142 lines
3.9 KiB
Markdown
142 lines
3.9 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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---
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## Description
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<section id='description'>
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<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.
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</section>
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## Instructions
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<section id='instructions'>
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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.
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</section>
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## Tests
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<section id='tests'>
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``` yml
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tests:
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- text: <code>knightTour</code> should be a function.
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testString: assert(typeof knightTour == 'function', '<code>knightTour</code> should be a function.');
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- text: <code>knightTour(6, 6)</code> should return a number.
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testString: assert(typeof knightTour(6, 6) == 'number', '<code>knightTour(6, 6)</code> should return a number.');
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- text: <code>knightTour(6, 6)</code> should return <code>35</code>.
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testString: assert.equal(knightTour(6, 6), 35, '<code>knightTour(6, 6)</code> should return <code>35</code>.');
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- text: <code>knightTour(5, 6)</code> should return <code>20</code>.
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testString: assert.equal(knightTour(5, 6), 20, '<code>knightTour(5, 6)</code> should return <code>20</code>.');
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- text: <code>knightTour(4, 6)</code> should return <code>10</code>.
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testString: assert.equal(knightTour(4, 6), 10, '<code>knightTour(4, 6)</code> should return <code>10</code>.');
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- text: <code>knightTour(7, 3)</code> should return <code>4</code>.
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testString: assert.equal(knightTour(7, 3), 4, '<code>knightTour(7, 3)</code> should return <code>4</code>.');
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- text: <code>knightTour(8, 6)</code> should return <code>47</code>.
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testString: assert.equal(knightTour(8, 6), 47, '<code>knightTour(8, 6)</code> should return <code>47</code>.');
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function knightTour(w, h) {
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// Good luck!
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}
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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function knightTour (w, h) {
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var b, 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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{
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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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{
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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++)
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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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</section>
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