Suppose a program has runtime proportional to nlogn, where n is the input size. If the program takes 500 milliseconds to process input of size one thousand, how long will it take to process input of size one million?

If computer A runs a program in 20 seconds and computer B runs the same program in 35 seconds, how much faster is A than B?

Imagine we have a small computer which contains a simplified version of a CPU and RAM. The CPU can execute a single program that is stored in the RAM, and while running the program it can access 3 memory locations: its internal register AL, and two RAM locations that we'll call address 1 and address 2. Since this is a simplified computer it is able to skip some of the steps to access memory that are in our textbook, but accessing RAM still takes longer than accessing AL. The only values this computer is capable of storing in memory are unsigned bytes (8 bit binary numbers), and when it starts running a program all 3 of its memory locations initially contain the value 00000000.  Here is a list of all of the instructions our imaginary computer can perform: Write [number] to AL This instruction takes the operand [number], which must be an 8-bit binary number, and puts it into AL. This overwrites whatever was in AL previously. It takes 3 cycles to complete: 1 cycle each to fetch, decode,…

For example, consider the following number Input: 102405Output: 112415 Input: 56004.