Bookshelf 2

Time Limit : 2000/1000ms (Java/Other)   Memory Limit : 131072/65536K (Java/Other)

Total Submission(s) : 91   Accepted Submission(s) : 41

Problem Description

Farmer John recently bought another bookshelf for the cow library, but the shelf is getting filled up quite quickly, and now the only available space is at the top.

FJ has N cows (1 ≤ N ≤ 20) each with some height of H_i (1 ≤H_i ≤ 1,000,000 - these are very tall cows). The bookshelf has a height ofB (1 ≤ B ≤ S, where S is the sum of the heights of all cows).

To reach the top of the bookshelf, one or more of the cows can stand on top of each other in a stack, so that their total height is the sum of each of their individual heights. This total height must be no less than the height of the bookshelf in order for the cows to reach the top.

Since a taller stack of cows than necessary can be dangerous, your job is to find the set of cows that produces a stack of the smallest height possible such that the stack can reach the bookshelf. Your program should print the minimal 'excess' height between the optimal stack of cows and the bookshelf.

 

Input

* Line 1: Two space-separated integers: N and B
* Lines 2..N+1: Line i+1 contains a single integer: H_i

 

Output

* Line 1: A single integer representing the (non-negative) difference between the total height of the optimal set of cows and the height of the shelf.

 

Sample Input

5 1631356

 

Sample Output

1

 

 

package DynamicProgrammingPackage;import java.util.Scanner;/** * 0-1背包 */public class Bookshelf {public static int[] stateArr = null;public static int[] h = new int[20];//放牛的高度public static int n;//一共多少头牛public static int maxh = 0;public static int sum = 0;public static void main(String[] args) {Scanner sc = new Scanner(System.in);while(sc.hasNextInt()) {n = sc.nextInt();maxh = sc.nextInt();sum = 0;for(int i=0; i<n; i++) {h[i] = sc.nextInt();sum += h[i];}stateArr = new int[sum+1];dp();int result = min();min();System.out.println(result);}}private static int min() {for(int i=0; i<=sum; i++) {if(maxh <= stateArr[i]) {return stateArr[i] - maxh;}}return 0;}private static void dp() {for(int i=0; i<n; i++) {ZeroOnePack(h[i], h[i]);}}private static void ZeroOnePack(int cost, int weight) {for(int i=sum; i>=weight; i--) {stateArr[i] = Math.max(stateArr[i], stateArr[i-weight]+cost);}}}