线段树 （矩形面积并&&周长并 - 来自notonlysuccess）
矩形面积并
hdu1542 Atlantis
题意:矩形面积并思路:浮点数先要离散化;然后把矩形分成两条边,上边和下边,对横轴建树,然后从下到上扫描上去,用cnt表示该区间下边比上边多几个,sum代表该区间内被覆盖的线段的长度总和
这里线段树的一个结点并非是线段的一个端点,而是该端点和下一个端点间的线段,所以题目中r+1,r-1的地方可以自己好好的琢磨一下
线段树操作:update:区间增减 query:直接取根节点的值
#include <cstdio>
#include <cstring>
#include <cctype>
#include <algorithm>
using namespace std;
#define lson l , m , rt << 1
#define rson m + 1 , r , rt << 1 | 1
const int maxn = 2222;
int cnt[maxn << 2];
double sum[maxn << 2];
double X[maxn];
struct Seg {
double h , l , r;
int s;
Seg(){}
Seg(double a,double b,double c,int d) : l(a) , r(b) , h(c) , s(d) {}
bool operator < (const Seg &cmp) const {
return h < cmp.h;
}
}ss[maxn];
void PushUp(int rt,int l,int r) {
if (cnt[rt]) sum[rt] = X[r+1] - X[l];
else if (l == r) sum[rt] = 0;
else sum[rt] = sum[rt<<1] + sum[rt<<1|1];
}
void update(int L,int R,int c,int l,int r,int rt) {
if (L <= l && r <= R) {
cnt[rt] += c;
PushUp(rt , l , r);
return ;
}
int m = (l + r) >> 1;
if (L <= m) update(L , R , c , lson);
if (m < R) update(L , R , c , rson);
PushUp(rt , l , r);
}
int Bin(double key,int n,double X[]) {//离散化
int l = 0 , r = n - 1;
while (l <= r) {
int m = (l + r) >> 1;
if (X[m] == key) return m;
if (X[m] < key) l = m + 1;
else r = m - 1;
}
return -1;
}
int main() {
int n , cas = 1;
while (~scanf("%d",&n) && n) {
int m = 0;
while (n --) {
double a , b , c , d;
scanf("%lf%lf%lf%lf",&a,&b,&c,&d);//左上和右下
X[m] = a;
ss[m++] = Seg(a , c , b , 1);
X[m] = c;
ss[m++] = Seg(a , c , d , -1);
}
sort(X , X + m);
sort(ss , ss + m);
int k = 1;
for (int i = 1 ; i < m ; i ++) {
if (X[i] != X[i-1]) X[k++] = X[i];
}
memset(cnt , 0 , sizeof(cnt));
memset(sum , 0 , sizeof(sum));
double ret = 0;
for (int i = 0 ; i < m - 1 ; i ++) {
int l = Bin(ss[i].l , k , X);
int r = Bin(ss[i].r , k , X) - 1;
if (l <= r) update(l , r , ss[i].s , 0 , k - 1, 1);
ret += sum[1] * (ss[i+1].h - ss[i].h);
}
printf("Test case #%d\nTotal explored area: %.2lf\n\n",cas++ , ret);
}
return 0;
}
矩形周长并
hdu1828 Picture
思路:与面积不同的地方是还要记录竖的边有几个(numseg记录),并且当边界重合的时候需要合并(用lbd和rbd表示边界来辅助)
线段树操作:update:区间增减 query:直接取根节点的值
include <cstdio>
#include <cstring>
#include <cctype>
#include <algorithm>
using namespace std;
#define lson l , m , rt << 1
#define rson m + 1 , r , rt << 1 | 1
const int maxn = 22222;
struct Seg{
int l , r , h , s;
Seg() {}
Seg(int a,int b,int c,int d):l(a) , r(b) , h(c) , s(d) {}
bool operator < (const Seg &cmp) const {
if (h == cmp.h) return s > cmp.s;
return h < cmp.h;
}
}ss[maxn];
bool lbd[maxn<<2] , rbd[maxn<<2];
int numseg[maxn<<2];
int cnt[maxn<<2];
int len[maxn<<2];
void PushUP(int rt,int l,int r) {
if (cnt[rt]) {
lbd[rt] = rbd[rt] = 1;
len[rt] = r - l + 1;
numseg[rt] = 2;
} else if (l == r) {
len[rt] = numseg[rt] = lbd[rt] = rbd[rt] = 0;
} else {
lbd[rt] = lbd[rt<<1];
rbd[rt] = rbd[rt<<1|1];
len[rt] = len[rt<<1] + len[rt<<1|1];
numseg[rt] = numseg[rt<<1] + numseg[rt<<1|1];
if (lbd[rt<<1|1] && rbd[rt<<1]) numseg[rt] -= 2;//两条线重合
}
}
void update(int L,int R,int c,int l,int r,int rt) {
if (L <= l && r <= R) {
cnt[rt] += c;
PushUP(rt , l , r);
return ;
}
int m = (l + r) >> 1;
if (L <= m) update(L , R , c , lson);
if (m < R) update(L , R , c , rson);
PushUP(rt , l , r);
}
int main() {
int n;
while (~scanf("%d",&n)) {
int m = 0;
int lbd = 10000, rbd = -10000;
for (int i = 0 ; i < n ; i ++) {
int a , b , c , d;
scanf("%d%d%d%d",&a,&b,&c,&d);//左下和右上
lbd = min(lbd , a);
rbd = max(rbd , c);
ss[m++] = Seg(a , c , b , 1);
ss[m++] = Seg(a , c , d , -1);
}
sort(ss , ss + m);
int ret = 0 , last = 0;
for (int i = 0 ; i < m ; i ++) {
if (ss[i].l < ss[i].r) update(ss[i].l , ss[i].r - 1 , ss[i].s , lbd , rbd - 1 , 1);
ret += numseg[1] * (ss[i+1].h - ss[i].h);
ret += abs(len[1] - last);
last = len[1];
}
printf("%d\n",ret);
}
return 0;
}