Loops may be nested, with one loop sitting in the body of another. The inner loop will be executed in full for every execution of the outer loop. Listing 7.14 illustrates writing marks into a matrix using nested for loops.

Listing 7.14. Illustrates nested for loops.

Output: 

How many rows? 4

How many columns? 12

What character? x

xxxxxxxxxxxx

xxxxxxxxxxxx

xxxxxxxxxxxx

xxxxxxxxxxxx

Analysis: The user is prompted for the number of rows and columns and for a character to print. The first for loop, on line 16, initializes a counter (i) to 0, and then the body of the outer for loop is run. On line 18, the first line of the body of the outer for loop, another for loop is established. A second counter (j) is also initialized to 0, and the body of the inner for loop is executed. On line 19, the chosen character is printed, and control returns to the header of the inner for loop. Note that the inner for loop is only one statement (the printing of the character). The condition is tested (j < columns) and if it evaluates true, j is incremented and the next character is printed. This continues until j equals the number of columns.

Once the inner for loop fails its test, in this case after 12 Xs are printed, execution falls through to line 20, and a new line is printed. The outer for loop now returns to its header, where its condition (i < rows) is tested. If this evaluates true, i is incremented and the body of the loop is executed.

In the second iteration of the outer for loop, the inner for loop is started over. Thus, j is reinitialized to 0 and the entire inner loop is run again.

The important idea here is that by using a nested loop, the inner loop is executed for each iteration of the outer loop. Thus the character is printed columns times for each row.

NOTE: As an aside, many C++ programmers use the letters i and j as counting variables. This tradition goes all the way back to FORTRAN, in which the letters i, j, k, l, m, and n were the only legal counting variables. Other programmers prefer to use more descriptive counter variable names, such as Ctrl and Ctr2. Using i and j in for loop headers should not cause much confusion, however.

You will remember that variables are scoped to the block in which they are created. That is, a local variable is visible only within the block in which it is created. It is important to note that counting variables created in the header of a for loop are scoped to the outer block, not the inner block. The implication of this is that if you have two for loops in the same function, you must give them different counter variables, or they may interfere with one another.

In Unit 5, "Functions," you learned how to solve the Fibonacci series problem using recursion. To review briefly, a Fibonacci series starts with 1, 1, 2, 3, and all subsequent numbers are the sum of the previous two:

1,1,2,3,5,8,13,21,34...

The nth Fibonacci number is the sum of the n-1 and the n-2 Fibonacci numbers. The problem solved in unit 5 was finding the value of the nth Fibonacci number. This was done with recursion. Listing 7.15 offers a solution using iteration.

Listing 7.15. Solving the nth Fibonacci numberusing iteration.

Output:

Which position? 4

3 is the 4th Fibonacci number.

Which position? 5

5 is the 5th Fibonacci number.

Which position? 20

6765 is the 20th Fibonacci number.

Which position? 100

3314859971 is the 100th Fibonacci number.

Analysis: Listing 7.15 solves the Fibonacci series using iteration rather than recursion. This approach is faster and uses less memory than the recursive solution. On line 13, the user is asked for the position to check. The function fib() is called, which evaluates the position. If the position is less than 3, the function returns the value 1. Starting with position 3, the function iterates using the following algorithm:

1. Establish the starting position: Fill variable answer with 2, minusTwo with 0 (answer-2), and minusOne with 1 (answer-1). Decrement the position by 3, because the first two numbers are handled by the starting position.

2. For every number, count up the Fibonacci series. This is done by

a. Putting the value currently in minusOne into minusTwo.

b. Putting the value currently in answer into minusOne.

c. Adding minusOne and minusTwo and putting the sum in answer.

d. Decrementing n.

3. When n reaches 0, return the answer.

This is exactly how you would solve this problem with pencil and paper. If you were asked for the fifth Fibonacci number, you would write:

1, 1, 2,

and think, "two more to do." You would then add 2+1 and write 3, and think, "one more to find." Finally you would write 3+2 and the answer would be 5. In effect, you are shifting your attention right one number each time through, and decrementing the number remaining to be found.

Note the condition tested on line 30 (n). This is a C++ idiom, and is exactly equivalent to n != 0. This for loop relies on the fact that when n reaches 0 it will evaluate false, because 0 is false in C++. The for loop header could have been written:

which might have been clearer. However, this idiom is so common in C++ that there is little sense in fighting it.

Compile, link, and run this program, along with the recursive solution offered in unit 5. Try finding position 25 and compare the time it takes each program. Recursion is elegant, but because the function call brings a performance overhead, and because it is called so many times, its performance is noticeably slower than iteration. Microcomputers tend to be optimized for the arithmetic operations, so the iterative solution should be blazingly fast.

Be careful how large a number you enter. fib grows quickly, and long integers will overflow after a while.