1963. Minimum Number of Swaps to Make the String Balanced

Difficulty: Medium

Topics: Two Pointers, String, Stack, Greedy

You are given a 0-indexed string s of even length n. The string consists of exactly n / 2 opening brackets '[' and n / 2 closing brackets ']'.

A string is called balanced if and only if:

• It is the empty string, or
• It can be written as AB, where both A and B are balanced strings, or
• It can be written as [C], where C is a balanced string.

You may swap the brackets at any two indices any number of times.

Return the minimum number of swaps to make s balanced.

Example 1:

• Input: s = "][]["
• Output: 1
• Explanation: You can make the string balanced by swapping index 0 with index 3.
  • The resulting string is "[[]]".

Example 2:

• Input: s = "]]][[["
• Output: 2
• Explanation: You can do the following to make the string balanced:
  • Swap index 0 with index 4. s = "[]][][".
  • Swap index 1 with index 5. s = "[[][]]".
  • The resulting string is "[[][]]".

Example 3:

• Input: s = "[]"
• Output: 0
• Explanation: The string is already balanced.

Constraints:

• n == s.length
• 2 <= n <= 106
• n is even.
• s[i] is either '[' or ']'.
• The number of opening brackets '[' equals n / 2, and the number of closing brackets ']' equals n / 2.

Hint:

1. Iterate over the string and keep track of the number of opening and closing brackets on each step.
2. If the number of closing brackets is ever larger, you need to make a swap.
3. Swap it with the opening bracket closest to the end of s.

Solution:

We can use a two-pointers approach, which is efficient given the constraints.

Approach:

1. Track Balance: As we iterate through the string, we can track the balance between opening and closing brackets:

   • Increment the balance when encountering '['.
   • Decrement the balance when encountering ']'.

2. Identify Imbalance: When the balance becomes negative, it indicates that there are more closing brackets ']' than opening brackets '[' at that point in the string. This is where we need to swap brackets to make the string balanced.

3. Count Swaps: To correct an imbalance:

   • Keep a counter max_imbalance to track the maximum imbalance observed during the iteration.
   • The required number of swaps is equal to (max_imbalance + 1) / 2, which effectively gives the minimum number of swaps needed to make the string balanced.

Let's implement this solution in PHP: 1963. Minimum Number of Swaps to Make the String Balanced

<?php
/**
 * @param String $s
 * @return Integer
 */
function minSwaps($s) {
    ...
    ...
    ...
    /**
     * go to ./solution.php
     */
}

// Example usage:
$s1 = "][][";
echo minSwaps($s1); // Output: 1

$s2 = "]]][[[";
echo minSwaps($s2); // Output: 2

$s3 = "[]";
echo minSwaps($s3); // Output: 0
?>

Explanation:

1. Balance Tracking:

   • balance keeps track of the difference between the number of '[' and ']'.
   • If balance becomes negative, it indicates that there are more ']' than '[' at that point.

2. Calculate Maximum Imbalance:

   • max_imbalance stores the largest imbalance encountered during the iteration.
   • If balance becomes negative, update max_imbalance with the larger of max_imbalance or -balance.

3. Calculate Swaps:

   • To fix an imbalance, the minimum swaps required is (max_imbalance + 1) / 2.

Time Complexity:

• The time complexity is O(n), where n is the length of the string. We iterate through the string once to determine the max_imbalance.
• The space complexity is O(1) as we use a few variables for tracking the balance and maximum imbalance.

This solution ensures that we meet the constraints, even for large inputs.

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