Lc1405

class Solution:
    def longestDiverseString(self, a: int, b: int, c: int) -> str:
        """  tc O(N) sc O(N)
        main idea: greedy 
        assuming a >=b >=c  
        there are 2 cases (1) a > 0, b=c=0, to produce longest, do aa* min(2,a)   
                          (2) a >= b >= 1 :   for use_a, do min(2,a);  for b if new_a < b: dont add b after a this time => because if you follow with b, if c == 0, next round b > a, b will use 2 cards => !!!! we have bbb 
        
        """
        def helper(a,b,c,aa,bb,cc):  # a >= b >= c 
            if a < b :
                return helper(b,a,c,bb,aa,cc)
            if b < c :
                return helper(a,c,b,aa,cc,bb)
            # Case1 
            if b == 0:
                return aa * min(2,a)
            # Case2 
            used_a = min(a,2)
            used_b = 1 if a - used_a >= b else 0
            return aa*used_a +bb*used_b + helper(a-used_a,b-used_b,c,aa,bb,cc)
        return helper(a,b,c,"a","b","c")