UVa 12171 题解

英文题面不怎么友好，大家还是自行通过紫书了解题面吧。。。

解题思路：

　　1. 面对500 ^ 3的数据范围，我们需要先用离散化解决掉爆空间的问题。

　　2. 由于我们要求的总体积包括内空部分的体积，我们可以用flood_fill来解决。

注意事项：（几个细节问题）

　　1. unique函数的正确使用姿势：如果是从一开始存数，注意最后要多减去1.

　　2. 染色时每个三维坐标上的点代表一个长方形，所以右端点不能染色。

　　  3. 可以用结构体封装一下各个操作。

AC代码：

#include <iostream>
#include <algorithm>
#include <cstring>
#include <queue>
#include <cstdio>
#include <cstdlib>

using namespace std;

const int dx[] = {1, -1,  0,  0,  0,  0};
const int dy[] = {0,  0,  1, -1,  0,  0};
const int dz[] = {0,  0,  0,  0,  1, -1};

int T, n, v, s;
int x1[507], y1[507], z1[507], x0[507], y0[507], z0[507];

int nx = 0, ny = 0, nz= 0;
int lx[110], ly[110], lz[110];
int color[104][104][104];

struct cell{
    int x, y, z;

    cell(int x = 0, int y = 0, int z = 0): x(x), y(y), z(z) {}

    void setvis() const { color[x][y][z] = 2; }

    bool getvis() const { return color[x][y][z] == 2; }

    bool issolid() const { return color[x][y][z] == 1; }

    bool invalid() const {
        if (x <= 0 || y <= 0 || z <= 0 || x >= nx || y >= ny || z >= nz ) return true;
        return false;
    }

    int area(int dir) const {
        if (dx[dir] != 0) return (ly[y + 1] - ly[y]) * (lz[z + 1] - lz[z]);
        else if (dy[dir] != 0) return (lx[x + 1] - lx[x]) * (lz[z + 1] - lz[z]);
        return (lx[x + 1] - lx[x]) * (ly[y + 1] - ly[y]);
    }

    int volume() const { return (lx[x + 1] - lx[x]) * (ly[y + 1] - ly[y]) * (lz[z + 1] - lz[z]); }

};

int read()
{
    int x = 0;
    int k = 1;
    char c = getchar();

    while (c > '9' || c < '0')
        if (c == '-') k = -1, c = getchar();
        else c = getchar();
    while (c >= '0' && c <= '9')
        x = x * 10 + c - '0',
        c = getchar();

    return k * x;
}

void  discretization(int* x, int& l)
{
    sort(x + 1, x + l + 1);
    l = unique(x + 1, x + l + 1) - x - 1;
}

int get_ID(int *x, int l, int k)
{
    return lower_bound(x + 1, x + l + 1, k) - x;
}

void flood_fill()
{
    cell c(1, 1, 1);
    c.setvis();
    queue<cell> q;
    q.push(c);
    while (!q.empty())
    {
        cell c = q.front();
        q.pop();
        v += c.volume();
        for (int i = 0; i < 6; ++i)
        {
            cell c2(c.x + dx[i], c.y + dy[i], c.z + dz[i]);
            if (c2.invalid()) continue;
            if (c2.issolid()) s += c2.area(i);
            else if (!c2.getvis())
            {
                c2.setvis();
                q.push(c2);
            }
        }
    }
    v = 1001 * 1001 * 1001 - v;
}

int main()
{
    T = read();
    while (T--)
    {
        v = 0, s = 0;
        memset(color, 0, sizeof(color));
        n = read();
        lx[2] = ly[2] = lz[2] = 0;
        lx[1] = ly[1] = lz[1] = 1001;
        nx = ny = nz = 2;
        for (int i = 1; i <= n; ++i)
            x0[i] = read(),
            y0[i] = read(),
            z0[i] = read(),
            x1[i] = read(),
            y1[i] = read(),
            z1[i] = read(),
            lx[++nx] = x0[i],
            lx[++nx] = x0[i] + x1[i],
            ly[++ny] = y0[i],
            ly[++ny] = y0[i] + y1[i],
            lz[++nz] = z0[i],
            lz[++nz] = z0[i] + z1[i];


        discretization(lx, nx);
        discretization(ly, ny);
        discretization(lz, nz);

        for (int t = 1; t <= n; ++t)
        {
            int sx = get_ID(lx, nx, x0[t]);
            int ex = get_ID(lx, nx, x0[t] + x1[t]);
            int sy = get_ID(ly, ny, y0[t]);
            int ey = get_ID(ly, ny, y0[t] + y1[t]);
            int sz = get_ID(lz, nz, z0[t]);
            int ez = get_ID(lz, nz, z0[t] + z1[t]);
            for (int i = sx; i < ex; ++i)
                for (int j = sy; j < ey; ++j)
                    for (int l = sz; l < ez; ++l)
                        color[i][j][l] = 1;
        }

        flood_fill();

        printf("%d %d
", s, v);
    }
}