标签:初始 延迟标记 最大连续 之间 tin 端点 add geo algo
题意:单点更新+区间查询(求和)。
树状数组 (218ms)
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>
using namespace std;
#define debug(x) cout << #x << " is " << x << endl
#define inc(i, a, b) for (int i = a; i <= b; ++i)
typedef long long ll;
const int INF = 0x3f3f3f3f, N = 5e4 + 5;
int t, n;
int c[N];
char str[10];
int lowbit(int x) { return x & -x; }
void add(int x, int v) {
for (; x <= n; x += lowbit(x)) c[x] += v;
}
int sum(int x) {
int res = 0;
for (; x; x -= lowbit(x)) res += c[x];
return res;
}
int main()
{
scanf("%d", &t);
for (int cas = 1; cas <= t; ++cas) {
scanf("%d", &n);
int x, y;
memset(c, 0, sizeof(c));
for (int i = 1; i <= n; ++i) {
scanf("%d", &x);
add(i, x);
}
printf("Case %d:\n", cas);
while (scanf("%s", str) && str[0] != ‘E‘) {
scanf("%d%d", &x, &y);
if (str[0] == ‘A‘) add(x, y);
else if (str[0] == ‘S‘) add(x, -y);
else printf("%d\n", sum(y) - sum(x - 1));
}
}
return 0;
}
线段树 (234ms)
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>
using namespace std;
#define debug(x) cout << #x << " is " << x << endl
#define inc(i, a, b) for (int i = a; i <= b; ++i)
typedef long long ll;
const int INF = 0x3f3f3f3f, N = 5e4 + 5;
struct Node {
int l, r, sum;
}tree[N<<2];
int t, n;
int a[N];
char str[10];
void push_up(int rt) {
tree[rt].sum = tree[rt<<1].sum + tree[rt<<1|1].sum;
}
void build(int rt, int l, int r) {
tree[rt].l = l, tree[rt].r = r;
if (l == r) { tree[rt].sum = a[l]; return; }
int mid = (l + r) >> 1;
build(rt<<1, l, mid);
build(rt<<1|1, mid + 1, r);
push_up(rt);
}
void update(int rt, int x, int v) {
if (tree[rt].l == tree[rt].r) { tree[rt].sum += v; return; }
int mid = (tree[rt].l + tree[rt].r) >> 1;
if (x <= mid) update(rt<<1, x, v);
else update(rt<<1|1, x, v);
push_up(rt);
}
int query(int rt, int l, int r) {
if (l <= tree[rt].l && r >= tree[rt].r) return tree[rt].sum;
int mid = (tree[rt].l + tree[rt].r) >> 1;
int ans = 0;
if (l <= mid) ans += query(rt<<1, l, r);
if (r > mid) ans += query(rt<<1|1, l, r);
return ans;
}
int main()
{
scanf("%d", &t);
for (int cas = 1; cas <= t; ++cas) {
scanf("%d", &n);
for (int i = 1; i <= n; ++i) scanf("%d", &a[i]);
build(1, 1, n);
int x, y;
printf("Case %d:\n", cas);
while (scanf("%s", str) && str[0] != ‘E‘) {
scanf("%d%d", &x, &y);
if (str[0] == ‘A‘) update(1, x, y);
else if (str[0] == ‘S‘) update(1, x, -y);
else printf("%d\n", query(1, x, y));
}
}
return 0;
}
zkw(张昆玮) 线段树 (202ms)
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>
using namespace std;
#define debug(x) cout << #x << " is " << x << endl
#define inc(i, a, b) for (int i = a; i <= b; ++i)
typedef long long ll;
const int INF = 0x3f3f3f3f, N = 5e4 + 5;
int t, n, m;
int tree[N<<2];
char str[10];
void push_up(int rt) {
tree[rt] = tree[rt<<1] + tree[rt<<1|1];
}
void build() {
for (m = 1; m <= n + 1; m <<= 1);
for (int i = m + 1; i <= m + n; ++i) scanf("%d", &tree[i]);
for (int i = m - 1; i; --i) push_up(i);
}
void update(int x, int v) {
for (x += m; x; x >>= 1) tree[x] += v;
