LKS - Large Knapsack


The knapsack problem or rucksack problem is a problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible. It derives its name from the problem faced by someone who is constrained by a fixed-size knapsack and must fill it with the most valuable items.

Just implement 0/1 Knapsack.

Input

First line contains two integers K and N, where K in the maximum knapsack size and N is the number of items. N lines follow where ith line describes ith item in the form vi and wi where vi is the value and wi is the weight of ith item.

Output

Output a single number - maximum value of knapsack. (All operations and the answer are guaranteed to fit in signed 32-bit integer.)

Time limit changed to 2s on 02.07.11.

Example

Input:
10 3
7 3
8 8
4 6

Output:
11

Constraints

K <= 2000000
N <= 500
Vi <= 10^7
Wi <= 10^7


hide comments
prezesstefan: 2021-06-19 04:05:25

Java: NZEC may mean you need memory-optimized DP (essentially == MLE).
Java is really tight, you will need O(K) memory (not O(nK) or not even O(2K)), plus time optimization too (do check out those geeksforgeeks links).

ahmed_samir13: 2021-04-27 11:08:33

i got AC one year ago , now i submit the same code , it give runtime error (SIGKILL) ?!!!!

brianmulyadi: 2020-12-10 08:02:13

I got acc in one go

nipun_baishnab: 2019-08-15 19:57:32

my fst day of learning knapsack and accepted in one go!!

spartan09: 2019-07-08 13:38:44

use int instead of long long int

mr_robo1: 2019-05-20 11:31:22

AC in first submission

itssanat: 2018-11-04 07:03:14

AC in one go :-) !!!!

jeet9: 2018-09-13 22:25:07

Memoized. Got AC in one go ! :D

luka_dzimba911: 2018-02-20 22:51:19

For all of you wondering how to get 0.0s learn branch and bound algorithm very useful and fun

very useful link:
https://www.slideshare.net/AbhishekSingh1904/0-1-knapsack-using-branch-and-bound?qid=7d155ea2-0377-4e83-b2f0-de118b4409a1&v=&b=&from_search=1

elliotto: 2018-02-12 23:03:31

*Edit: nevermind, i used a different compiler and it was fine.

Did you guys need to use iteration to pass this one? I've used recursion with O(n*K) space complexity, and hence at most O(n*K) time complexity. However, I'm getting time-out.

I know that iteration would be faster, but' thought this was more about dynamic programming (reducing time complexity) so didn't think it would be needed?

Last edit: 2018-02-12 23:25:55

Added by:Ace
Date:2013-06-24
Time limit:2s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64