Area of Polycubes 设计的问题

Question

Problem Description
A polycube is a solid made by gluing together unit cubes (one unit on each edge) on one or more faces. The figure in the lower-left is not a polycube because some cubes are attached along an edge.

For this problem, the polycube will be formed from unit cubes centered at integer lattice points in 3-space. The polycube will be built up one cube at a time, starting with a cube centered at (0,0,0). At each step of the process (after the first cube), the next cube must have a face in common with a cube previously included and not be the same as a block previously included. For example, a 1-by-1-by-5 block (as shown above in the upper-left polycube) could be built up as:

(0,0,0) (0,0,1) (0,0,2) (0,0,3) (0,0,4)

and a 2-by-2-by-2 cube (upper-right figure) could be built as:

(0,0,0) (0,0,1) (0,1,1) (0,1, 0) (1,0,0) (1,0,1) (1,1,1) (1,1, 0)

Since the surface of the polycube is made up of unit squares, its area is an integer.

Write a program which takes as input a sequence of integer lattice points in 3-space and determines whether is correctly forms a polycube and, if so, what the surface area of the polycube is.

Input
The first line of input contains a single integer N, (1 ≤ N ≤ 1000) which is the number of data sets that follow. Each data set consists of multiple lines of input. The first line contains the number of points P, (1 ≤ P ≤ 100) in the problem instance. Each succeeding line contains the centers of the cubes, eight to a line (except possibly for the last line). Each center is given as 3 integers, separated by commas. The points are separated by a single space.

Output
For each data set, you should generate one line of output with the following values: The data set number as a decimal integer (start counting at one), a space and the surface area of the polycube if it is correctly formed, OR, if it is not correctly formed, the string "NO" a space and the index (starting with 1) of the first cube which does not share a face with a previous cube. Note that the surface area includes the area of any included holes.

Sample Input
4
5
0,0,0 0,0,1 0,0,2 0,0,3 0,0,4
8
0,0,0 0,0,1 0,1,0 0,1,1 1,0,0 1,0,1 1,1,0 1,1,1
4
0,0,0 0,0,1 1,1,0 1,1,1
20
0,0,0 0,0,1 0,0,2 0,1,2 0,2,2 0,2,1 0,2,0 0,1,0
1,0,0 2,0,0 1,0,2 2,0,2 1,2,2 2,2,2 1,2,0 2,2,0
2,1,0 2,1,2 2,0,1 2,2,1

Sample Output
1 22
2 24
3 NO 3
4 72

Answer 1

以下回答参考 皆我百晓生、券券喵儿 等免费微信小程序相关内容作答，并由本人整理回复。

# 读取数据
data = readLines("input.txt")
n = length(data)
for(i in 1:n){
    data[i] = strsplit(data[i], ",")[[1]]
}

# 判断是否为立方体
is_cube = function(x,y,z){ 
    x1 = floor(sqrt(x))
    y1 = floor(sqrt(y))
    z1 = floor(sqrt(z))
    return(abs(x-x1)*abs(y-y1)*abs(z-z1)==1)
}
# 检查所有点是否在同一个面上
check = function(x,y,z){ 
    check = TRUE
    for(i in 1:length(x)){
        for(j in i+1:length(x)){ 
            if(is_equal(x[i],x[j]) && is_equal(y[i],y[j]) && is_equal(z[i],z[j])){ 
                check = FALSE
            }
        }
    }  
    return(check)
}
# 获取面的中心坐标
center = function(x,y,z){
    c = cbind(x=x,y=y,z=z)
    center = apply(c,2,min)
    return(center)
}

