S1. Crazy Fencing
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You need to paint a wooden fence between your house and your neighbour’s
house. You want to determine the area of the fence, in order to
determine how much paint you will use.
However, the fence is made out of \(N\) non-uniform pieces of wood, and your
neighbour believes that they have an artistic flair. In particular, the
pieces of wood may be of various widths. The bottom of each piece of
wood will be horizontal, both sides will be vertical, but its top may be
cut on an angle. Two such pieces of wood are shown below:
Thankfully, the fence has been constructed so that adjacent pieces of
wood have the same height on the sides where they touch, which makes the
fence more visually appealing.
\(N \leq 10\,000\)
\((1 \le h_i \le 100, 1 \le i \le N+1)\)
\((1 \le w_i \le 100, 1 \le i \le N)\)
The first line of the input will be a positive integer \(N\), where \(N \leq 10\,000\).
The second line of input will contain \(N+1\) space-separated integers \(h_1,\ldots, h_{N+1}\) \((1 \le h_i \le 100, 1 \le i \le N+1)\) describing the left and
right heights of each piece of wood. Specifically, the left height of
the \(i\)th piece of wood is
\(h_i\) and the right height of the
\(i\)th piece of wood is
\(h_{i+1}\).
The third line of input will contain \(N\) space-separated integers \(w_i\) \((1 \le w_i \le 100, 1 \le i \le N)\) describing the width of the \(i\)th piece of wood.
Output the total area of the fence.
3
2 3 6 2
4 1 118.5The fence looks like the following:
When looking from left to right, the individual areas of the pieces
of wood are \(10 = 4\cdot (2+3)/2\),
\(4.5 = 1\cdot(3+6)/2\), and \(4 = 1 \cdot (6+2)/2\), for a total area of
18.5.
4
6 4 9 7 3
5 2 4 175The fence looks like the following:
When looking from left to right, the individual areas of the pieces
of wood are 25, 13, 32, and 5, for a total area of 75.
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S1. Crazy Fencing
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S1. Crazy Fencing