snackProblem DescriptionFinally, at the end of the day, it is time for a well-deserved snack. Rar the Cat opens up the pack of green beans he has been keeping all day. However, instead of a pack of beautiful green beans, he finds mud overflowing out of the bag! Oh no! Carefully, he lays out the green beans and mud balls on the table in one line. Since the green beans are all dirty, he has decided to play a game with Kang the Penguin using the dirty green beans and mud.There are N green beans and mud balls on the table. A green bean with a diameter of D mm will garner Rar the Cat D points. However, a mud ball will decrease Rar the Cat's total points by 2. To win the game, Rar the Cat has to find a consecutive section within the line of green beans and mud balls that can garner him the most points.Write a program that, when given the profile of the line of green beans and mud balls, outputs the maximum number of points Rar the Cat can get from this game.InputThe first line of input will contain one integer, N.The second line of input will contain N characters, containing one of these: - a number from '1' to '9', indicating a green bean with that size. - 'M', indicating a mudballOutputYour output should contain one integer, the maximum number of points Rar the Cat can get from this game.Your output should end with a newline.LimitsSubtask 1 (30%): 1 <= N <= 100Subtask 2 (70%): 1 <= N <= 1 000 000Sample Input 1515M81Sample Output 113
Question
snackProblem DescriptionFinally, at the end of the day, it is time for a well-deserved snack. Rar the Cat opens up the pack of green beans he has been keeping all day. However, instead of a pack of beautiful green beans, he finds mud overflowing out of the bag! Oh no! Carefully, he lays out the green beans and mud balls on the table in one line. Since the green beans are all dirty, he has decided to play a game with Kang the Penguin using the dirty green beans and mud.There are N green beans and mud balls on the table. A green bean with a diameter of D mm will garner Rar the Cat D points. However, a mud ball will decrease Rar the Cat's total points by 2. To win the game, Rar the Cat has to find a consecutive section within the line of green beans and mud balls that can garner him the most points.Write a program that, when given the profile of the line of green beans and mud balls, outputs the maximum number of points Rar the Cat can get from this game.InputThe first line of input will contain one integer, N.The second line of input will contain N characters, containing one of these: - a number from '1' to '9', indicating a green bean with that size. - 'M', indicating a mudballOutputYour output should contain one integer, the maximum number of points Rar the Cat can get from this game.Your output should end with a newline.LimitsSubtask 1 (30%): 1 <= N <= 100Subtask 2 (70%): 1 <= N <= 1 000 000Sample Input 1515M81Sample Output 113
Solution
The problem is asking to find the maximum sum of a subarray in an array. The array contains both positive and negative numbers. The positive numbers are represented by the digits '1' to '9' and the negative numbers are represented by the letter 'M', which is equivalent to -2.
Here are the steps to solve the problem:
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First, read the integer N from the input, which represents the number of green beans and mud balls.
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Then, read the next line of input, which contains N characters. Each character can be a digit from '1' to '9' or the letter 'M'. Convert each digit to its integer value and each 'M' to -2, and store them in an array.
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Now, you need to find the maximum sum of a subarray in the array. You can use the Kadane's algorithm to solve this problem. The algorithm is as follows:
- Initialize a variable
max_so_farto 0 and another variablemax_ending_hereto 0. - For each number in the array, add the number to
max_ending_here. Ifmax_ending_herebecomes less than 0, set it to 0. Ifmax_so_faris less thanmax_ending_here, setmax_so_fartomax_ending_here. - After going through all the numbers in the array,
max_so_farwill be the maximum sum of a subarray.
- Initialize a variable
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Print
max_so_faras the maximum number of points Rar the Cat can get from this game.
This solution works in O(N) time, where N is the number of green beans and mud balls.
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