Given a string S of parentheses ‘(‘ or ‘)’ where, . The task is to find minimum number of parentheses ‘(‘ or ‘)’ (at any positions) we must add to make the resulting parentheses string is valid.
Input: str = "())" Output: 1 One '(' is required at beginning. Input: str = "(((" Output: 3 Three ')' is required at end.
Approach: We keep the track of balance of the string i:e the number of ‘(‘ minus the number of ‘)’. A string is valid if its balance is 0, and also every prefix has non-negative balance.
Now, consider the balance of every prefix of S. If it is ever negative (say, -1), we must add a ‘(‘ bracket at the beginning. Also, if the balance of S is positive (say, +P), we must add P times ‘)’ brackets at the end.
Below is the implementation of the above approach:
if ($bal == -1)
$ans += 1;
$bal += 1;
return $bal + $ans;
// Driver code
$p = “())”;
// Function to print required answer
// This code is contributed by ita_c
Time Complexity: O(N), where N is the length of S.
Space Complexity: O(1).
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