Copy Books | The Walking Dad

Copy Books | The Walking Dad

Copy Books

Problem Definition

Given an array A of integer with size of n( means n books and number of pages of each book) and k people to copy the book. You must distribute the continuous id books to one people to copy. (You can give book A[1],A[2] to one people, but you cannot give book A[1], A[3] to one people, because book A[1] and A[3] is not continuous.) Each person have can copy one page per minute. Return the number of smallest minutes need to copy all the books.

Example
Given array A = [3,2,4], k = 2.

Return 5( First person spends 5 minutes to copy book 1 and book 2 and second person spends 4 minutes to copy book 3. )

Challenge
Could you do this in O(n*k) time ?

Solution

O(n^2 * k) solution

DP:
minutes[i][j] = min( max( minutes[i-1][t], sum(t+1, j) ), where 1 <= i <= k, 0 <= j <= n - 1, 0 <= t < j

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