Valid Parenthesis String

LeetCode 678 | Difficulty: Medium

Medium

Problem Description

Given a string s containing only three types of characters: '(', ')' and '*', return true if s *is valid*.

The following rules define a valid string:

- Any left parenthesis `'('` must have a corresponding right parenthesis `')'`.

- Any right parenthesis `')'` must have a corresponding left parenthesis `'('`.

- Left parenthesis `'('` must go before the corresponding right parenthesis `')'`.

- `'*'` could be treated as a single right parenthesis `')'` or a single left parenthesis `'('` or an empty string `""`.

Example 1:

Input: s = "()"
Output: true

Example 2:

Input: s = "(*)"
Output: true

Example 3:

Input: s = "(*))"
Output: true

Constraints:

- `1 <= s.length <= 100`

- `s[i]` is `'('`, `')'` or `'*'`.

Topics: String, Dynamic Programming, Stack, Greedy

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Approach

Dynamic Programming

Break the problem into overlapping subproblems. Define a state (what information do you need?), a recurrence (how does state[i] depend on smaller states?), and a base case. Consider both top-down (memoization) and bottom-up (tabulation) approaches.

When to use

Optimal substructure + overlapping subproblems (counting ways, min/max cost, feasibility).

Stack

Use a stack (LIFO) to track elements that need future processing. Process elements when a "trigger" condition is met (e.g., finding a smaller/larger element). Monotonic stack maintains elements in sorted order for next greater/smaller element problems.

When to use

Matching brackets, next greater element, evaluating expressions, backtracking history.

Greedy

At each step, make the locally optimal choice. The challenge is proving the greedy choice leads to a global optimum. Look for: can I sort by some criterion? Does choosing the best option now ever hurt future choices?

When to use

Interval scheduling, activity selection, minimum coins (certain denominations), Huffman coding.

String Processing

Consider character frequency counts, two-pointer approaches, or building strings efficiently. For pattern matching, think about KMP or rolling hash. For palindromes, expand from center or use DP.

When to use

Anagram detection, palindrome checking, string transformation, pattern matching.

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Solutions

Solution 1: C# (Best: 144 ms)

Metric	Value
Runtime	144 ms
Memory	35.8 MB
Date	2022-01-12

Solution

public class Solution {
    public bool CheckValidString(string s) {
        int cmin=0, cmax = 0;
    for (int i = 0; i < s.Length; i++)
    {
        char c = s[i];
        if(c == '(')
        {
            cmax++;
            cmin++;
        }
        else if(c == ')')
        {
            cmax--;
            cmin = Math.Max(0, cmin-1);
        }
        else
        {
            cmax++;
            cmin = Math.Max(0, cmin-1);
        }
        
        if(cmax <0) return false;
    }
    
    return cmin == 0;
    }
}

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Complexity Analysis

Approach	Time	Space
Dynamic Programming	$O(n)$	$O(n)$
Stack	$O(n)$	$O(n)$

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Interview Tips

Key Points

• Discuss the brute force approach first, then optimize. Explain your thought process.
• Define the DP state clearly. Ask: "What is the minimum information I need to make a decision at each step?"
• Consider if you can reduce space by only keeping the last row/few values.
• Think about what triggers a pop: is it finding a match, or finding a smaller/larger element?
• LeetCode provides 4 hint(s) for this problem — try solving without them first.

💡 Hints

Hint 1: Use backtracking to explore all possible combinations of treating '*' as either '(', ')', or an empty string. If any combination leads to a valid string, return true.

Hint 2: DP[i][j] represents whether the substring s[i:j] is valid.

Hint 3: Keep track of the count of open parentheses encountered so far. If you encounter a close parenthesis, it should balance with an open parenthesis. Utilize a stack to handle this effectively.

Hint 4: How about using 2 stacks instead of 1? Think about it.