Nested loops into mathematical model to count number of operations

Question

I\'m reading the book \'Algorithms - Fourth edition\' by Sedgewick and Wayne and I must admit that some parts in the \"Analysis of Algorithms\" chapter are confusing me! Thi

Answer 1

If you can understand the N(N-1)(N-2) part, here's a thought:

Take a combination of 3 numbers, i, j, k, whatever 3 that fall into the range 0 <= i,j,k < N and different one from another (this is also taken care in the code and that's why the formula is N(N-1)(N-2) and not N^3.

Now, lets say the numbers are 13, 17, 42. It doesn't really matters whoch numbers they are. In how many ways can you put them in line?

13-17-42
13-42-17
17-13-42
17-42-13
42-13-17
42-17-13

Six!

How many of these ways can appear in the code? Only one! (that's taken care in the initializaton of j and k).

So, the total number of N(N-1)(N-2) should be divided by 6.