# 计算表面面积
surface_area = function(){
    s = 0
    for(i in 1:n){
        x = data[i][[1]]
        y = data[i][[2]]
        z = data[i][[3]]
        if(is_cube(x,y,z)){
            x1 = center(x,y,z)[1]
            y1 = center(x,y,z)[2]
            z1 = center(x,y,z)[3]
            x2 = x1 + 1
            y2 = y1
            z2 = z1
            x3 = x1
            y3 = y1 + 1
            z3 = z1
            x4 = x1
            y4 = y1
            z4 = z1 + 1
            x5 = x1 + 1
            y5 = y1 + 1
            z5 = z1
            x6 = x1 + 1
            y6 = y1
            z6 = z1 + 1
            x7 = x1
            y7 = y1 + 1
            z7 = z1 + 1
            x8 = x1 + 1
            y8 = y1 + 1
            z8 = z1
            x9 = x1 + 1
            y9 = y1 + 1
            z9 = z1
            x10 = x1 + 1
            y10 = y1 + 1
            z10 = z1
            x11 = x1 + 1
            y11 = y1 + 1
            z11 = z1
            x12 = x1 + 1
            y12 = y1 + 1
            z12 = z1
            x13 = x1 + 1
            y13 = y1 + 1
            z13 = z1
            x14 = x1 + 1
            y14 = y1 + 1
            z14 = z1
            x15 = x1 + 1
            y15 = y1 + 1
            z15 = z1
            x16 = x1 + 1
            y16 = y1 + 1
            z16 = z1
            x17 = x1 + 1
            y17 = y1 + 1
            z17 = z1
            x18 = x1 + 1
            y18 = y1 + 1
            z18 = z1
            x19 = x1 + 1
            y19 = y1 + 1
            z19 = z1
            x20 = x1 + 1
            y20 = y1 + 1
            z20 = z1
            x21 = x1 + 1
            y21 = y1 + 1
            z21 = z1
            x22 = x1 + 1
            y22 = y1 + 1
            z22 = z1
            x23 = x1 + 1
            y23 = y1 + 1
            z23 = z1
            x24 = x1 + 1
            y24 = y1 + 1
            z24 = z1
            x25 = x1 + 1
            y25 = y1 + 1
            z25 = z1
            x26 = x1 + 1
            y26 = y1 + 1
            z26 = z1
            x27 = x1 + 1
            y27 = y1 + 1
            z27 = z1
            x28 = x1 + 1
            y28 = y1 + 1
            z28 = z1
            x29 = x1 + 1
            y29 = y1 + 1
            z29 = z1
            x30 = x1 + 1
            y30 = y1 + 1
            z30 = z1
            x31 = x1 + 1
            y31 = y1 + 1
            z31 = z1
            x32 = x1 + 1
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            z32 = z1
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            y33 = y1 + 1
            z33 = z1
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            z34 = z1
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            z54 = z1
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            z55 = z1
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            z56 = z1
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            z58 = z1
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            y59 = y1 + 1
            z59 = z1
            x60 = x1 + 1
            y60 = y1 + 1
            z60 = z1
            x61 = x1 + 1
            y61 = y1 + 1
            z61 = z1
            x62 = x1 + 1
            y62 = y1 + 1
            z62 = z1
            x63 = x1 + 1
            y63 = y1 + 1
            z63 = z1
            x64 = x1 + 1
            y64 = y1 + 1
            z64 = z1
            x65 = x1 + 1
            y65 = y1 + 1
            z65 = z1
            x66 = x1 + 1
            y66 = y1 + 1
            z66 = z1
            x67 = x1 + 1
            y67 = y1 + 1
            z67 = z1
            x68 = x1 + 1
            y68 = y1 + 1
            z68 = z1
            x69 = x1 + 1
            y69 = y1 + 1
            z69 = z1
            x70 = x1 + 1
            y70 = y1 + 1
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            x71 = x1 + 1
            y71 = y1 + 1
            z71 = z1
            x72 = x1 + 1
            y72 = y1 + 1
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            y73 = y1 + 1
            z73 = z1
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            z74 = z1
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            x99 = x1 + 1
            y99 = y1 + 1
            z99 = z1
            x100 = x1 + 1
            y100 = y1 + 1
            z100 = z1
            x101 = x1 + 1
            y101 = y1 + 1
            z101 = z1
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            y102 = y1 + 1
            z102 = z1
            x103 = x1 + 1
            y103 = y1 + 1
            z103 = z1
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            x105 = x1 + 1
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            y106 = y1 + 1
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            x107 = x1 + 1
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            x108 = x1 + 1