}
int query(int l, int r) {
int res = 0;
for (l = l + m - 1, r = r + m + 1; l ^ r ^ 1; l >>= 1, r >>= 1) {
if (~l & 1) res += tree[l ^ 1];
if (r & 1) res += tree[r ^ 1];
}
return res;
}
int main()
{
scanf("%d", &t);
for (int cas = 1; cas <= t; ++cas) {
scanf("%d", &n);
build();
int x, y;
printf("Case %d:\n", cas);
while (scanf("%s", str) && str[0] != ‘E‘) {
scanf("%d%d", &x, &y);
if (str[0] == ‘A‘) update(x, y);
else if (str[0] == ‘S‘) update(x, -y);
else printf("%d\n", query(x, y));
}
}
return 0;
}
题意:单点更新+区间查询(最值)。
??模板题。
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>
using namespace std;
#define debug(x) cout << #x << " is " << x << endl
#define inc(i, a, b) for (int i = a; i <= b; ++i)
typedef long long ll;
const int INF = 0x3f3f3f3f, N = 2e5 + 5;
struct Node {
int l, r, dat;
}tree[N<<2];
int n, m;
int a[N];
char op[3];
void push_up(int rt) {
tree[rt].dat = max(tree[rt<<1].dat, tree[rt<<1|1].dat);
}
void build(int rt, int l, int r) {
tree[rt].l = l, tree[rt].r = r;
if (l == r) { tree[rt].dat = a[l]; return; }
int mid = (l + r) >> 1;
build(rt<<1, l, mid);
build(rt<<1|1, mid + 1, r);
push_up(rt);
}
void update(int rt, int x, int v) {
if (tree[rt].l == tree[rt].r) { tree[rt].dat = v; return; }
int mid = (tree[rt].l + tree[rt].r) >> 1;
if (x <= mid) update(rt<<1, x, v);
else update(rt<<1|1, x, v);
push_up(rt);
}
int query(int rt, int l, int r) {
if (l <= tree[rt].l && r >= tree[rt].r) return tree[rt].dat;
int mid = (tree[rt].l + tree[rt].r) >> 1;
int res = 0;
if (l <= mid) res = max(res, query(rt<<1, l, r));
if (r > mid) res = max(res, query(rt<<1|1, l, r));
return res;
}
int main()
{
while (~scanf("%d%d", &n, &m)) {
for (int i = 1; i <= n; ++i) scanf("%d", &a[i]);
build(1, 1, n);
int x, y;
while (m--) {
scanf("%s%d%d", op, &x, &y);
if (op[0] == ‘Q‘) printf("%d\n", query(1, x, y));
else if (op[0] == ‘U‘) update(1, x, y);
}
}
return 0;
}
题意:区间更新+区间查询(求和)。
??模板题,延迟标记。
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>
using namespace std;
#define debug(x) cout << #x << " is " << x << endl
#define inc(i, a, b) for (int i = a; i <= b; ++i)
typedef long long ll;
const int INF = 0x3f3f3f3f, N = 1e5 + 5;
struct Node {
int l, r;
ll sum, add;
}tree[N<<2];
int n, q;
int a[N];
char op[3];
void push_down(int rt) {
if (tree[rt].add) {
tree[rt<<1].sum += tree[rt].add * (tree[rt<<1].r - tree[rt<<1].l + 1);
tree[rt<<1|1].sum += tree[rt].add * (tree[rt<<1|1].r - tree[rt<<1|1].l + 1);
tree[rt<<1].add += tree[rt].add;
tree[rt<<1|1].add += tree[rt].add;
tree[rt].add = 0;
}
}
void push_up(int rt) {
tree[rt].sum = tree[rt<<1].sum + tree[rt<<1|1].sum;
}
void build(int rt, int l, int r) {
tree[rt].l = l, tree[rt].r = r;
if (l == r) { tree[rt].sum = a[l]; return; }
int mid = (l + r) >> 1;
build(rt<<1, l, mid);
build(rt<<1|1, mid + 1, r);
push_up(rt);
}
void update(int rt, int l, int r, int d) {
if (l <= tree[rt].l && r >= tree[rt].r) {
tree[rt].sum += (ll)d * (tree[rt].r - tree[rt].l + 1);
tree[rt].add += d;
