Discussion on Sherlock and Cost Challenge

1 year ago+ 2 comments

Here's a PHP solution to solve this problem:

<?php

function cost($B) {
    $n = count($B);

    // dp array where dp[0] means A[i] is 1 and dp[1] means A[i] is B[i]
    $dp = array_fill(0, 2, 0);

    for ($i = 1; $i < $n; $i++) {
        $prevDp0 = $dp[0];
        $prevDp1 = $dp[1];

        // When A[i] is 1
        $dp[0] = max(
            $prevDp0 + abs(1 - 1), // A[i-1] is 1
            $prevDp1 + abs(1 - $B[$i - 1]) // A[i-1] is B[i-1]
        );

        // When A[i] is B[i]
        $dp[1] = max(
            $prevDp0 + abs($B[$i] - 1), // A[i-1] is 1
            $prevDp1 + abs($B[$i] - $B[$i - 1]) // A[i-1] is B[i-1]
        );
    }

    // The result is the maximum value when A[n-1] is either 1 or B[n-1]
    return max($dp[0], $dp[1]);
}

// Example usage:
$B = [10, 1, 10, 1, 10];
echo cost($B); // Output: 36

?>

Explanation:

Dynamic Programming Table (dp):
- dp[0]: The maximum cost when A[i] is set to 1.
- dp[1]: The maximum cost when A[i] is set to B[i].
Transition between states:
- For each i from 1 to n-1, we update dp[0] and dp[1] based on the previous values:
  - If A[i] is 1, the cost can come from either A[i-1] being 1 or B[i-1].
  - If A[i] is B[i], the cost can come from either A[i-1] being 1 or B[i-1].
Final Result:
- The result will be the maximum value between dp[0] and dp[1] at the end of the array, which represents the maximum cost achievable by either setting A[n-1] to 1 or B[n-1].

This solution efficiently computes the desired result with a time complexity of O(n), making it suitable for large inputs within the constraints.

11 months ago+ 0 comments

Sherlock Holmes, the world-renowned detective, is often depicted as a figure whose work transcends monetary concerns. However, the cost of his services is sometimes referenced subtly throughout Sir Arthur Conan Doyle's stories. While Sherlock's cases often involve the wealthy, like in The Adventure of the Speckled Band, he is also known to take on cases out of sheer intellectual curiosity, regardless of the client's ability to pay. Dr. Watson mentions in some instances wakeboard bindings that Holmes waived his fee entirely for those in dire straits, revealing that his primary motivation was solving complex mysteries, rather than financial gain.

11 months ago+ 0 comments

In Arthur Conan Doyle's tales, Sherlock Holmes often grappled with the complexities of cost, not just in monetary terms but also in terms of personal sacrifice and societal impact. Whether it was the financial ramifications of his various cases or the toll they took on his personal life, the concept of cost was a recurring theme in his adventures. For instance, Holmes's unwavering commitment to solving mysteries often led him to neglect his own well-being and relationships, underscoring the idea that true dedication KN Car Brand can come at a significant personal cost. Similarly, his cases frequently involved financial transactions, revealing the intricate ways in which crime and economics intersect. Through Holmes's experiences, Doyle explored how the pursuit of justice and the resolution of intricate problems involve weighing not just the immediate costs but also the broader, often intangible, repercussions.

Explanation:

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