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Fl03Hw2 - Home Work 2 Fall 2003 CSE 4081 5211 Due Points 50...

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Home Work 2 Fall 2003 CSE 4081/ 5211 Due: 10/7/03 Points: 50 1) Prove that X^2 = O(2^X) For c=1, X^2 <= 2^X, for every X>=4. Hence for (c=1, N0=4) the definition of big-O follows. 2) Set up its recurrence equation and find the general solution. procedure no-use (set S) if (set size == 1) then // complexity O(1) do nothing; else for each subset S1 of S print S1; // Complexity O(2^n) no-use (S – next element s belonging to S) // T(n-1) end if end procedure Recurrence equation, T(n) = T(n-1) + 2^n + c Solving by telescoping: T(n) = T(n-1) + 2^n +c = T(n-2) + 2^(n-1)+2^n +c +c = … = T(1) + 2^n + 2^(n-1) + 2^(n-2) + … +2^2 + (n-1)c = O(2^n) 3) Generate a list of ten unique numbers between 1 and 999 (e.g., 50, 2, 895, 59, 400, 300, 25, 19, 600, 932). Input 8 1 4 9 0 3 5 2 7 6 a) Show the whole sorting procedure of Insertion sort. 8 1 4 9 0 3 5 2 7 6 1 8 4 9 0 3 5 2 7 6 1 4 8 9 0 3 5 2 7 6 1 4 8 9 0 3 5 2 7 6 0 1 4 8 9 3 5 2 7 6 0 1 3 4 8 9 5 2 7 6 0 1 3 4 5 8 9 2 7 6 0 1 2 3 4 5 8 9 7 6 0 1 2 3 4 5 7 8 9 6 0 1 2 3 4 5 6 7 8 9
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b) Show the whole sorting procedure of Quick sort (rearrange the number carefully, so that the algorithm makes three or more recursive calls).
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