3042. Count Prefix and Suffix Pairs I

[mah-shamim]

Topics: Array, String, Trie, Rolling Hash, String Matching, Hash Function

You are given a 0-indexed string array words.

Let's define a boolean function isPrefixAndSuffix that takes two strings, str1 and str2:

• isPrefixAndSuffix(str1, str2) returns true if str1 is both a prefix¹ and a suffix² of str2, and false otherwise.

For example, isPrefixAndSuffix("aba", "ababa") is true because "aba" is a prefix of "ababa" and also a suffix, but isPrefixAndSuffix("abc", "abcd") is false.

Return an integer denoting the number of index pairs (i, j) such that i < j, and isPrefixAndSuffix(words[i], words[j]) is true.

Example 1:

• Input: words = ["a","aba","ababa","aa"]
• Output: 4
• Explanation: In this example, the counted index pairs are:
  i = 0 and j = 1 because isPrefixAndSuffix("a", "aba") is true.
  i = 0 and j = 2 because isPrefixAndSuffix("a", "ababa") is true.
  i = 0 and j = 3 because isPrefixAndSuffix("a", "aa") is true.
  i = 1 and j = 2 because isPrefixAndSuffix("aba", "ababa") is true.
  Therefore, the answer is 4.

Example 2:

• Input: words = ["pa","papa","ma","mama"]
• Output: 2
• Explanation: In this example, the counted index pairs are:
  i = 0 and j = 1 because isPrefixAndSuffix("pa", "papa") is true.
  i = 2 and j = 3 because isPrefixAndSuffix("ma", "mama") is true.
  Therefore, the answer is 2.

Example 3:

• Input: words = ["abab","ab"]
• Output: 0
• Explanation: In this example, the only valid index pair is i = 0 and j = 1, and isPrefixAndSuffix("abab", "ab") is false.
  Therefore, the answer is 0.

Constraints:

• 1 <= words.length <= 50
• 1 <= words[i].length <= 10
• words[i] consists only of lowercase English letters.

Hint:

1. Iterate through all index pairs (i, j), such that i < j, and check isPrefixAndSuffix(words[i], words[j]).
2. The answer is the total number of pairs where isPrefixAndSuffix(words[i], words[j]) == true.

Footnotes

1. Prefix A prefix of a string is a substring that starts from the beginning of the string and extends to any point within it. ↩

2. Suffix A suffix of a string is a substring that begins at any point in the string and extends to its end. ↩

[mah-shamim]

We need to iterate through all index pairs (i, j) where i < j and check whether the string words[i] is both a prefix and a suffix of words[j]. For each pair, we can use PHP's built-in functions substr() to check for prefixes and suffixes.

Let's implement this solution in PHP: 3042. Count Prefix and Suffix Pairs I

<?php
/**
 * @param String[] $words
 * @return Integer
 */
function countPrefixAndSuffixPairs($words) {
    // Initialize a counter to keep track of valid index pairs
    $count = 0;
    
    // Loop through all index pairs (i, j) where i < j
    for ($i = 0; $i < count($words); $i++) {
        for ($j = $i + 1; $j < count($words); $j++) {
            // Check if words[i] is both a prefix and a suffix of words[j]
            if (isPrefixAndSuffix($words[$i], $words[$j])) {
                $count++;
            }
        }
    }
    
    return $count;
}

/**
 * Function to check if str1 is both a prefix and a suffix of str2
 *
 * @param $str1
 * @param $str2
 * @return bool
 */
function isPrefixAndSuffix($str1, $str2) {
    // Check if str1 is a prefix and a suffix of str2
    return (substr($str2, 0, strlen($str1)) === $str1 && substr($str2, -strlen($str1)) === $str1);
}

// Example Test Cases
$words1 = ["a", "aba", "ababa", "aa"];
$words2 = ["pa", "papa", "ma", "mama"];
$words3 = ["abab", "ab"];

echo countPrefixAndSuffixPairs($words1) . "\n";  // Output: 4
echo countPrefixAndSuffixPairs($words2) . "\n";  // Output: 2
echo countPrefixAndSuffixPairs($words3) . "\n";  // Output: 0
?>

Explanation:

1. countPrefixAndSuffixPairs($words):

   • This function loops through all possible index pairs (i, j) such that i < j.
   • It calls isPrefixAndSuffix() to check if words[i] is both a prefix and a suffix of words[j].
   • If the condition is true, it increments the count.

2. isPrefixAndSuffix($str1, $str2):

   • This helper function checks whether str1 is both a prefix and a suffix of str2.
   • It uses substr() to extract the prefix and suffix of str2 and compares them with str1.
   • If both conditions are true, it returns true, otherwise, it returns false.

Time Complexity:

• The time complexity is O(n² x m), where n is the length of the words array, and m is the average length of the strings in the array. This is due to the nested loops and the substr() operations.

Example Output:

For the given input arrays:

• ["a", "aba", "ababa", "aa"] -> Output: 4
• ["pa", "papa", "ma", "mama"] -> Output: 2
• ["abab", "ab"] -> Output: 0

This solution should work efficiently within the given constraints.

[kovatz]

Thanks to solving the problem of "Count Prefix and Suffix Pairs I"

[mah-shamim]

Thanks