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 fixedsize 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 i^{th} line describes i^{th} item in the form v_{i} and w_{i} where v_{i} is the value and w_{i} is the weight of i^{th} item.
Output
Output a single number  maximum value of knapsack. (All operations and the answer are guaranteed to fit in signed 32bit 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
V_{i} <= 10^7
W_{i} <= 10^7
hide comments
sanjay:
20160528 14:07:53
TOP DOWN DP WITH MEMORY OPTIMISATION. :) 

ranjanakash166:
20160329 20:30:22
its getting internal error in c++ 5.1 while the same code got AC in c++ 4.3.2!!! 

darragh:
20160220 21:32:58
If you want to know how to do it in 0.0 time just look up best first branch and bound. 

minhthai:
20160218 11:49:53
even O(k) space in java cannot get AC :(( any hint? 

Shubham Khandelwal:
20160203 18:32:06
Was getting TLE but changing array type from long long to int, turned to AC. O(N*k) gets AC 

manas0008:
20160202 17:33:20
Do only space optimisation but not time.First try WACHOVIA problem. 

sudip_95:
20160128 09:35:05
solved in 1.45s after optimizing. Can't understand how it can be solved in 0.00s. Can anyone explain how? 

shantanu tripathi:
20160111 16:44:25
lots of optimization needed from memory to time complexity.... nice :) 

jefry33:
20151212 07:42:33
Guys, can you help me? how to decrease memory for this problem? i using dynamic programming and it using large memory in Array... 

hnvahidi:
20151122 23:23:38
I got TLE , just changed array type from long long to int and got AC :O

Added by:  @ce 
Date:  20130624 
Time limit:  2s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 