Please help me with this interesting problem

Revision en1, by nirwandogra, 2020-08-29 05:07:24

Your given a a list of people and their skillsset. We need to form a team out of these people with as many people as we want. The only condition is each of the skills has a maximum allowed amount in the team formed. i.e Sum of ith skill from all people in the team should be <= Maximum allowed value of the ith skill.

Input starts with 3 integers N S M i.e number of people , total number of skills and total number of edges . Next M lines follow with 3 integers A B C meaning person A has skill B with total amount C. This is followed by S lines with 2 integers X Y where X = skill number and Y = maximum amount of skill X that is allowed to be in the team.

Example Input: 4 2 7 1 1 1 2 1 1 2 2 1 3 1 1 3 2 1 4 2 1 5 2 1 1 2 2 2

Output: 3

In the above example there are multiple options to build a team. We can choose 2,3 to form the team and in this case the total skill = 2 and 2. Person 2 has skills 1 and 2, and person 3 also has skills 1 and 2. We cannot add any more elements since then we will exceed the total skills level allowed in a team. The subset = 1,4,5 or 1,2,5 or 1,3,5 is optimal because the skills level is not breached.

I tried to formulate a maxflow graph but the issue is if a node is chosen then all the edges from it have to be chosen so this wasn't boiling to a network flow graph. I wanted to know if this is a NP-Hard problem and how do we prove that indeed a problem is Np-hard.

Tags maxflow, nphard, #mincost flow, #competitive-programming

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  Rev. Lang. By When Δ Comment
en3 English nirwandogra 2020-08-29 05:39:40 121
en2 English nirwandogra 2020-08-29 05:08:17 22
en1 English nirwandogra 2020-08-29 05:07:24 1485 Initial revision (published)