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.


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 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.


10 3
7 3
8 8
4 6



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

hide comments
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:

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
akashbhalotia: 2017-12-24 10:16:35

This should help if you stuck for a long time. See the second program in this link :

rohit9934: 2017-07-05 17:59:10

use the optimized knapsack
int will work fine.

vivace: 2017-06-15 11:47:42

How are people getting 0.00 seconds on this one . My space optimised 0-1 knapsack dp of order O(nW) took 1 second even in C.

Added by:Shikhar
Time limit:2s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64