坐标离散化

原理：从稀疏矩阵中把有效数据提出来，放在一个新的坐标系中

#include <cstdio>
#include <iostream>
#include <vector>
#include <cmath>
#include <queue>
#include <algorithm>
#include <cstring>

const int INF = 1e6;
const int maxn = 510;

using namespace std;

int W, H, N;
int X1[maxn], X2[maxn], Y1[maxn], Y2[maxn];
int mp[maxn][maxn];
 
//填充用
bool fld[maxn * 6][maxn * 6];

//对x1 x2进行坐标离散化，返回离散化之后的值
int compress(int *x1, int *x2, int w){
	vector <int> xs;
	
	//将线及线周围入栈 
	for(int i = 0; i < N; i++)
		for(int d = -1; d <= 1; d++){
			int tx1 = x1[i] + d;
			int tx2 = x2[i] + d;
			if(1 <= tx1 && tx1 <= w)
				xs.push_back(tx1);
			if(1 <= tx2 && tx2 <= w)
				xs.push_back(tx2);
		}
	
	//排序，去重
	sort(xs.begin(), xs.end());
	xs.erase(unique(xs.begin(), xs.end()), xs.end());
	
	//将线的位置更新 
	for(int i = 0; i < N; i++){
		x1[i] = find(xs.begin(), xs.end(), x1[i]) - xs.begin();
		x2[i] = find(xs.begin(), xs.end(), x2[i]) - xs.begin();
	}
	
	return xs.size();
} 

void solve(){
	//坐标离散化 
	W = compress(X1, X2, W);
	H = compress(Y1, Y2, H);
	
	//填充直线区域
	memset(fld, 0, sizeof(fld));
	for(int i = 0; i < N; i++)
		for(int j = Y1[i]; j <= Y2[i]; j++)
			for(int k = X1[i]; k <= X2[i]; k++)
				fld[j][k] = true;
				
	//求区域个数
	int ans = 0;
	for(int i = 0 ; i < H; i++){
		for(int j = 0; j < W; j++){	
			if(fld[i][j])continue;
			ans++;
			
			//宽度优先 
			queue <pair<int, int> > que;
			que.push(make_pair(i, j));
			while(!que.empty()){
				int sx = que.front().first;
				int sy = que.front().second;
				que.pop();
				int dx[4] = {-1,1,0,0};
				int dy[4] = {0,0,-1,1};
				
				for(int i = 0; i < 4; i++){
					int tx = sx + dx[i];
					int ty = sy + dy[i];
					if(H <= tx || tx < 0 || W <= ty || ty < 0)continue;
					if(fld[tx][ty])continue;
					fld[tx][ty] = true;
					que.push(make_pair(tx, ty));
				}
			} 
		} 
	}
	printf("%d\n",  ans);	
}

//测试函数 
int main(){
	freopen ("D:\\钢铁程序员\\程序数据\\072坐标离散化.txt","r",stdin);
	scanf("%d%d%d", &W, &H, &N);
	for(int i = 0; i < N; i++)
		scanf("%d%d%d%d", &X1[i], &X2[i], &Y1[i], &Y2[i]);
	
	solve();
	return 0;
}