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Desain dan Analisis Algoritma

Desain dan Analisis Algoritma. Pertemuan 4 Asymptotic Notations. Big Oh. t(n) Є O(f(n)) Baca : OoG t(n) ada di O f(n) t(n) Є O(f(n)) jika OoG t(n) ≤ OoG f(n) Contoh 7n Є O(n 2 ), 100n + 5 Є O(n 2 ), 0.5n(n - 1) O(n 2 ). Big Oh.

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Desain dan Analisis Algoritma

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  1. Desain dan Analisis Algoritma Pertemuan4 Asymptotic Notations

  2. Big Oh t(n) Є O(f(n)) • Baca : OoG t(n) ada di O f(n) • t(n) Є O(f(n)) jika OoG t(n) ≤ OoG f(n) • Contoh 7n Є O(n2), 100n + 5 Є O(n2), 0.5n(n - 1) O(n2)

  3. Big Oh Untuk membuktikan apakah t(n) Є O(f(n)) OoG t(n) ≤ OoG f(n) • Limit • Jika ada konstanta c dan integer positif no sedemikian hingga t(n) ≤ cf(n) untuk semua n ≥ no

  4. Big-O

  5. Big Oh • Buktikan bahwa 100n + 5 Є O(n2)

  6. Big Omega t(n) Є Ω(f(n)) • Baca : OoG t(n) ada di omega f(n) • t(n) Є Ω(f(n)) jika OoG t(n) ≥ OoG f(n) • Contoh, untuk algoritma polinom t(n) Є Ω(n) • Contoh 3n3Є Ω(n2), 0.5n(n - 1) Є Ω(n2)

  7. Big Omega Untuk membuktikan apakah t(n) Є Ω(f(n)) OoG t(n) ≥ OoG f(n) • Limit • Jika ada konstanta c dan integer positif no sedemikian hingga t(n) >= cf(n) untuk semua n ≥ no

  8. Big Omega • Buktikan bahwa n3Є Ω(n2)

  9. Big theta t(n) ЄӨ(f(n)) • Baca : OoG t(n) ada di Ө f(n) • t(n) ЄӨ(f(n)) jika OoG t(n) = OoG f(n) • Contoh 2n2 + log n ЄӨ(n2), 2n4 + 3n2ЄӨ(n4)

  10. Big theta Untuk membuktikan apakah t(n) ЄӨ(f(n)) OoG t(n) = OoG g(n) • Limit • Jika ada konstanta c1, c2 dan integer positif no sedemikian hingga c2g(n) ≤ t(n) ≤ c1g(n) untuk semua n ≥ no

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