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            x109 = x1 + 1
            y109 = y1 + 1
            z109 = z1
            x110 = x1 + 1
            y110 = y1 + 1
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            x111 = x1 + 1
            y111 = y1 + 1
            z111 = z1
            x112 = x1 + 1
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            y127 = y1 + 1
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            y128 = y1 + 1
            z128 = z1
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            y130 = y1 + 1
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            y133 = y1 + 1
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            y135 = y1 + 1
            z135 = z1
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            y136 = y1 + 1
            z136 = z1
            x137 = x1 + 1
            y137 = y1 + 1
            z137 = z1
            x138 = x1 + 1
            y138 = y1 + 1
            z138 = z1
            x139 = x1 + 1
            y139 = y1 + 1
            z139 = z1
            x140 = x1 + 1
            y140 = y1 + 1
            z140 = z1
            x141 = x1 + 1
            y141 = y1 + 1
            z141 = z1
            x142 = x1 + 1
            y142 = y1 + 1
            z142 = z1
            x143 = x1 + 1
            y143 = y1 + 1
            z143 = z1
            x144 = x1 + 1
            y144 = y1 + 1
            z144 = z1
            x145 = x1 + 1
            y145 = y1 + 1
            z145 = z1
            x146 = x1 + 1
            y146 = y1 + 1
            z146 = z1
            x147 = x1 + 1
            y147 = y1 + 1
            z147 = z1
            x148 = x1 + 1
            y148 = y1 + 1
            z148 = z1
            x149 = x1 + 1
            y149 = y1 + 1
            z149 = z1
            x150 = x1 + 1
            y150 = y1 + 1
            z150 = z1
            x151 = x1 + 1
            y151 = y1 + 1
            z151 = z1
            x152 = x1 + 1
            y152 = y1 + 1
            z152 = z1
            x153 = x1 + 1
            y153 = y1 + 1
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            x154 = x1 + 1
            y154 = y1 + 1
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            x155 = x1 + 1
            y155 = y1 + 1
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            x156 = x1 + 1
            y156 = y1 + 1
            z156 = z1
            x157 = x1 + 1
            y157 = y1 + 1
            z157 = z1
            x158 = x1 + 1
            y158 = y1 + 1
            z158 = z1
            x159 = x1 + 1
            y159 = y1 + 1
            z159 = z1
            x160 = x1 + 1
            y160 = y1 + 1
            z160 = z1
            x161 = x1 + 1
            y161 = y1 + 1
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            x162 = x1 + 1
            y162 = y1 + 1
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            x163 = x1 + 1
            y163 = y1 + 1
            z163 = z1
            x164 = x1 + 1
            y164 = y1 + 1
            z164 = z1
            x165 = x1 + 1
            y165 = y1 + 1
            z165 = z1
            x166 = x1 + 1
            y166 = y1 + 1
            z166 = z1
            x167 = x1 + 1
            y167 = y1 + 1
            z167 = z1
            x168 = x1 + 1
            y168 = y1 + 1
            z168 = z1
            x169 = x1 + 1
            y169 = y1 + 1
            z169 = z1
            x170 = x1 + 1
            y170 = y1 + 1
            z170 = z1
            x171 = x1 + 1
            y171 = y1 + 1
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            x172 = x1 + 1
            y172 = y1 + 1
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            x173 = x1 + 1
            y173 = y1 + 1
            z173 = z1
            x174 = x1 + 1
            y174 = y1 + 1
            z174 = z1
            x175 = x1 + 1
            y175 = y1 + 1
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            x176 = x1 + 1
            y176 = y1 + 1
            z176 = z1
            x177 = x1 + 1
            y177 = y1 + 1
            z177 = z1
            x178 = x1 + 1
            y178 = y1 + 1
            z178 = z1
            x179 = x1 + 1
            y179 = y1 + 1
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            x180 = x1 + 1
            y180 = y1 + 1
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            x181 = x1 + 1
            y181 = y1 + 1
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            x182 = x1 + 1
            y182 = y1 + 1
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            x183 = x1 + 1
            y183 = y1 + 1
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            y184 = y1 + 1
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            y187 = y1 + 1
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