If we create the frequency map and then iterate through the values of the map. Each iteration the minimum number of characters required for the current key will be T1-1 where T1 is the count of characters of current key. Now for frequency of next character will be reduced from T2 to T2-(T1-1). T2` = T2-(T1-1)-1 will be the remaining frequency of next character so we can repeat the same procedure and at the end if we are left with 0,1 or 2 then it is possible to create a string with all the characters such that no two same characters are adjacent.

Could this be a possible solution?