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curriculum/challenges/english/10-coding-interview-prep/rosetta-code/knights-tour.md

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+---
+id: 5a23c84252665b21eecc7ed5
+title: Knight's tour
+challengeType: 5
+forumTopicId: 302297
+---
+
+## Description
+
+<section id='description'>
+<a href="https://en.wikipedia.org/wiki/Knight%27s_tour">Knight's Tour</a>Problem: You have an empty <code>w</code> * <code>h</code> chessboard, but for a single knight on some square. The knight must perform a sequence of legal moves that result in the knight visiting every square on the chessboard exactly once. Note that it is <i>not</i> a requirement that the tour be "closed"; that is, the knight need not end within a single move of its start position.
+</section>
+
+## Instructions
+
+<section id='instructions'>
+Write a function that takes <code>w</code> and <code>h</code> as parameters and returns the number of initial positions from where it is possible to achieve the task stated above.
+</section>
+
+## Tests
+
+<section id='tests'>
+
+```yml
+tests:
+  - text: <code>knightTour</code> should be a function.
+    testString: assert(typeof knightTour == 'function');
+  - text: <code>knightTour(6, 6)</code> should return a number.
+    testString: assert(typeof knightTour(6, 6) == 'number');
+  - text: <code>knightTour(6, 6)</code> should return <code>35</code>.
+    testString: assert.equal(knightTour(6, 6), 35);
+  - text: <code>knightTour(5, 6)</code> should return <code>20</code>.
+    testString: assert.equal(knightTour(5, 6), 20);
+  - text: <code>knightTour(4, 6)</code> should return <code>10</code>.
+    testString: assert.equal(knightTour(4, 6), 10);
+  - text: <code>knightTour(7, 3)</code> should return <code>4</code>.
+    testString: assert.equal(knightTour(7, 3), 4);
+  - text: <code>knightTour(8, 6)</code> should return <code>47</code>.
+    testString: assert.equal(knightTour(8, 6), 47);
+```
+
+</section>
+
+## Challenge Seed
+
+<section id='challengeSeed'>
+<div id='js-seed'>
+
+```js
+function knightTour(w, h) {
+
+}
+```
+
+</div>
+</section>
+
+## Solution
+
+<section id='solution'>
+
+```js
+function knightTour(w, h) {
+  var b,
+    cnt = 0;
+
+  var dx = [-2, -2, -1, 1, 2, 2, 1, -1];
+  var dy = [-1, 1, 2, 2, 1, -1, -2, -2];
+
+  function init_board() {
+    var i, j, k, x, y;
+    // * b is board; a is board with 2 rows padded at each side
+
+    for (i = 0; i < h; i++) {
+      for (j = 0; j < w; j++) {
+        b[i][j] = 255;
+      }
+    }
+
+    for (i = 0; i < h; i++) {
+      for (j = 0; j < w; j++) {
+        for (k = 0; k < 8; k++) {
+          (x = j + dx[k]), (y = i + dy[k]);
+          if (b[i][j] == 255) b[i][j] = 0;
+          if (x >= 0 && x < w && y >= 0 && y < h) b[i][j]++;
+        }
+      }
+    }
+  }
+
+  function walk_board(x, y) {
+    var i, nx, ny, least;
+    var steps = 0;
+    // printf(E"H"E"J"E"%d;%dH"E"32m[]"E"m", y + 1, 1 + 2 * x);
+
+    while (1) {
+      // * occupy cell
+      b[y][x] = 255;
+
+      // * reduce all neighbors' neighbor count
+      for (i = 0; i < 8; i++)
+        if (y + dy[i] >= 0 && x + dx[i] >= 0 && y + dy[i] < h && x + dx[i] < w)
+          b[y + dy[i]][x + dx[i]]--;
+
+      // find neighbor with lowest neighbor count
+      least = 255;
+      for (i = 0; i < 8; i++) {
+        if (y + dy[i] >= 0 && x + dx[i] >= 0 && y + dy[i] < h && x + dx[i] < w)
+          if (b[y + dy[i]][x + dx[i]] < least) {
+            nx = x + dx[i];
+            ny = y + dy[i];
+            least = b[ny][nx];
+          }
+      }
+
+      if (least > 7) {
+        return steps == w * h - 1;
+      }
+
+      steps++;
+      (x = nx), (y = ny);
+    }
+  }
+
+  function solve(x, y) {
+    b = new Array(h);
+    for (var i = 0; i < h; i++) b[i] = new Array(w);
+
+    init_board();
+    if (walk_board(x, y)) {
+      cnt++;
+    }
+  }
+
+  for (var i = 0; i < h; i++) {
+    for (var j = 0; j < w; j++) {
+      solve(j, i);
+    }
+  }
+
+  return cnt;
+}
+```
+
+</section>