Python "why" questions
Lie Ryan
lie.1296 at gmail.com
Fri Aug 13 20:43:50 CEST 2010
Sorry the message gets cuts off by an accidental press of send button.
On 08/14/10 04:31, Lie Ryan wrote:
> On 08/10/10 06:36, Bartc wrote:
>> And if the context is Python, I doubt whether the choice of 0-based over a
>> 1-based makes that much difference in execution speed.
>
> And I doubt anyone cares about execution speed when deciding whether to
> use 1-based or 0-based array. The reason why you want to choose the
> alternative that use less conversion to the other system is to simplify
> the source code.
>
> Many common mathematical/physics/economics formulas are expressed much
> simply if we use 0-based counting:
>
> * arithmetic series:
> - 1-based: s(n) = a + (n - 1) * d
> - 0-based: s(n) = a + n * d
> * geometric series:
> - 1-based: g(n) = a * r**(n - 1)
> - 0-based: g(n) = a * r**n
> * equation of motion:
> - 1-based: x(t) = a + 1/2 * a * (t - 1)**2
> - 0-based: x(t) = a + 1/2 * a * t**2
> * exponential growth/decay:
> - 1-based: d(t) = a * e**(k * (t - 1))
> - 0-based: d(t) = a * e**(k*t)
>
>
> In fact, most textbooks would already uses 0-based formula for some of
> these formulas already. Most physics and economic textbooks would show
> the base 0 variation of the formula, and refers to t=0 as the point in
> time where the "event" started.
>
> I often used this model of thinking for 0-based array indices (and
> negative indices):
>
> -7 -6 -5 -4 -3 -2 -1
> +---+---+---+---+---+---+---+
> | c | h | a | r | l | i | e |
> +---+---+---+---+---+---+---+
> 0 1 2 3 4 5 6 (7)
>
> instead of:
>
so to repeat, I often use this model of thinking:
-7 -6 -5 -4 -3 -2 -1
+---+---+---+---+---+---+---+
| c | h | a | r | l | i | e |
+---+---+---+---+---+---+---+
0 1 2 3 4 5 6 (7)
instead of:
-7 -6 -5 -4 -3 -2 -1
+---+---+---+---+---+---+---+
| c | h | a | r | l | i | e |
+---+---+---+---+---+---+---+
0 1 2 3 4 5 6
that is, the indices refers to the "gap" between the array entries. The
"gap index" model highlights the naturalness of using 0-based array,
negative indices, array slicing, and half-open.
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