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A fix can work for an ordinary input and still fail at the boundary because it changes the wrong rule: how far a loop runs, how negative numbers are rounded, or what “close to zero” means. These three illustrative Python examples show the invariant each fix must preserve and the boundary tests that expose the mistake.
Why does adding one to a range cause an index error?
The convincing fix
If a loop seems to miss the last item, it may be tempting to add one to its stop:
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items = ["a", "b", "c"]
for i in range(len(items) + 1):
print(items[i])This prints the three items, then raises IndexError. The extra iteration uses index 3, but the valid indices are 0, 1, and 2.
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range() excludes its stop. For a sequence of length n, range(n) already produces the legal nonnegative indices, from 0 through n - 1. The length is a count, not the last index. The Python tutorial explains the exclusive endpoint and uses range(len(sequence)) to generate sequence indices: The range() function.
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For this example, use:
for i in range(len(items)):
print(items[i])If the goal is simply to process every item, iteration over the values avoids managing indices:
for item in items:
print(item)Test the boundary
Check an empty sequence, a singleton, and a typical longer sequence. The empty case should run zero iterations; the singleton should run once. In an index-based loop, also verify that the first invalid index is never accessed.
Why can changing an index to the previous position select the wrong item?
The convincing fix
Subtracting one can look like the right way to retrieve the previous item:
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previous = items[index - 1]It works for an index greater than zero. At index == 0, however, the expression becomes items[-1]. Python sequence indices below zero count backward from the end, so this selects the last item rather than reporting that there is no previous item.
Decide whether wrapping is intended
If moving backward from the first item is supposed to wrap around, items[-1] may be exactly right. If there is no previous item at the beginning, handle that case before indexing:
if index == 0:
previous = None
else:
previous = items[index - 1]That example assumes None is an appropriate result for the application. Another contract might raise an exception or return a separate status; make the boundary behavior explicit rather than relying on negative indexing by accident.
Indexing and slicing also differ at edges. A slice uses a start-inclusive, stop-exclusive interval, and out-of-range slice endpoints are clamped to the sequence bounds. That does not make an invalid direct index safe. See the Python reference on common sequence operations.
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Test the boundary
For a “previous item” operation, test the first position, an interior position, the last position, an empty sequence, and an index outside the valid range. Specify whether the first position wraps, returns a sentinel, or fails; each is a different contract.
Why can a division fix change the answer for negative values?
The convincing fix
For positive inputs, replacing int(a / b) with a // b can appear to produce the same whole-number result. For negative nonmultiples, the operations differ:
int(-1 / 2) # 0
-1 // 2 # -1Converting a float to int truncates toward zero. Floor division rounds down toward minus infinity. Thus -1 // 2 is -1, not zero. Python documents these distinct behaviors in its numeric types reference.
Choose the operation from the contract
Neither operation is a universal correction for the other. Use truncation when the specification requires discarding the fractional part toward zero; use floor division when it requires the mathematical floor. If the inputs are integers and the task is an exact integer quotient, avoid converting them to floating point without a reason.
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Test the boundary
Include positive and negative nonmultiples, exact multiples, and values on either side of zero. In particular, test a negative fraction whose magnitude is less than one: that is where truncation gives zero while floor gives a negative integer.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.How should boundary tests be chosen?
Start with the invariant the code is meant to enforce, then test the values immediately around where that invariant changes. A useful compact checklist is:
- For sequence loops and indexing: empty, singleton, first valid, last valid, and first invalid positions.
- For arithmetic: positive and negative inputs, zero, exact results, and nonmultiples near zero.
- For each test: assert the specified result or failure, not merely that the code runs without an exception.
These are practical test cases derived from the behaviors above, not a guarantee that any one short test set covers every application. The edge behavior belongs in the function’s contract as well as its tests.
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