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id	title	challengeType	forumTopicId	dashedName
5a23c84252665b21eecc7e06	Cut a rectangle	1	302242	cut-a-rectangle

--description--

A given rectangle is made from m × n squares. If m and n are not both odd, then it is possible to cut a path through the rectangle along the square edges such that the rectangle splits into two connected pieces with the same shape (after rotating one of the pieces by 180°). All such paths for 2 × 2 and 4 × 3 rectangles are shown below.

--instructions--

Write a function that calculates the number of different ways to cut an m × n rectangle.

--hints--

cutRectangle should be a function.

assert(typeof cutRectangle == 'function');

cutRectangle(2, 2) should return a number.

assert(typeof cutRectangle(2, 2) == 'number');

cutRectangle(2, 2) should return 2.

assert.equal(cutRectangle(2, 2), 2);

cutRectangle(4, 3) should return 9.

assert.equal(cutRectangle(4, 3), 9);

cutRectangle(4, 4) should return 22.

assert.equal(cutRectangle(4, 4), 22);

cutRectangle(8, 3) should return 53.

assert.equal(cutRectangle(8, 3), 53);

cutRectangle(7, 4) should return 151.

assert.equal(cutRectangle(7, 4), 151);

--seed--

--seed-contents--

function cutRectangle(w, h) {

}

--solutions--

function cutRectangle(w, h) {
  if (w % 2 == 1 && h % 2 == 1) return;

  var dirs = [[0, -1], [-1, 0], [0, 1], [1, 0]];

  var grid = new Array(h);
  for (var i = 0; i < grid.length; i++) grid[i] = new Array(w);
  var stack = [];

  var half = Math.floor((w * h) / 2);
  var bits = Math.pow(2, half) - 1;
  var result = 0;
  for (; bits > 0; bits -= 2) {
    for (var i = 0; i < half; i++) {
      var r = Math.floor(i / w);
      var c = i % w;
      grid[r][c] = (bits & (1 << i)) != 0 ? 1 : 0;
      grid[h - r - 1][w - c - 1] = 1 - grid[r][c];
    }

    stack.push(0);
    grid[0][0] = 2;
    var count = 1;
    while (stack.length != 0) {
      var pos = stack.pop();
      var r = Math.floor(pos / w);
      var c = pos % w;

      for (var dir of dirs) {
        var nextR = r + dir[0];
        var nextC = c + dir[1];

        if (nextR >= 0 && nextR < h && nextC >= 0 && nextC < w) {
          if (grid[nextR][nextC] == 1) {
            stack.push(nextR * w + nextC);
            grid[nextR][nextC] = 2;
            count++;
          }
        }
      }
    }

    if (count == half) {
      result++;
    }
  }

  return result;
}

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