Fix the Code: Un-Mutating a List

Your friend is trying to write a function to accomplish the following transformations:

x = [3, 3, 3, 3, 3, 3, 3]

// Each time x is called, the following results are shown:

change(x, 0)  // [3, 3, 3, 3, 3, 3, 3]
change(x, 1)  // [3, 2, 2, 2, 2, 2, 3]
change(x, 2)  // [3, 2, 1, 1, 1, 2, 3]
change(x, 3)  // [3, 2, 1, 0, 1, 2, 3]

Note: The change() function should not mutate the original list. After each call to the function, the original x should still equal [3, 3, 3, 3, 3, 3, 3].

She comes up with the following code:

def change(x, times):
  for i in range(len(x)):
    j = 1
    while j <= times:
      if i >= j and i < len(x)-j:
        x[i] -= 1
      j += 1
  return x

Oops! The code appears to mutate the original list. Fix this incorrect code so that the function no longer mutates the original list.

See below:

Examples

x = [3, 3, 3, 3, 3, 3, 3]

// What we want:
change(x, 2) => [3, 2, 1, 1, 1, 2, 3]

change(x, 2) => [3, 2, 1, 1, 1, 2, 3]

// What we get:
change(x, 2) => [3, 2, 1, 1, 1, 2, 3]  // Good so far...

change(x, 2) => [3, 1, -1, -1, -1, 1, 3] // List is mutated :(

Notes

• If this is confusing, copy and paste the incorrect code in a REPL environment and play around with the code to understand what the function is doing.
• Hint: Try to make a copy of the input list.
• If this looks familiar, it is part of a solution for the Concentric Rug problem.