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How to handle this kind of questions?
By jatinxkirito, history, 7 months ago, In English

Can anybody please tell how do you handle this kind of questions. I can't seem to find a solution.

Fofo, the richest man in the city has a big problem and he believes that you are the only one capable of solving it. He has recently completed N projects and earned A[i] profit for every project. He now wants to build M warehouses such that each warehouse can accommodate K bundles of money. The money bundles must be distributed such that the following conditions are true: • The profit earned from a project is not distributed among more than one warehouse. • The warehouse can contain more than one project's profit, provided that the total number of bundles does not exceed K. Now he wants your help by determining the smallest value for K so that he can place all the bundles in the M warehouses. Find the smallest possible value of K such that the profit earned from all projects is distributed across the M warehouses.

Tags dp, help
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7 months ago, # |
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Auto comment: topic has been updated by jatinxkirito (previous revision, new revision, compare).

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7 months ago, # |
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i think we can solve this by binary search ,since for all the possible values of k ( greater than the minimum ) we can accomodate the bundles of money so we can see a monotonic graph which proves we can apply binary search.

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    7 months ago, # ^ |
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    actually problem is after that. how do we check that if the given k is possible. We have to optimally fit the cash blocks without breaking them.

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7 months ago, # |
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Strongly NP-complete.

There are multiple approaches if the constraints are low enough for bitmask DP.

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    7 months ago, # ^ |
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    Can you please provide a reference

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    7 months ago, # ^ |
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    From the article:

    On the other hand, bin packing is solvable in pseudo-polynomial time for any fixed number of bins K

    And in case of binary search

    solvable in polynomial time for any fixed bin capacity B

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      7 months ago, # ^ |
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      "fixed" means it's treated like a constant in complexity analysis, for example $$$N^K$$$ is a polynomial for fixed $$$K$$$.

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    7 months ago, # ^ |
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    Thanks a lot

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7 months ago, # |
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infosys

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