【题解】【直方图】【堆栈】【Codility】StoneWall

Cover "Manhattan skyline" using the minimum number of rectangles.

You
are going to build a stone wall. The wall should be straight and N meters long,
and its thickness should be constant; however, it should have different heights
in different places. The height of the wall is specified by a zero-indexed array
H of N positive integers. H[I] is the height of the wall from I to I+1 meters to
the right of its left end. In particular, H[0] is the height of the wall‘s left
end and H[N?1] is the height of the wall‘s right end.

The
wall should be built of cuboid stone blocks (that is, all sides of such blocks
are rectangular). Your task is to compute the minimum number of blocks needed to
build the wall.

For
example, given array H containing N = 9 integers:

H[0] = 8 H[1] = 8 H[2] = 5 H[3] = 7 H[4] = 9 H[5] = 8 H[6] = 7 H[7] = 4 H[8] = 8

the
function should return 7. The figure shows one possible arrangement of seven
blocks.

src="https://img.php1.cn/3cd4a/1eebe/cd5/ff61bfdd3c0af92e.webp">

Assume
that:

• N is an integer within the
  range [ class="number">1.. class="number">100,000];


• each element of array H is
  an integer within the range [ class="number">1.. class="number">1,000,000,000].

Complexity:

• expected worst-case time
  complexity is O(N);


• expected worst-case space
  complexity is O(N), beyond input storage (not counting the storage required
  for input arguments).

Elements
of input arrays can be modified.

思路：

其实Codility的叙述风格真的太啰嗦了，他们Solution还写得比较有趣，其实就是用的下图这种贪心算法，遍历数组遇到比栈顶小的就pop，横着切一刀分割出来一个矩形。

注意边界条件的先后顺序。

title="NewImage.png" border="0" alt="NewImage" src="https://img8.php1.cn/3cdc5/fd8c/807/b6d85695340f9b12.jpeg"
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