Josephus Problem - Off By One

Affected page https://www.freecodecamp.org/learn/coding-interview-prep/rosetta-code/josephus-problem

Your code

function josephus(init, kill) {
  // Setup
  let currPrisoner = 0;
  const prisoners = Array(init).fill(true);
  // Execute prisoners
  console.log("Kill Sequence:");
  for (let numAlive = init; numAlive > 1; numAlive--) {
    // Find next prisoner
    for (let numSkip = kill; numSkip > 0; numSkip--) {
      do {
        currPrisoner = (currPrisoner + 1) % init;
      } while (!prisoners[currPrisoner]);
    }
    // Execute prisoner
    console.log(currPrisoner);
    prisoners[currPrisoner] = false;
  }
  // Return last man standing
  console.log("Last Man Standing:");
  console.log(prisoners.indexOf(true));
  return prisoners.indexOf(true);
}

josephus(5, 2);

Expected behavior The code that passes the test suite (given above) provides different output than the traditional description of the problem. I think the test suite has an ‘off by one’ error in initializing the starting position.

Current output with solution that passes test suite:

Kill Sequence:
2
4
1
0
Last Man Standing:
3

Expected output per problem description:

Kill Sequence:
1
3
0
4
Last Man Standing:
2

Relevant portion of problem description:

For example, if there are n=5 prisoners and k=2, the order the prisoners are killed in (let’s call it the “killing sequence”) will be 1, 3, 0, and 4, and the survivor will be 2.

See also discussion here: https://forum.freecodecamp.org/t/solution-to-rosetta-code-challenge-josephus-problem/460203

Proposed Fix Change test suite to

josephus(30,3) should return 28

josephus(30,5) should return 2

josephus(20,2) should return 8

josephus(17,6) should return 1

josephus(29,4) should return 1

Bug reported by jsdisco on the forum.

[jeremylt]

I agree that the original solution is pretty convoluted.

[Sembauke]

@alirezaghey, You can always open a PR. After that, we can give feedback and suggest changes if needed.