return;
}
push_down(rt);
int mid = (tree[rt].l + tree[rt].r) >> 1;
if (l <= mid) update(rt<<1, l, r, d);
if (r > mid) update(rt<<1|1, l, r, d);
push_up(rt);
}
ll query(int rt, int l, int r) {
if (l <= tree[rt].l && r >= tree[rt].r) return tree[rt].sum;
push_down(rt);
int mid = (tree[rt].l + tree[rt].r) >> 1;
ll res = 0;
if (l <= mid) res += query(rt<<1, l, r);
if (r > mid) res += query(rt<<1|1, l, r);
return res;
}
int main()
{
scanf("%d%d", &n, &q);
for (int i = 1; i <= n; ++i) scanf("%d", &a[i]);
build(1, 1, n);
while (q--) {
int x, y, z;
scanf("%s%d%d", op, &x, &y);
if (op[0] == ‘C‘) {
scanf("%d", &z);
update(1, x, y, z);
}
else if (op[0] == ‘Q‘) printf("%lld\n", query(1, x, y));
}
return 0;
}
题意:市长选举贴高度相同的海报,后面的海报可以贴在前面的上面,最后可以看见的海报。
??离散化用线段树,注意对于如 \([1,10],[1,4],[6,10]\) 等端点重合的样例,离散化将 5 压缩掉,因此需要在距离大于 1 的点中进行插点,不影响最终结果,在 \(2 * N\) 个点中插点,最多 \(4 * N-1\),因此取 \(N=4e4\)。
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>
using namespace std;
#define debug(x) cout << #x << " is " << x << endl
#define inc(i, a, b) for (int i = a; i <= b; ++i)
typedef long long ll;
const int INF = 0x3f3f3f3f, N = 4e4 + 5;
struct Node {
int l, r, lazytag;
}tree[N<<2];
int cas, n, ans;
int pl[N], pr[N], seg[N<<1];
int vis[N<<1];
void push_down(int rt) {
if (tree[rt].lazytag) {
tree[rt<<1].lazytag = tree[rt<<1|1].lazytag = tree[rt].lazytag;
tree[rt].lazytag = 0;
}
}
void build(int rt, int l, int r) {
tree[rt].l = l, tree[rt].r = r;
tree[rt].lazytag = 0;
if (l == r) return;
int mid = (l + r) >> 1;
build(rt<<1, l, mid);
build(rt<<1|1, mid + 1, r);
}
void update(int rt, int l, int r, int x) {
if (l <= tree[rt].l && r >= tree[rt].r) {
tree[rt].lazytag = x;
return;
}
push_down(rt);
int mid = (tree[rt].l + tree[rt].r) >> 1;
if (l <= mid) update(rt<<1, l, r, x);
if (r > mid) update(rt<<1|1, l, r, x);
}
void query(int rt) {
if (tree[rt].lazytag && !vis[tree[rt].lazytag]) {
ans++;
vis[tree[rt].lazytag] = 1;
return;
}
if (tree[rt].l == tree[rt].r) return;
push_down(rt);
query(rt<<1);
query(rt<<1|1);
}
int main()
{
scanf("%d", &cas);
while (cas--) {
int cnt = 0;
memset(vis, 0, sizeof(vis));
scanf("%d", &n);
for (int i = 1; i <= n; ++i) {
scanf("%d%d", &pl[i], &pr[i]);
seg[++cnt] = pl[i];
seg[++cnt] = pr[i];
}
sort(seg + 1, seg + cnt + 1);
int m = unique(seg + 1, seg + cnt + 1) - (seg + 1);
for (int i = m; i >= 2; --i)
if (seg[i] - seg[i-1] > 1) seg[++m] = seg[i-1] + 1;
sort(seg + 1, seg + m + 1);
build(1, 1, m);
for (int i = 1; i <= n; ++i) {
int x = lower_bound(seg + 1, seg + m + 1, pl[i]) - seg;
int y = lower_bound(seg + 1, seg + m + 1, pr[i]) - seg;
update(1, x, y, i);
}
ans = 0;
query(1);
printf("%d\n", ans);
}
return 0;
}
题意:区间更新+所有数的和。
??延迟标记,最后输出 tree[1].sum
即可。
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>
using namespace std;
#define debug(x) cout << #x << " is " << x << endl
#define inc(i, a, b) for (int i = a; i <= b; ++i)
typedef long long ll;
const int INF = 0x3f3f3f3f, N = 1e5 + 5;
struct Node {
int l, r, sum, tag;
