out) {

            if (isFound) {
                return;
            }

            if (startIndex == num.length()) {
                // @note: input is [1,2], then should return false
                // @note: not working if ==3, must be >=3
                //          input: "112358", out will be "[1, 1, 2, 3, 5, 8]"
                if (out.size() >= 3) {
                    isFound = true;
                }
                return;
            }

            for (int i = startIndex; i < num.length(); i++) {

                String current = num.substring(startIndex, i + 1); // @note：+1

                // skip invalid
                // 检测str的长度大于19就break，因为long的十进制数长度是19位
                if ((current.length() > 1 && current.charAt(0) == '0') || current.length() > 19) {
                    break; // because all the rest will all start with 0
                }

                long curNum = Long.valueOf(current);
                long n = (long) out.size();

                if (out.size() >= 2 && curNum != out.get((int) (n - 1)) + out.get((int) (n - 2))) {
                    continue;
                }

                out.add(curNum);
                dfs(num, i + 1, out);
                out.remove(out.size() - 1);
            }
        }
    }
}

############

class Solution {
    public boolean isAdditiveNumber(String num) {
        int n = num.length();
        for (int i = 1; i < Math.min(n - 1, 19); ++i) {
            for (int j = i + 1; j < Math.min(n, i + 19); ++j) {
                if (i > 1 && num.charAt(0) == '0') {
                    break;
                }
                if (j - i > 1 && num.charAt(i) == '0') {
                    continue;
                }
                long a = Long.parseLong(num.substring(0, i));
                long b = Long.parseLong(num.substring(i, j));
                if (dfs(a, b, num.substring(j))) {
                    return true;
                }
            }
        }
        return false;
    }

    private boolean dfs(long a, long b, String num) {
        if ("".equals(num)) {
            return true;
        }
        if (a + b > 0 && num.charAt(0) == '0') {
            return false;
        }
        for (int i = 1; i < Math.min(num.length() + 1, 19); ++i) {
            if (a + b == Long.parseLong(num.substring(0, i))) {
                if (dfs(b, a + b, num.substring(i))) {
                    return true;
                }
            }
        }
        return false;
    }
}

class Solution:
    def isAdditiveNumber(self, num: str) -> bool:

        def dfs(startIndex: int, out: List[int]) -> bool:
            # equal check is here
            if len(out) >= 3 and out[-1] != out[-2] + out[-3]:
                return False
            if startIndex == len(num):
                return len(out) >= 3

            for i in range(startIndex, len(num)):
                current = num[startIndex: i + 1]
                if (len(current) > 1 and current[0] == '0'):
                    break

                out.append(int(current))
                if dfs(i + 1, out):
                    return True
                out.pop()

            return False

        if not num:
            return False
        return dfs(0, [])


class Solution:
    def isAdditiveNumber(self, num: str) -> bool:
        def dfs(a, b, num):
            if not num:
                return True
            if a + b > 0 and num[0] == '0':
                return False
            for i in range(1, len(num) + 1):
                if a + b == int(num[:i]):
                    if dfs(b, a + b, num[i:]):
                        return True
            return False

        n = len(num)
        for i in range(1, n - 1): # 1st cut
            if i > 1 and num[0] == '0': # 0 + 1 = 1 is fine, but 00 + 1 is wrong
                break
            for j in range(i + 1, n): # 2nd cut, so making it a 3-segments
                if j - i > 1 and num[i] == '0':
                    break
                if dfs(int(num[:i]), int(num[i:j]), num[j:]): # better than below, early stop
                    return True
        return False

########

class Solution(object):
  def isAdditiveNumber(self, num):
    """
    :type num: str
    :rtype: bool
    """
    n = len(num)
    for x in range(0, n / 2):
      if x > 0 and num[0] == "0":
        break
      for y in range(x + 1, n):
        if y - x > 1 and num[x + 1] == "0":
          break
        i, j, k = 0, x, y
        while k < n:
          a = int(num[i:j + 1])
          b = int(num[j + 1:k + 1])
          add = str(int(a + b))
          if not num.startswith(add, k + 1):
            break
          if len(add) + 1 + k == len(num):
            return True
          i = j + 1
          j = k
          k = k + len(add)
    return False

class Solution {
public:
    bool isAdditiveNumber(string num) {
        int n = num.size();
        for (int i = 1; i < min(n - 1, 19); ++i) {
            for (int j = i + 1; j < min(n, i + 19); ++j) {
                if (i > 1 && num[0] == '0') break;
                if (j - i > 1 && num[i] == '0') continue;
                auto a = stoll(num.substr(0, i));
                auto b = stoll(num.substr(i, j - i));
                if (dfs(a, b, num.substr(j, n - j))) return true;
            }
        }
        return false;
    }

    bool dfs(long long a, long long b, string num) {
        if (num == "") return true;
        if (a + b > 0 && num[0] == '0') return false;
        for (int i = 1; i < min((int) num.size() + 1, 19); ++i)
            if (a + b == stoll(num.substr(0, i)))
                if (dfs(b, a + b, num.substr(i, num.size() - i)))
                    return true;
        return false;
    }
};

func isAdditiveNumber(num string) bool {
	n := len(num)
	var dfs func(a, b int64, num string) bool
	dfs = func(a, b int64, num string) bool {
		if num == "" {
			return true
		}
		if a+b > 0 && num[0] == '0' {
			return false
		}
		for i := 1; i < min(len(num)+1, 19); i++ {
			c, _ := strconv.ParseInt(num[:i], 10, 64)
			if a+b == c {
				if dfs(b, c, num[i:]) {
					return true
				}
			}
		}
		return false
	}
	for i := 1; i < min(n-1, 19); i++ {
		for j := i + 1; j < min(n, i+19); j++ {
			if i > 1 && num[0] == '0' {
				break
			}
			if j-i > 1 && num[i] == '0' {
				continue
			}
			a, _ := strconv.ParseInt(num[:i], 10, 64)
			b, _ := strconv.ParseInt(num[i:j], 10, 64)
			if dfs(a, b, num[j:]) {
				return true
			}
		}
	}
	return false
}

func min(a, b int) int {
	if a < b {
		return a
	}
	return b
}

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