## Problem Statement | |||||||||||||

Class name: Space3d Method name: getDensityVolume Parameters: String[], int Returns: long Dr. Bob is a research physicist who deals with matter and anti-matter gases. Given the physical coordinates of rectangular prism volumes of gases, he needs to know what the total volume is that has a certain density. Densities are cumulative, in this sense (i.e, if two identical volumes have densities of 1 each, then that volume has a total density of 2). The "matter" volumes would have a positive density, and the "anti-matter" volumes would have a negative density. A density of zero indicates an empty region. The String[] will contain elements defining each volume of gas by two x, two y, two z coordinates, and a density. For instance, parameters of "(2,0,1),(5,5,5),1", "(3,3,3),(4,4,4),-1" means that the 3-dimensional region bounded on two opposite corners by the points (2,0,1) and (5,5,5) has a density of 1, and the region bounded by (3,3,3) and (4,4,4) has a density of -1. So, added together, the region (3,3,3)-(4,4,4) has density 0. Note that quotes are included only for clarity, and will not be in the Strings in the String[]. Given these Strings and a density to search for, determine the total volume with exactly this density. The method signature is: public long getVolume(String[] al, int density); In the String[], x, y, and z coordinates are between -1000 and 1000, inclusive. In the String[], Density is between -10 and 10, inclusive. The density to find is bounded by -150 <= x <= 150, x != 0. The String[] will contain between 1 and 15 elements, inclusive. Note: -Any input that defines a gas with no volume can be ignored (such as "(0,0,0),(1,1,0),1"). -Any input that defines a gas with no density can be ignored (such as "(0,0,0),(1,1,1),0"). Examples: -If the String[] contains "(0,0,0),(2,2,2),1" "(1,1,1),(3,3,3),1", and density to search for is 1, the volume with density 1 is the two cubes minus their intersection = 2*2*2 + 2*2*2 - 1 - 1 = 14. -If the String[] contains "(0,0,0),(5,5,5),1", "(1,1,1),(4,4,4),-2", "(2,2,2),(3,3,3),2", and the density to search for is 1, the regions with density 1 are the unit-thick cubic shell from (0,0,0)-(5,5,5), and the region (2,2,2)-(3,3,3), for a total of 99. -If the String[] contains: "(-1000,-1000,-1000),(1000,1000,-999),1" "(-1000,-1000,-1000),(-999,1000,1000),1" "(-1000,-1000,-1000),(1000,-999,1000),1" "(-1000,1000,-1000),(1000,999,1000),1" "(-1000,-1000,1000),(1000,1000,999),1" "(1000,-1000,-1000),(999,1000,1000),1" with a density to search for of 1, the resulting area is a 2000x2000x2000 cube one unit thick, but the edges and corners have densities of 2 and 3 respectively, so the returned volume is 23952024. | |||||||||||||

## Definition | |||||||||||||

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