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Problem · Greedy

Max Subjects Number

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A student is taking a test on n different subjects. For each n^th subject they have already answered answered[i] questions and have time to answer a total of q more questions overall. For each n^th subject, the number of questions answered has to be at least needed[i] in order to pass. Determine the maximum number of subjects the student can pass if the additional answered questions are optimally distributed among the subjects.

For example, there are n = 2 subjects and needed = [4, 5] answered questions, respectively, to pass. The student has answered answered = [2, 4] questions in the two subjects so far, and can answer another q = 2 questions in all subjects combined. The best outcome is to answer an additional question in the second subject to pass it, and it is not possible to pass the first subject. The maximum number of subjects that can be passed is 1.

Function Description

Complete the function maxSubjectsNumber in the editor below. The function must return an integer that represents the maximum number of subjects that can be passed.

maxSubjectsNumber has the following parameter(s):

answered[answered[0],...answered[n-1]]: an array of integers
needed[needed[0],...needed[n-1]]: an array of integers
q: an integer

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Examples

01 · Example 1

answered = [24, 27, 0]
needed = [51, 52, 100]
q = 100
return = 2

Here answered = [2, 4, 0] and needed = [5, 7, 100]. The additional answers needed to pass are [3, 3, 100]. The best distribution is at least 7 - 2 = 5 questions among the first two subjects. It would take all 100 questions to pass the third subject.

02 · Example 2

answered = [24, 27, 0]
needed = [51, 52, 100]
q = 200
return = 3

03 · Example 3

answered = [2, 4]
needed = [4, 5]
q = 1
return = 1

There are n = 2 subjects and needed = [4, 5] answered questions, respectively, to pass. The student has answered answered = [2, 4] questions in the two subjects so far, and can answer another q = 1 questions in all subjects combined. The best outcome is to answer an additional question in the second subject to pass it, and it is not possible to pass the first subject. The maximum num of subjects that can be passed is 1 :)

Constraints

1 ≤ n ≤ 10^5
0 ≤ answered[i], needed[i] ≤ 10^9