}tree[N<<2];
int cas, n, q;
void push_up(int rt) {
tree[rt].sum = tree[rt<<1].sum + tree[rt<<1|1].sum;
}
void push_down(int rt) {
if (tree[rt].tag) {
tree[rt<<1].tag = tree[rt<<1|1].tag = tree[rt].tag;
int mid = (tree[rt].l + tree[rt].r) >> 1;
tree[rt<<1].sum = (mid - tree[rt].l + 1) * tree[rt].tag;
tree[rt<<1|1].sum = (tree[rt].r - mid) * tree[rt].tag;
tree[rt].tag = 0;
}
}
void build(int rt, int l, int r) {
tree[rt].l = l, tree[rt].r = r;
tree[rt].tag = 0;
if (l == r) { tree[rt].sum = 1; return; }
int mid = (l + r) >> 1;
build(rt<<1, l, mid);
build(rt<<1|1, mid + 1, r);
push_up(rt);
}
void update(int rt, int l, int r, int x) {
if (l <= tree[rt].l && r >= tree[rt].r) {
tree[rt].sum = x * (tree[rt].r - tree[rt].l + 1);
tree[rt].tag = x;
return;
}
push_down(rt);
int mid = (tree[rt].l + tree[rt].r) >> 1;
if (l <= mid) update(rt<<1, l, r, x);
if (r > mid) update(rt<<1|1, l, r, x);
push_up(rt);
}
int main()
{
scanf("%d", &cas);
for (int i = 1; i <= cas; ++i) {
scanf("%d%d", &n, &q);
build(1, 1, n);
int x, y, z;
while (q--) {
scanf("%d%d%d", &x, &y, &z);
update(1, x, y, z);
}
printf("Case %d: The total value of the hook is %d.\n", i, tree[1].sum);
}
return 0;
}
题意:区间涂色(可覆盖),求最终可看到几种颜色,以及这些颜色的段数。
??类似于第四题,延迟标记。
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>
using namespace std;
#define debug(x) cout << #x << " is " << x << endl
#define inc(i, a, b) for (int i = a; i <= b; ++i)
typedef long long ll;
const int INF = 0x3f3f3f3f, N = 8e3 + 5;
struct Node {
int l, r, tag;
}tree[N<<2];
int n, last;
int vis[N];
void push_down(int rt) {
if (~tree[rt].tag) {
tree[rt<<1].tag = tree[rt<<1|1].tag = tree[rt].tag;
tree[rt].tag = -1;
}
}
void build(int rt, int l, int r) {
tree[rt].l = l, tree[rt].r = r;
tree[rt].tag = -1;
if (l == r) return;
int mid = (l + r) >> 1;
build(rt<<1, l, mid);
build(rt<<1|1, mid + 1, r);
}
void update(int rt, int l, int r, int x) {
if (l <= tree[rt].l && r >= tree[rt].r) {
tree[rt].tag = x;
return;
}
push_down(rt);
int mid = (tree[rt].l + tree[rt].r) >> 1;
if (l <= mid) update(rt<<1, l, r, x);
if (r > mid) update(rt<<1|1, l, r, x);
}
void query(int rt) {
if (tree[rt].l == tree[rt].r) {
if (~tree[rt].tag && tree[rt].tag != last) {
vis[tree[rt].tag]++;
}
last = tree[rt].tag;
return;
}
push_down(rt);
query(rt<<1);
query(rt<<1|1);
}
int main()
{
while (~scanf("%d", &n)) {
memset(vis, 0, sizeof(vis));
build(1, 1, 8000);
int x, y, z;
while (n--) {
scanf("%d%d%d", &x, &y, &z);
update(1, x + 1, y, z);
}
last = -1;
query(1);
for (int i = 0; i <= 8000; ++i) {
if (vis[i]) printf("%d %d\n", i, vis[i]);
}
puts("");
}
return 0;
}
题意:农夫 Jorn 的 n 中奶牛排成一列,q 个查询,输出区间最大高度差。
树状数组
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>
using namespace std;
#define debug(x) cout << #x << " is " << x << endl
#define inc(i, a, b) for (int i = a; i <= b; ++i)
typedef long long ll;
const int INF = 0x3f3f3f3f, N = 5e4 + 5;
int n, q;
int a[N], minn[N], maxn[N];
int lowbit(int x) { return x & -x; }
void update(int x, int v) {
