[CERC2017]Lunar Landscape

题意翻译

(具体字母格式懒得操作) 月球的景观 题目描述 一个卫星正在为探测车在月球上寻找一个合适的降落区。降落区被看做在平面直角坐标系中的一个方形区域。 这颗卫星已经照了n张照片,每张照片都涵盖了月球表面的一块正方形区域。经过对相机的精细校准,可以保证所有照片涵盖的区域都和坐标对齐——正方形四个角的坐标都为整数。由于卫星的轨道一直在变化,所以照片有两种形式: ·A类照片的边缘和坐标轴平行。对于这样的照片,题目将会给出它中心的坐标(x,y)和它的边长a(a为偶数)。 ·B类照片的边缘和坐标轴呈45°角。对于这样的照片,题目将会给出它中心的坐标(x,y)和它对角线的长度d(d为偶数)。 求出卫星图片拍摄到平面的总大小。 输入输出格式 输入格式: 第一行有一个整数n(1≤n≤200000)表示照片的数量。接下来n行中第j行的格式是"A xj yj aj"或"B xj yj dj" ,分别表示这张照片的类型是A或B。 xj和yj是这张图片中心的坐标(1000≤xj,yj≤1000)。aj和dj为偶数(2≤aj,dj≤1000),分别表示正方形的边长和对角线长度。 输出格式: 输出平面总的大小,保留两位小数。答案必须和标准答案严格相等(精度问题零容忍↖(^ω^)↗)。

题目描述

A satellite is surveying a possible rover landing area on the moon. The landing area is modeled as a square grid embedded in the standard coordinate system. The satellite has taken $n$ photos, each capturing a square area of the surface. Careful camera calibration has ensured that all photos are aligned with the grid — all four vertices have integer coordinates. Due to the satellite’s changing orbit there are two types of photos: - Photos of type ``A`` have sides that are parallel to coordinate axes. Such a photo is specified by giving the integer coordinates $(x, y)$ of the square’s middle point and the length of its side $a$ — always an even integer. - Photos of type ``B`` have sides at a $45^{\circ}$ angle to the coordinate axes. Such a photo is specified by giving the integer coordinates $(x, y)$ of the square’s middle point and the length of its diagonal $d$ — always an even integer. Find the total surface area captured in the satellite photos.

输入输出格式

输入格式


The first line contains an integer $n(1 \le n \le 200 000)$ — the number of photos. The $j-th$ of the following $n$ lines is either of the form “$A \ x_j \ y_j \ a_j$” or “$B \ x_j \ y_j \ d_j$” representing a photo of type ``A`` or ``B``,respectively. The $x_j$ and $y_j$ are the integer coordinates of the middle point of the photo $(-1 000 \le x_j, y_j \le 1 000)$. The $a_j$ and $d_j$ are even integers $(2 \le a_j, d_j \le 1 000)$ — the side length and the diagonal length, respectively.

输出格式


Output a number with exactly two digits after the decimal point — the total area of the surface. The answer has to exactly correspond to the judge’s solution (no rounding errors are tolerated).

输入输出样例

输入样例 #1

2
A 0 0 2
B 1 0 2

输出样例 #1

5.00

输入样例 #2

8
A -7 10 4
B 3 10 8
A -6 6 6
A -2 5 8
B 3 -1 8
B -7 -4 8
A 3 9 2
B 8 6 6

输出样例 #2

205.50