on_loops.Rmd

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$\newcommand{L}[1]{\| #1 \|}\newcommand{VL}[1]{\L{ \vec{#1} }}\newcommand{R}[1]{\operatorname{Re}\,(#1)}\newcommand{I}[1]{\operatorname{Im}\, (#1)}$

## “for” and “while”, “break” and “else:”

In Brisk introduction to Python, we saw the use of `break` in `for` and `while`
loops.

`for` and `while` loops that use `break`, can be followed by `else:`
clauses.  The `else:` clause executes only when there was no `break`
during the loop.

In the next fragment, we are doing an inefficient search for prime numbers
from 2 through 30.  In this basic `for` loop, we use the `is_prime`
variable as a flag to indicate whether we have found the current number to be
prime:

```{python}
primes = []
for x in range(2, 30):
    # Assume x is prime until shown otherwise
    is_prime = True
    for p in primes:
        # x exactly divisible by prime -> x not prime
        if (x % p) == 0:
            is_prime = False
            break
    if is_prime:
        primes.append(x)

print("Primes in 2 through 30", primes)
```

Using a flag variable like `is_prime` is a common pattern, so Python allows
us to do the same thing with an extra `else:` clause:

```{python}
primes = []
for x in range(2, 30):
    for p in primes:
        # x exactly divisible by prime -> x not prime
        if (x % p) == 0:
            break
    else:
        # else: block executes if no 'break" in previous loop
        primes.append(x)

print("Primes in 2 through 30", primes)
```

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