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Hello Python

Simulate Fisher-Yates Shuffling

Practice ExerciseIntermediateMediumArrayFisher-Yates Shuffle

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Problem

Implement fisher_yates(values, choices). Return a shuffled copy. For i from n-1 down to 1, choices[n-1-i] is a valid j in [0,i]; swap indexes i and j.

Starter code

def fisher_yates(values, choices):
    pass
Test cases

deterministic-swaps

{
  "args": [
    [
      1,
      2,
      3,
      4
    ],
    [
      1,
      0,
      1
    ]
  ]
}

Expected: [3,4,1,2]

self-swaps

{
  "args": [
    [
      1,
      2,
      3
    ],
    [
      2,
      1
    ]
  ]
}

Expected: [1,2,3]

Wizard outline
  1. Step 1: Protect the caller input

    Create the output list without mutating the supplied sequence. The exercise contract returns a shuffled copy.

  2. Step 2: Place the final element

    Use one supplied choice to swap the last position. Fisher-Yates fixes one tail position per iteration.

  3. Step 3: Place every remaining tail position

    Walk backward and consume one choice per swap. After placing index i, later positions never need to move again.

Footguns and prerequisites
  • Choosing j from the full array at every step biases the permutation.
  • Mutating values violates the returned-copy contract.
  • functions
  • lists and tuples
  • control flow
Reviewed references
Recommended approach and implementation

Copy the input and perform the supplied Fisher-Yates swap for every shrinking suffix boundary.

Why it works: At boundary i, the supplied choice selects one of exactly i+1 remaining candidates for position i. The swap fixes that position and never revisits it, yielding the specified permutation without mutating input.

def fisher_yates(values, choices):
    shuffled = list(values)
    for offset, index in enumerate(range(len(shuffled) - 1, 0, -1)):
        choice = choices[offset]
        shuffled[index], shuffled[choice] = shuffled[choice], shuffled[index]
    return shuffled