hw1sol - CSCI4041 Homework1 Solution Key Spring 2009...

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CSCI4041 Homework1 Solution Key Spring 2009 1 [20pt] [10pt] Pseudocode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 SORT(A,n) // A: array, n: size of array for i <- 1 to n-1 // find small lest smallest <- i for j <- i+1 to n if(A[j] < A[smallest]) then smallest <- j end end // j loop // swap i and smallest Temp <- A[i] A[i] <- A[smallest] A[smallest] <- Temp end // i loop end // SORT (-1) for each incorrect loop start/end index (-1) for each mistakes of keeping smallest index in i-loop [4pt] Loop invariant For each iteration of I-loop (line 1-13), every element of index < i is sorted in increasing order (2pt), and every element of index i is greater than every element of index < i (2pt). [2pt] According to the loop invariant, left n-1 elements are sorted, and n-th element is greater than its n-1 left elements in n-th iteration. So n-th iteration is not needed. [2pt] Best case: Θ (n 2 ) [2pt] Worst case: Θ (n 2 ) 2. [20pt] [10] Pseudocode 1 2 3 4 5 6 7 8 9 10 11 12 13 FIND_MIN_MAX(A,s,t) // A: array, i:start index, t: last index, returns array with 2 elements {min, max} if s=t then return {A[s], A[s]} end mid <- s + floor( (t-s+1)/2)
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