AdditiveNumber.java

package leetcode;

/**
 * Project Name : Leetcode
 * Package Name : leetcode
 * File Name : AdditiveNumber
 * Creator : Edward
 * Date : Jan, 2018
 * Description : 306. Additive Number
 */
public class AdditiveNumber {
    /**
     * Additive number is a string whose digits can form 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.

     For example:
     "112358" is an additive number because 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
     "199100199" is also an additive number, the additive sequence is: 1, 99, 100, 199.
     1 + 99 = 100, 99 + 100 = 199
     Note: Numbers in the additive sequence cannot have leading zeros,
     so sequence 1, 2, 03 or 1, 02, 3 is invalid.

     Given a string containing only digits '0'-'9', write a function to determine if it's an additive number.

     第一个数的范围： (n-1)/2
     第二个数的范围： n-j>=i && n-j>=j-i

     1 1 2 3 5 8

     1 99 100 199

     x1 = 100
     x2 = 199
     sum = 199

     time : O(n^2)不确定
     space : O(1)

     * @param num
     * @return
     */
    public boolean isAdditiveNumber(String num) {
        for (int i = 1; i <= num.length() / 2; i++) {
            for (int j = 1; Math.max(i, j) <= num.length() - i - j; j++) {
                if (isValid(i, j, num)) return true;
            }
        }
        return false;
    }

    private boolean isValid(int i, int j, String num) {
        if (num.charAt(0) == '0' && i > 1) return false;
        if (num.charAt(i) == '0' && j > 1) return false;
        String sum = "";
        Long x1 = Long.parseLong(num.substring(0, i));
        Long x2 = Long.parseLong(num.substring(i, i + j));
        for (int start = i + j; start != num.length(); start += sum.length()) {
            x2 = x2 + x1;
            x1 = x2 - x1;
            sum = x2.toString();
            if (!num.startsWith(sum, start)) {
                return false;
            }
        }
        return true;
    }
}