- I met this problem as a subproblem many times and tried to find a solution for it but failed ,So I make an elegent statement for the problem asking for someone's help :
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Could you give a publicly available link instead of screenshots? Or at least tell where the problem is from? This looks fishy.
The problem is written by me in a word file and I take a screenshot of it , so it doesn't have a public link
Edited , Bro
The reason why I asked for a link ia to prevent cheating, but considering the statement you sent doesn't even have a bound on the sum of $$$k_i$$$ i will assume youre not.
This is the maximum bipartite matching problem, you can read about it here https://cp-algorithms.com/graph/kuhn_maximum_bipartite_matching.html
However, this is an advanced topic and you should probably worry about other things more. If you're encountering this problem a lot youre probably making the wrong reductions.
Ok my friend, I appreciate that but this really wasn't meant to be cheating in any way, can you provide a solution to this problem using Kuhn's Algorithm for Maximum Bipartite Matching?
I understood the topic , but can't it be solved in time complexity less than O(n*m) time , if we don't need the number of matchings, just need whether or not the solution exists
Kuhn is faster than $$$O(nm)$$$ in practice with the heuristics they talk about there. There is also a $$$O(n\sqrt{n})$$$ that as far as i know is hard to distinguish from kuhn. Asking if there is a perfect matching doesn't help in this problem.
Also, if you are thinking on how to solve a specific problem, send that specific problem instead. A lot of times when beginners ask for help they make wrong reductions and leave out important information, that's probably what is happening here.
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