feat(hanoi): create exercise

20_hanoi/README.md

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+# Exercise 20 - hanoi
+
+Good job, you have come a very long way. You should be proud of yourself for making it this far! At this point, you hopefully feel comfortable with recursion, and so, this **final recursive exercise** should give you a proper challenge and take your abilities to the *next* level.
+
+Tower of Hanoi is a classic challenge in which we have 3 towers. Tower 2 and tower 3 are empty. Tower 1 has `n` disks. The goal is to move all disks from tower 1 to tower 3 so that they are in the exact same order. For instance:
+
+```javascript
+[[3, 2, 1], [], []] 
+
+// ...
+
+[[], [], [3, 2, 1]]
+```
+
+The rules are as follows:
+- Each disk has a length. For abstraction purposes, we will imagine each disk as an integer with that disk's length.
+- We can only move 1 disk at a time between any of the towers
+- The towers are modelled as stacks. We can move disks from the top of one stack to the top of another stack with the `Array.prototype.pop` and `Array.prototype.push` methods.
+- **Disks can only be placed on top of disks that are smaller**. For instance, we cannot have the tower `[3, 4]` but `[4, 3]` is fine.
+
+Your task is to create a function, `hanoi(n)`, that when given the number of disks in the starting tower (`n`), will return an array containing the steps that have to be taken in order to get from the initial state to the final state. Each step will be a string in the form:
+
+```javascript
+`Move disc ${discNumber} from tower ${fromTower} to tower ${toTower}`
+```
+
+The function **must** return a solution in the minimum number of moves. i.e. there will be no duplicates in the solution array returned.
+
+For example, here is the expected output of `hanoi(3)`:
+
+```javascript
+[
+  "Move disc 1 from tower 1 to tower 3",
+  "Move disc 2 from tower 1 to tower 2",
+  "Move disc 1 from tower 3 to tower 2",
+  "Move disc 3 from tower 1 to tower 3",
+  "Move disc 1 from tower 2 to tower 1",
+  "Move disc 2 from tower 2 to tower 3",
+  "Move disc 1 from tower 1 to tower 3",
+]
+```

20_hanoi/hanoi.js

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+const hanoi = function() {
+
+};
+
+// Do not edit below this line
+module.exports = hanoi;

20_hanoi/hanoi.spec.js

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+const hanoi = require("./hanoi");
+
+describe("hanoi", () => {
+  test("hanoi(1) should solve the puzzle in 1 move", () => {
+    const result = hanoi(1);
+    expect(result).toEqual(["Move disc 1 from tower 1 to tower 3"]);
+  });
+
+  test.skip("hanoi(2) should solve the puzzle in 3 moves", () => {
+    const result = hanoi(2);
+    expect(result).toEqual([
+      "Move disc 1 from tower 1 to tower 2",
+      "Move disc 2 from tower 1 to tower 3",
+      "Move disc 1 from tower 2 to tower 3",
+    ]);
+  });
+
+  test.skip("hanoi(3) should solve the puzzle in 7 moves", () => {
+    const result = hanoi(3);
+    expect(result).toEqual([
+      "Move disc 1 from tower 1 to tower 3",
+      "Move disc 2 from tower 1 to tower 2",
+      "Move disc 1 from tower 3 to tower 2",
+      "Move disc 3 from tower 1 to tower 3",
+      "Move disc 1 from tower 2 to tower 1",
+      "Move disc 2 from tower 2 to tower 3",
+      "Move disc 1 from tower 1 to tower 3",
+    ]);
+  });
+
+  test.skip("hanoi(4) should solve the puzzle in 15 moves", () => {
+    const result = hanoi(4);
+    expect(result).toEqual([
+      "Move disc 1 from tower 1 to tower 2",
+      "Move disc 2 from tower 1 to tower 3",
+      "Move disc 1 from tower 2 to tower 3",
+      "Move disc 3 from tower 1 to tower 2",
+      "Move disc 1 from tower 3 to tower 1",
+      "Move disc 2 from tower 3 to tower 2",
+      "Move disc 1 from tower 1 to tower 2",
+      "Move disc 4 from tower 1 to tower 3",
+      "Move disc 1 from tower 2 to tower 3",
+      "Move disc 2 from tower 2 to tower 1",
+      "Move disc 1 from tower 3 to tower 1",
+      "Move disc 3 from tower 2 to tower 3",
+      "Move disc 1 from tower 1 to tower 2",
+      "Move disc 2 from tower 1 to tower 3",
+      "Move disc 1 from tower 2 to tower 3",
+    ]);
+  });
+});
+

20_hanoi/solution/hanoi-solution.js

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+const hanoi = function (
+  n,
+  fromTower = 0,
+  storageTower = 1,
+  toTower = 2,
+  steps = [],
+) {
+  if (n <= 0) {
+    return steps;
+  }
+
+  hanoi(n - 1, fromTower, toTower, storageTower, steps);
+
+  steps.push(
+    `Move disc ${n} from tower ${fromTower + 1} to tower ${toTower + 1}`,
+  );
+
+  hanoi(n - 1, storageTower, fromTower, toTower, steps);
+
+  return steps;
+};
+
+// Do not edit below this line
+module.exports = hanoi;

20_hanoi/solution/hanoi-solution.spec.js

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+const hanoi = require("./hanoi-solution");
+
+describe("hanoi", () => {
+  test("hanoi(1) should solve the puzzle in 1 move", () => {
+    const result = hanoi(1);
+    expect(result).toEqual(["Move disc 1 from tower 1 to tower 3"]);
+  });
+
+  test("hanoi(2) should solve the puzzle in 3 moves", () => {
+    const result = hanoi(2);
+    expect(result).toEqual([
+      "Move disc 1 from tower 1 to tower 2",
+      "Move disc 2 from tower 1 to tower 3",
+      "Move disc 1 from tower 2 to tower 3",
+    ]);
+  });
+
+  test("hanoi(3) should solve the puzzle in 7 moves", () => {
+    const result = hanoi(3);
+    expect(result).toEqual([
+      "Move disc 1 from tower 1 to tower 3",
+      "Move disc 2 from tower 1 to tower 2",
+      "Move disc 1 from tower 3 to tower 2",
+      "Move disc 3 from tower 1 to tower 3",
+      "Move disc 1 from tower 2 to tower 1",
+      "Move disc 2 from tower 2 to tower 3",
+      "Move disc 1 from tower 1 to tower 3",
+    ]);
+  });
+
+  test("hanoi(4) should solve the puzzle in 15 moves", () => {
+    const result = hanoi(4);
+    expect(result).toEqual([
+      "Move disc 1 from tower 1 to tower 2",
+      "Move disc 2 from tower 1 to tower 3",
+      "Move disc 1 from tower 2 to tower 3",
+      "Move disc 3 from tower 1 to tower 2",
+      "Move disc 1 from tower 3 to tower 1",
+      "Move disc 2 from tower 3 to tower 2",
+      "Move disc 1 from tower 1 to tower 2",
+      "Move disc 4 from tower 1 to tower 3",
+      "Move disc 1 from tower 2 to tower 3",
+      "Move disc 2 from tower 2 to tower 1",
+      "Move disc 1 from tower 3 to tower 1",
+      "Move disc 3 from tower 2 to tower 3",
+      "Move disc 1 from tower 1 to tower 2",
+      "Move disc 2 from tower 1 to tower 3",
+      "Move disc 1 from tower 2 to tower 3",
+    ]);
+  });
+});