155 lines
3.2 KiB
Markdown
155 lines
3.2 KiB
Markdown
---
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id: 5a23c84252665b21eecc7ed5
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title: Knight's tour
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challengeType: 5
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forumTopicId: 302297
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dashedName: knights-tour
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---
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# --description--
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[Knight's Tour](https://en.wikipedia.org/wiki/Knight%27s_tour)Problem: You have an empty `w` \* `h` 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 *not* a requirement that the tour be "closed"; that is, the knight need not end within a single move of its start position.
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# --instructions--
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Write a function that takes `w` and `h` as parameters and returns the number of initial positions from where it is possible to achieve the task stated above.
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# --hints--
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`knightTour` should be a function.
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```js
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assert(typeof knightTour == 'function');
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```
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`knightTour(6, 6)` should return a number.
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```js
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assert(typeof knightTour(6, 6) == 'number');
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```
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`knightTour(6, 6)` should return `35`.
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```js
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assert.equal(knightTour(6, 6), 35);
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```
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`knightTour(5, 6)` should return `20`.
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```js
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assert.equal(knightTour(5, 6), 20);
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```
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`knightTour(4, 6)` should return `10`.
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```js
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assert.equal(knightTour(4, 6), 10);
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```
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`knightTour(7, 3)` should return `4`.
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```js
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assert.equal(knightTour(7, 3), 4);
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```
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`knightTour(8, 6)` should return `47`.
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```js
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assert.equal(knightTour(8, 6), 47);
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```
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# --seed--
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## --seed-contents--
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```js
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function knightTour(w, h) {
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}
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```
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# --solutions--
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```js
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function knightTour(w, h) {
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var b,
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cnt = 0;
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var dx = [-2, -2, -1, 1, 2, 2, 1, -1];
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var dy = [-1, 1, 2, 2, 1, -1, -2, -2];
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function init_board() {
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var i, j, k, x, y;
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// * b is board; a is board with 2 rows padded at each side
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for (i = 0; i < h; i++) {
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for (j = 0; j < w; j++) {
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b[i][j] = 255;
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}
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}
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for (i = 0; i < h; i++) {
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for (j = 0; j < w; j++) {
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for (k = 0; k < 8; k++) {
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(x = j + dx[k]), (y = i + dy[k]);
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if (b[i][j] == 255) b[i][j] = 0;
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if (x >= 0 && x < w && y >= 0 && y < h) b[i][j]++;
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}
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}
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}
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}
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function walk_board(x, y) {
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var i, nx, ny, least;
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var steps = 0;
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// printf(E"H"E"J"E"%d;%dH"E"32m[]"E"m", y + 1, 1 + 2 * x);
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while (1) {
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// * occupy cell
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b[y][x] = 255;
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// * reduce all neighbors' neighbor count
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for (i = 0; i < 8; i++)
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if (y + dy[i] >= 0 && x + dx[i] >= 0 && y + dy[i] < h && x + dx[i] < w)
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b[y + dy[i]][x + dx[i]]--;
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// find neighbor with lowest neighbor count
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least = 255;
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for (i = 0; i < 8; i++) {
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if (y + dy[i] >= 0 && x + dx[i] >= 0 && y + dy[i] < h && x + dx[i] < w)
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if (b[y + dy[i]][x + dx[i]] < least) {
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nx = x + dx[i];
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ny = y + dy[i];
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least = b[ny][nx];
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}
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}
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if (least > 7) {
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return steps == w * h - 1;
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}
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steps++;
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(x = nx), (y = ny);
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}
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}
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function solve(x, y) {
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b = new Array(h);
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for (var i = 0; i < h; i++) b[i] = new Array(w);
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init_board();
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if (walk_board(x, y)) {
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cnt++;
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}
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}
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for (var i = 0; i < h; i++) {
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for (var j = 0; j < w; j++) {
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solve(j, i);
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}
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}
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return cnt;
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}
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```
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