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authorJulian T <julian@jtle.dk>2020-02-11 12:24:56 +0100
committerJulian T <julian@jtle.dk>2020-02-11 12:24:56 +0100
commit6db1a2cdd3b96731f2e092d55d8c2136eabc52d0 (patch)
tree2be8fae8ce82d708ed9f00f376dda14420850e80 /sem1/algo/mm3/opgaver.md
parent57305119e05559c1c37e903aef89cd43f44c42c9 (diff)
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-# Opgave 1
-
-## Exercise 9.2
-
-**T(n) = 3T(n/2) + n**
-
-a = 3
-b = 2
-d(n) = n
-
-a ? d(b) -> 3 > 2
-
-Svaret er derfor O(n^log2(3)) = O(n^1.59)
-
-**T(n) = 3T(n/2) + n^2**
-
-3 ? 2^2 -> 3 < 4
-
-d(n) = n^2 hvilket betyder at O(n^2)
-
-**T(n) = 8T(n/2) + n^2**
-
-8 ? 2^3 -> 8 = 8
-
-d(n) = n^3 hvilket betyder at O(n^3 log2(n))
-
-## Evercise 9.3
-
-**T(n) = 4T(n/3) + n**
-
-a = 4
-b = 3
-d(n) = n
-
-4 ? 3 -> 4 > 3
-
-Derfor er svaret O(n^log3(4)) = O(n^1.26)
-
-**T(n) = 4T(n/3) + n^2**
-
-4 ? 3^2 -> 4 < 9
-
-d(n) = n^2 hvilket betyder at O(n^2)
-
-**T(n) = 9T(n/3) + n^2**
-
-9 ? 3^2 -> 9 = 9
-
-d(n) = n^2 hvilket betyder at O(n^2 log2(n))