Off-by-one errors and infinite loops

Written Explanation

Off-by-one errors

The name comes from being wrong by exactly one. There are three typical forms:

1. Wrong comparison: i < 5 when you meant i <= 5, or the reverse.
2. Wrong start: counting from 0 when you meant 1.
3. The fence-post problem: a fence with 5 sections needs 6 posts, not 5. Counting items and counting gaps between them differ by one.

A formula helps. For a loop with step 1 from a up to b:

Check it: from 3 to 7 inclusive is 5 runs (7 - 3 + 1), not 4. The numbers 7 - 3 = 4 count the gaps, not the values.

The first-and-last test

For any loop, do this before running it:

1. First iteration. What is the first value? Is that right?
2. Last iteration. What is the last value for which the condition is still true? Is that the last value I want?
3. One past the end. What is the first value that makes the condition false? Does the loop stop there?

These three questions catch nearly every off-by-one bug, and they cost ten seconds. It is the same habit as the boundary values you tested in BEG-012-L02.

Infinite loops

A loop is infinite when its condition never becomes false (and no break is reached). The usual causes:

• The update is missing, as in while (i < 5) { print(i); }.
• The update goes the wrong way: for (int i = 10; i > 0; i++) counts up forever (until the value overflows, which BEG-009-L07 showed is not an escape you can rely on).
• The wrong variable is updated: the condition reads a, the body changes b.
• A continue skips the update in a while, as in L04.
• The condition can never be false by design, such as while (true) without a reachable break.

Some infinite loops are written on purpose (a server waits for requests forever), but even those have a way to stop, such as a break or the server being shut down.

The compiler can see some of them

If the compiler can prove that a loop never ends, then code after it can never run, and Java reports an error:

while (true) {
    System.out.println("tick");
}
System.out.println("done");   // unreachable

The compiler message (JDK 21) is:

L06b.java:6: error: unreachable statement
        System.out.println("done");
        ^
1 error

Here the error is a hint: the line after the loop can never run, so there is probably a missing break. Most infinite loops, though, are not caught, because the condition uses variables whose values only the running program knows.

Stopping a runaway program

If your program is stuck, stop it yourself. In a terminal, press Ctrl+C. In an IDE the Run or Debug panel normally has a red Stop button, though its exact place depends on the IDE and its version. If a loop prints endlessly, stop it quickly, since the output can fill the screen or a log file.

Prevention: do not change the counter in the body

Changing the loop variable inside the body is a classic way to create both bugs:

for (int i = 0; i < 10; i++) {
    System.out.print(i + " ");
    i++;                       // second update: i skips every other value
}

This prints 0 2 4 6 8. The loop is not wrong in Java's eyes, but the reader expects ten iterations, and gets five. If you want every second value, put i += 2 in the header.

A debugging routine

When a loop misbehaves:

1. Print the counter and the accumulated values inside the body.
2. Trace the first, the second, and the last iteration on paper.
3. Check the condition at the boundary: < or <=?
4. Check the update line: is it there, is it on the right variable, does it move toward the end?
5. Only then use a debugger to step through (L07).