2014
02-14

Area of Polycubes

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.

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.

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.

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 

1 22
2 24
3 NO 3
4 72 

// Area of Polycubes

#include <iostream>
using namespace std;

const int MAXP = 100;

int dis(int *p1, int *p2)
{
int d = 0;
for(int i = 0; i < 3; ++i)
{
d += abs(p1[i] - p2[i]);
}
return d;
}

int main()
{
int N;
cin>>N;
int points[MAXP][3];
for(int no = 0; no < N; ++no)
{
int P;
cin>>P;

fscanf(stdin, "%d,%d,%d", &points[0][0], &points[0][1], &points[0][2]);
int area = 6;
bool iscorrect = true;

cout<<no + 1<<" ";
for(int i = 1; i < P; ++i)
{
fscanf(stdin, "%d,%d,%d", &points[i][0], &points[i][1], &points[i][2]);
if(!iscorrect)
{
continue;
}

area += 6;

int j = 0;
bool isconnected = false;
while(j < i)
{
int d = dis(points[i], points[j]);

if(d == 0)
{
break;
}

if(d == 1)
{
isconnected = true;
area -= 2;
}

j++;
}
if(j != i || !isconnected)
{
iscorrect = false;
cout<<"NO "<<i + 1<<endl;
}
}
if(iscorrect)
{
cout<<area<<endl;
}
}
return 0;
}

1. 给你一组数据吧：29 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 1000。此时的数据量还是很小的，耗时却不短。这种方法确实可以，当然或许还有其他的优化方案，但是优化只能针对某些数据，不太可能在所有情况下都能在可接受的时间内求解出答案。