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Book Allocation

Hard

Minimize the maximum pages

In simple words

Guess a max pages-per-student; if the books split within that limit try smaller, otherwise bigger.

The idea

Allowing more pages per student needs fewer students — monotone. Binary search the smallest 'max pages' that still uses at most m students.

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candidates114

Step 1 of 26. Brute force: try every page-limit until the books fit 2 students. Values: 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203. candidates 114.

1/26
Brute force
timeO(sum·n)spaceO(1)

Try every limit.

1let best = -1;2for (let cap = maxPage; cap <= sum && best < 0; cap++)3  if (studentsNeeded(cap) <= students) best = cap;4return best;

Input

array
[90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, …]

Memory

try
—
candidates
114
limit
—

Output

limit
—
answer
—

Check yourself

3 quick questions about this walkthrough. A wrong answer costs nothing.

Examples

Example 1

Input:
pages = [12, 34, 67, 90], students = 2
Output:
113
Explanation:
Split so the busiest student reads 113 pages.

Example 2

Input:
pages = [25, 46, 28, 49, 24], students = 4
Output:
71
Explanation:
Fairest max load is 71.

Example 3

Input:
pages = [5, 17, 100, 11], students = 4
Output:
100
Explanation:
One book of 100 forces max 100.

Practice this problem:GeeksforGeeks(opens in a new tab)

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