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Code Golf

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Required fields*

Required fields*

Only one from each set

Your input is a non-empty set of non-empty sets of positive integers. For example:

{{1}, {2, 3}, {2,4}, {1,4}}

Your task is to output the maximal number of elements that can be picked from the sets with the following conditions:

  • You can only pick at most 1 element from a set
  • You can't pick the same element from 2 different sets

In this example you can pick 1 from the first set, 3 from the second set, 2 from the third set and 4 from the last set, for a total of 4 elements.

Io is flexible. You can take a list, instead of sets, etc.

There are no gaps in the numbers (eg. {{2,3},{3,4}} is not a valid input). Or in other words, the input flattened must contain all numbers [1,n] where n is the largest number in the input.

This is , so shortest code wins.

Examples

{{1}}
-> 1
{{1}, {2, 3}, {2,4}, {1,4}}
-> 4
{{1}, {2}, {1,2,3,4}}
-> 3
{{1}, {2}, {2,3}}
-> 3
{{1, 2, 3}, {2, 4, 5, 6}, {3, 5, 6, 7}, {1, 2}, {2, 3}, {1, 3}}
-> 5
{{1,2,3,4,5}, {1,2}, {2,3}, {1,3}}
-> 4
{{1,2},{1,3},{1,4},{2,3},{2,4},{3,4},{1,2,3},{1,2,4},{1,3,4},{2,3,4},{5,6,7,8,9,10}}
-> 5
{{1,4}, {2,3}, {1,3}, {1,2,3}}
-> 4

Background

Recently @AnishSharma posted this question on Stack Overflow. This is a slightly modified version of that question

Answer*

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  • 1
    \$\begingroup\$ TIL about lengths function. Thanks! \$\endgroup\$ Commented Jan 23, 2022 at 16:47
  • 1
    \$\begingroup\$ @pajonk - You're welcome. It's quite disconcerting when you accidentally learn something potentially useful while deliberately trying to write difficult-to-understand code, isn't it? This has often happened to me, too... \$\endgroup\$ Commented Jan 23, 2022 at 18:51
  • \$\begingroup\$ You're absolutely right... BTW, you "stole" the test setup from me, but not the table function (for -1) ;-) \$\endgroup\$ Commented Jan 23, 2022 at 19:51
  • \$\begingroup\$ @pajonk - Dang, you're right! But if I use table instead of unique, it'd be the same as you using lengths instead of sapply(,length)... we should flip a coin somehow do decide who gets to use the other's function... \$\endgroup\$ Commented Jan 23, 2022 at 22:19
  • 1
    \$\begingroup\$ "pajonk_guesses_heads" ends in letter s ≠ t (by odd/even position). \$\endgroup\$ Commented Jan 24, 2022 at 7:33

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