Question

1. (4 points) 1a) Use pseudocode to specify a brute-force algorithm that determines when given as input a sequence of $n$ positive integers whether there are two distinct terms of the sequence that have as sum a third term. The algorithm should loop through all triples of terms of the sequence, checking whether the sum of the first two terms equals the third. 1b) Give a big-O estimate for the complexity of the brute-force algorithm from part (a). 1c) Devise a more efficient algorithm for solving the problem that first sorts the input sequence and then checks for each pair of terms whether their difference is in the sequence. 1d) Give a big-O estimate for the complexity of this algorithm. Is it more efficient than the brute-force algorithm?

          1. (4 points)
1a) Use pseudocode to specify a brute-force algorithm that determines when given as input a sequence of $n$
positive integers whether there are two distinct terms of the sequence that have as sum a third term. The
algorithm should loop through all triples of terms of the sequence, checking whether the sum of the first two
terms equals the third.
1b) Give a big-O estimate for the complexity of the brute-force algorithm from part (a).
1c) Devise a more efficient algorithm for solving the problem that first sorts the input sequence and then checks
for each pair of terms whether their difference is in the sequence.
1d) Give a big-O estimate for the complexity of this algorithm. Is it more efficient than the brute-force
algorithm?

1. (4 points)
1a) Use pseudocode to specify a brute-force algorithm that determines when given as input a sequence of n
positive integers whether there are two distinct terms of the sequence that have as sum a third term. The
algorithm should loop through all triples of terms of the sequence, checking whether the sum of the first two
terms equals the third.
1b) Give a big-O estimate for the complexity of the brute-force algorithm from part (a).
1c) Devise a more efficient algorithm for solving the problem that first sorts the input sequence and then checks
for each pair of terms whether their difference is in the sequence.
1d) Give a big-O estimate for the complexity of this algorithm. Is it more efficient than the brute-force
algorithm?

Added by Alicia M.

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