View source for Code:for patterns

Here are some example codes that write essentially the same instruction over and over.
Let's see how to abstract these patterns out using variables.  Try and work the problems before flipping over to the solutions section.

== Problems ==

<source lang="python">
# Replace text in a formula.
#          A    B    C
vals = ["1", "", "2", # 1
        "",  "", "3", # 2
        "",  "", "" ] # 3
out = "A1 + C1 * C2"
out = out.replace("A1", vals[0])
out = out.replace("A2", vals[3])
out = out.replace("A3", vals[6])

out = out.replace("B1", vals[1])
out = out.replace("B2", vals[4])
out = out.replace("B3", vals[7])

out = out.replace("C1", vals[2])
out = out.replace("C2", vals[5])
out = out.replace("C3", vals[8])

# Increment items in a list.
fed[5] = fed[5] + 1
fed[4] = fed[4] + 1
fed[3] = fed[3] + 1

# Append a line to a string.
if n >= 1:
    out = out + "%f %f %f\n"%(a[0][0], a[0][1], a[0][2])
if n >= 2:
    out = out + "%f %f %f\n"%(a[1][0], a[1][1], a[1][2])
if n >= 3:
    out = out + "%f %f %f\n"%(a[2][0], a[2][1], a[2][2])
if n >= 4:
    out = out + "%f %f %f\n"%(a[3][0], a[3][1], a[3][2])

# Iterate the linear congruential random number generator.
i = len(x)-1
x.append(x[i]*61 % 900)
i = len(x)-1
x.append(x[i]*61 % 900)
i = len(x)-1
x.append(x[i]*61 % 900)
i = len(x)-1
x.append(x[i]*61 % 900)
i = len(x)-1
x.append(x[i]*61 % 900)
</source>

First, assume the loop control variable is "i", and try and write each one of these as a loop body that uses the variable "i" to make the pattern.  Next, add the "for i in (...):" syntax on top by figuring out how many times / what values of "i" the loop should run.

== Solutions ==

<source lang="python">
# Replace text in a formula.
#          A    B    C
def substitute_str(fmt, vals): # substitute_str : str -> [str] -> str
    out = fmt
    n = 0
    for i in ["A1", "B1", "C1", "A2", "B2", "C2", "A3", "B3", "C3"]:
        out = out.replace(i, vals[n])
        n = n + 1
    return out
print substitute_str("A1 + C1*C2", vals)

# Increment items in a list.
def sow_list_6(fed, n): # sow_list : [int] -> int -> [int]
    out = fed[:] # copy all elements of fed by slicing all of them
    for i in range(n):
        out[5-i] = out[5-i] + 1
    return out

# Increment items in a list (advanced).
def sow_list(ABC, fed, start, n): # [int] -> [int] -> int -> int -> ([int], [int], int)
    ABC = ABC[:] # copy ABC
    fed = fed[:] # copy fed
    for i in range(n):
        pos = (start + i) % 12 # use mod to get an index in the circular
                                        # range 0, 1, 2, 3, ..., 10, 11, 0, 1, 2
        if pos < 6: # positions 0, 1, ..., 5 are ABC
            ABC[pos] = ABC[pos] + 1
        else: # positions 6, 7, ..., 11 map to fed 5, 4, ..., 0
            fed[5-(pos-6)] = fed[5-(pos-6)] + 1
    return ABC, fed, pos

# Append a line to a string.
def print_atoms(a): # print_atoms : [[float]] -> str
    out = "Atomic coordinates (in Angstrom)\n"
    for i in range(len(a)): # loop over all items in a
        if len(a) > i: # This test is no longer needed.  Do you see why?
            out = out + "%f %f %f\n"%(a[i][0], a[i][1], a[i][2])
    return out

# Iterate the linear congruential "random" number generator.
x = [1] # start with a `seed' value
for i in range(5): # generate 5 numbers
    x.append(x[i]*62 % 900)
</source>