This problem is an addition to the familiar stack question(<https://leetcode.com/problems/minimum-add-to-make-parentheses-valid/>) where we have to return the minimum number of additions to make the parentheses string valid. But that question consists of only '(' and ')'. What will happen if we extend that question to other types of parentheses like '[', ']', '{', '}'. I just came across this in a discussion among my friends and need help on how to approach.

For example: [[[{{}]]){)}) -> [[[{{**}**}]]**]** **(**){**(**)}**(**)
in this case answer is 5 additions to make it valid.

I couldn't come up with a proper approach. 2 approaches I considered are:

1. Similar to normal question, we push the opening types '(', '{', '[' to the stack as we browse through the string and if we find closing type ')', '}', ']' we check the top of the stack, if they both compliment each other, we pop and continue else we increment the counter and continue without popping out. After traversing the string, we output the answer as sum of counter and stack's size. In this approach the above example will not work as that extra '{' will break the approach.
2. Another approach is similar to above ie. we push the opening type of parentheses and if we find a closing type and if the stack's top compliment it, we pop and continue with the string, else we will pop out till we get a matching string and for every pop we increment the counter. After traversing the string, the total value is sum of counter and stack's size. But that will not work for cases like {{{{]}}}} where the character ']' will pop out everything and it will increase the answer.

I was also thinking of combining these, more like a Dynamic Programming where we will take the maximum of either seeing the top most value or seeing till we get a match in the stack or if stack becomes empty. But I am not sure on whether these 2 are the only cases to consider.