Copy Books

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.

样例

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. )

挑战

Could you do this in O(n*k) time ?

class Solution {
public:
    /**
     * @param pages: a vector of integers
     * @param k: an integer
     * @return: an integer
     */
    int copyBooks(vector<int> &pages, int k) {
        // write your code here
        int n = pages.size();
	    if (n < 1 || k < 1)
	    {
		    return 0;
	    }

	    if (k >= n)
	    {
		    int result = INT_MIN;
		    for (int i = 0; i < n; i++)
		    {
			    if (pages[i] > result)
			    {
				    result = pages[i];
			    }
		    }

		    return result;
	    }
	    int buf[k][n];
	    buf[0][0] = pages[0];
	    for (int i = 1; i < n; i++)
	    {
		    buf[0][i] = buf[0][i-1] + pages[i];
	    }

	    for (int i = 1; i < k; i++)
	    {
		    for (int j = n-1; j >= i; j--)
		    {
			    int sum = 0;
			    buf[i][j] = INT_MAX;
			    for (int k = j; k >= i-1; k--)
			    {
				    int temp = max(buf[i-1][k], sum);
				    buf[i][j] = min(buf[i][j], temp);
				    sum += pages[k];
			    }
		    }
	    }

	    return buf[k-1][n-1];
    }
};