p130 segment 4.2 Let's translate these algorithms into Java code. If we use long integers, we could write the following statements (see attached program).

• Run the program for n = 10000. The sum should be 50005000. How quick did each algorithm run?
• Run the program for n = 100000 (one hundred thousand). The sum should be 5000050000.

Keep adding zeros to n until the computer takes about ten seconds. Or go steps of hundred thousand,

Attachment

// @author Frank M. Carrano, Timothy M. Henry // @version 5.0 // Computing the sum of the consecutive integers from 1 to n: long n = 10000; // ten thousand // Algorithm A long sum = 0; for (long i = 1; i <= n; i++) sum = sum + i; System.out.println(sum); // Algorithm B sum = 0; for (long i = 1; i <= n; i++) { for (long j = 1; j <= i; j++) sum = sum + 1; } // end for System.out.println(sum); // Algorithm C sum = n * (n + 1) / 2; System.out.println(sum);

• n = 100000,
• n = 200000,
• n = 300000, ...

How big would n have been twenty years ago? How big will n be in twenty years?

If an algorithm were the only algorithm you tried and it was too slow, what should you do? Use a faster computer? Work harder for a different algorithm?