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

This should help if you stuck for a long time. See the second program in this link : https://www.geeksforgeeks.org/space-optimized-dp-solution-0-1-knapsack-problem/

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.

meenaranga: 2017-06-10 19:15:28

unbelievable turned long long to int got ac??

cichipi_: 2017-06-10 18:45:18

normal knapsack...N*K time complexity...i think input file doesn't contain k = 2000000 and n=500....cz if so then n*k = 1e9...-> tle

snehalkr: 2017-06-05 13:06:49

LONG LONG INT GAVE TLE INT 1.54 Sec

prasoonbatham: 2017-05-24 17:47:46

Space optimized java solution gives tle. Same code accepted in cpp.


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