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longest increasing subsequence

algorithm to find the longest increasing subsequence in an array of numbers

en-GB/ˈlɒŋɡɪst ɪnˈkɹiːsɪŋ sʌbsɪkwəns/
en-US/ˈlɑŋɡɪst ˌɪnˈkɹisɪŋ ˈsʌbˌsikwəns/

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optimization problem