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Lecture 5

Lecture 5. Quiz 2. Input: A nonnegative integer n S:=0 for i :=0 to n do S:=S + i * i return S What Doest this Algorithm Compute What is its basic operation How many times is the basic operation executed? What is the efficiency class of this algorithm

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Lecture 6

Lecture 6. Merge Sort: Algorithm . Merge-Sort (A, left, right) if left ? right return else middle ? ( left+right )/2 ? Merge-Sort (A, left, middle) Merge-Sort (A, middle+1, right) Merge (A, left, middle, right). Recursive Call. Merge-Sort: Merge. Sorted. A:. merge.

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Lecture 7

Lecture 7. Solution by Substitution Method . T(n) = 2 T(n/2) + n Substitute n/2 into the main equation 2T(n/2) = 2(2(T(n/4)) + n/2) = 4T(n/4) + n And T(n) = 4T (n/4) + 2n Again by substituting n/4, we can see 4T(n/4) = 4(2T(n/8)) + (n/4) = 8T(n/8) + n And T(n) = 8T(n/8) + 3n

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Lecture 5

Lecture 6

Lecture 7