// Source : https://leetcode.com/problems/splitting-a-string-into-descending-consecutive-values/
// Author : Hao Chen
// Date   : 2021-05-03

/***************************************************************************************************** 
 *
 * You are given a string s that consists of only digits.
 * 
 * Check if we can split s into two or more non-empty substrings such that the numerical values of the 
 * substrings are in descending order and the difference between numerical values of every two 
 * adjacent substrings is equal to 1.
 * 
 * 	For example, the string s = "0090089" can be split into ["0090", "089"] with numerical 
 * values [90,89]. The values are in descending order and adjacent values differ by 1, so this way is 
 * valid.
 * 	Another example, the string s = "001" can be split into ["0", "01"], ["00", "1"], or ["0", 
 * "0", "1"]. However all the ways are invalid because they have numerical values [0,1], [0,1], and 
 * [0,0,1] respectively, all of which are not in descending order.
 * 
 * Return true if it is possible to split s​​​​​​ as described above, or false otherwise.
 * 
 * A substring is a contiguous sequence of characters in a string.
 * 
 * Example 1:
 * 
 * Input: s = "1234"
 * Output: false
 * Explanation: There is no valid way to split s.
 * 
 * Example 2:
 * 
 * Input: s = "050043"
 * Output: true
 * Explanation: s can be split into ["05", "004", "3"] with numerical values [5,4,3].
 * The values are in descending order with adjacent values differing by 1.
 * 
 * Example 3:
 * 
 * Input: s = "9080701"
 * Output: false
 * Explanation: There is no valid way to split s.
 * 
 * Example 4:
 * 
 * Input: s = "10009998"
 * Output: true
 * Explanation: s can be split into ["100", "099", "98"] with numerical values [100,99,98].
 * The values are in descending order with adjacent values differing by 1.
 * 
 * Constraints:
 * 
 * 	1 <= s.length <= 20
 * 	s only consists of digits.
 ******************************************************************************************************/

class Solution {
private:
    int pos;
public:
    bool getNum(string& s, long target) {
        
        long n = 0;
        while(s[pos] == '0') pos++; 
        while(pos < s.size()){
            n = (n*10 + s[pos++] - '0') ;
            if (n == target) return true;
            if (n > target ) return false; // n is already greater than target
        }
        return target == n;
    }
    
    long firstNum(string& s, int len) {
        long n = 0;
        while(s[pos] == '0') pos++; 
        for(; pos< s.size() && len > 0; pos++, len--) {
            n = (n*10 + s[pos] - '0') ;
        }
        return n;  
    }
    
    bool splitString(string s) {
        pos = 0;
        long num;
        for (int len=1; len<= s.size()/2+1; len++) {
            pos = 0;
            num = firstNum(s, len); 
            if (pos >= s.size()) continue; // only have one number
            
            bool result = true;
            while( pos < s.size() ) {
                if (getNum(s, --num) == false){
                    result = false;
                    break;
                }
            }
            if (result) return true;
        }
        return false;
    }
};