Consider two algorithms A and B that solve the same class of problems. The time complexity of A is 5000n. The time complexity for B is ceiling(1.1") or 1.17 Find the time required to execute each for n=10, n=100, n= 1000, n=1000000 Tabulate your results? which algorithm has better performance for n>1000 Exercise 2: Find an upper bound and a lower bound for each of the function f(x). 1) f(x)=x²+2x+1. 2) f(x)=3x²+2x²+x. 3) f(n)-(6n+4)(1+ign) Exercise 3: Consider the algorithm below: 1. in; 2. while (iz 1){ 3. x=x+1 4. i-i/2} Trace the algorithm, and fill the table that indicates the number of times x-x+1 for the following values of n n 8 16 32 i (range) (8.42.1) #times x=x+1 executed 4 Find a theta notation in terms of n for the number of times the statement x-x+1 is executed based on generalizing the results above for n=2". Note that if n=2", then k-log2(n). Exercise 4:

Consider two algorithms A and B that solve the same class of problems. The time complexity of A is 5000n. The time complexity for B is ceiling(1.1") or 1.17 Find the time required to execute each for n=10, n=100, n= 1000, n=1000000 Tabulate your results? which algorithm has better performance for n>1000 Exercise 2: Find an upper bound and a lower bound for each of the function f(x). 1) f(x)=x²+2x+1. 2) f(x)=3x²+2x²+x. 3) f(n)-(6n+4)(1+ign) Exercise 3: Consider the algorithm below: 1. in; 2. while (iz 1){ 3. x=x+1 4. i-i/2} Trace the algorithm, and fill the table that indicates the number of times x-x+1 for the following values of n n 8 16 32 i (range) (8.42.1) #times x=x+1 executed 4 Find a theta notation in terms of n for the number of times the statement x-x+1 is executed based on generalizing the results above for n=2". Note that if n=2", then k-log2(n). Exercise 4: