Question

help in design of algorithm

answers with steps for study guide

(2 points) Why shouldn't we measure time efficiency based on the number of seconds or milliseconds it takes the algorithm 1. to run? is the number of times the most important operation of the (2 points) The 2. algorithm occ Ccurs (3 points) Find the binary representation of the following numbers: 3. BINARY REPRESENTATION (in bits) NUMBER 777 14 684,739 4. (8 points) Write the input size metric and the basic operation of the following algorithms: ALGORITHM INPUT SIZE BASIC OPERATION (the number of times the basic operation will need to execute) Computing the Computing n! Finding the largest element in a list of sum of n numbers n numbers Euclid's algorithm

Answer 1

1) since the time taken in millisecond for an algorithm to execute depends on the size of the input and varies form system to system we should measure the time efficiency using milliseconds.

2) Running time

3)To convert to binary divide by to and put the remainder on the right repeat until zero is reached.

ie for 777/2=388 and remainder is 1

next step:-current ans=1 and 388/2=194 remainder=0

next step=current ans=01 and 194/2=97 remainder=0

next step=current ans=001 and 97/2=48 remainder=1

next step=current ans=1001 and 48/2=24 remainder=0

next step=current ans=01001 and 24/2=12 remainder=0

next step=current ans=001001 and 12/2=6 remainder=0

next step=current ans=0001001 and 6/2=3 remainder=0

next step=current ans=00001001 and 3/2=1 remainder=1

next step=current ans=100001001 and 1/2=0 remainder=1

final ans=1100001001

777 - 1100001001_b

14-1110_b

684739-10100111001011000011_b

₄₎

Algorithm	Input size	Basic operation
computing the sum of n numbers	n	addition
computing n!	n	multiplication
find the largest element in a list of n numbers	n	greater than or lesser than operation
Euclid's algorithm	2 numbers	mod