Challenge: Pack the Bag

Lab Java Intermediate 20 points

A hiker's bag holds at most W kg. Each item has a weight and a value and can be packed once or not at all. Print the biggest total value that fits.

Input

Line 1: n W (W ≤ 10⁴). Then n lines weight value.

Output

The best total value.

Example

Input

Output

Sample input available Sample output available

Editor

Java

Hints

dp[i][w] = best value with the first i items and capacity w.

Leave item i: dp[i-1][w]. Take it (if it fits): val + dp[i-1][w - weight].

Solution explanation

The table has (n + 1) × (W + 1) cells, each filled in O(1): O(n·W).

Show solution

import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt(), W = sc.nextInt();
        int[] wt = new int[n], val = new int[n];
        for (int i = 0; i < n; i++) {
            wt[i] = sc.nextInt();
            val[i] = sc.nextInt();
        }
        long[][] dp = new long[n + 1][W + 1];
        for (int i = 1; i <= n; i++) {
            for (int w = 0; w <= W; w++) {
                dp[i][w] = dp[i - 1][w];
                if (wt[i - 1] <= w) dp[i][w] = Math.max(dp[i][w], val[i - 1] + dp[i - 1][w - wt[i - 1]]);
            }
        }
        System.out.println(dp[n][W]);
    }
}

Output

Answer