for (; x <= n; x += lowbit(x)) {
maxn[x] = max(maxn[x], v);
minn[x] = min(minn[x], v);
}
}
int ask(int l, int r) {
int ma = a[l], mi = a[l];
while (r >= l) {
ma = max(ma, a[r]); mi = min(mi, a[r]);
for (r--; r - lowbit(r) >= l; r -= lowbit(r))
ma = max(ma, maxn[r]), mi = min(mi, minn[r]);
}
return ma - mi;
}
int main()
{
scanf("%d%d", &n, &q);
memset(minn, 0x3f, sizeof(minn));
for (int i = 1; i <= n; ++i) {
scanf("%d", &a[i]);
update(i, a[i]);
}
int x, y;
while (q--) {
scanf("%d%d", &x, &y);
printf("%d\n", ask(x, y));
}
return 0;
}
线段树
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>
using namespace std;
#define debug(x) cout << #x << " is " << x << endl
#define inc(i, a, b) for (int i = a; i <= b; ++i)
typedef long long ll;
const int INF = 0x3f3f3f3f, N = 5e4 + 5;
struct Node {
int l, r, high, low;
}tree[N<<2];
int n, q;
int a[N];
void push_up(int rt) {
tree[rt].high = max(tree[rt<<1].high, tree[rt<<1|1].high);
tree[rt].low = min(tree[rt<<1].low, tree[rt<<1|1].low);
}
void build(int rt, int l, int r) {
tree[rt].l = l, tree[rt].r = r;
if (l == r) {
tree[rt].high = tree[rt].low = a[l];
return;
}
int mid = (l + r) >> 1;
build(rt<<1, l, mid);
build(rt<<1|1, mid + 1, r);
push_up(rt);
}
int query(int rt, int l, int r, int f) {
if (l <= tree[rt].l && r >= tree[rt].r) {
if (f) return tree[rt].high;
else return tree[rt].low;
}
int mid = (tree[rt].l + tree[rt].r) >> 1;
int res; if (f) res = 0; else res = INF;
if (l <= mid) {
if (f) res = max(res, query(rt<<1, l, r, 1));
else res = min(res, query(rt<<1, l, r, 0));
}
if (r > mid) {
if (f) res = max(res, query(rt<<1|1, l, r, 1));
else res = min(res, query(rt<<1|1, l, r, 0));
}
return res;
}
int main()
{
scanf("%d%d", &n, &q);
for (int i = 1; i <= n; ++i) scanf("%d", &a[i]);
build(1, 1, n);
int x, y;
while (q--) {
scanf("%d%d", &x, &y);
printf("%d\n", query(1, x, y, 1) - query(1, x, y, 0));
}
return 0;
}
题意:区间修改(开方)+区间查询(求和)。
??每个点更新不一样,只能单点修改,由于 \(2^{64}\) 开 7 次方取整为 1,故还可加限制条件每个点最多更新 7 次,以及区间和等于区间长度时不需继续更新,注意输入数组不开 long long
会 TLE。
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>
using namespace std;
#define debug(x) cout << #x << " is " << x << endl
#define inc(i, a, b) for (int i = a; i <= b; ++i)
typedef long long ll;
const int INF = 0x3f3f3f3f, N = 1e5 + 5;
struct Node {
int l, r;
ll sum;
}tree[N<<2];
int n, m, cas;
ll a[N];
void push_up(int rt) {
tree[rt].sum = tree[rt<<1].sum + tree[rt<<1|1].sum;
}
void build(int rt, int l, int r) {
tree[rt].l = l, tree[rt].r = r;
if (l == r) { tree[rt].sum = a[l]; return; }
int mid = (l + r) >> 1;
build(rt<<1, l, mid);
build(rt<<1|1, mid + 1, r);
push_up(rt);
}
void update(int rt, int l, int r) {
if (tree[rt].sum == ll(tree[rt].r - tree[rt].l + 1)) return;
if (tree[rt].l == tree[rt].r) {
tree[rt].sum = (ll)sqrt(tree[rt].sum);
return;
}
int mid = (tree[rt].l + tree[rt].r) >> 1;
if (l <= mid) update(rt<<1, l, r);
if (r > mid) update(rt<<1|1, l, r);
push_up(rt);
}
ll query(int rt, int l, int r) {
if (l <= tree[rt].l && r >= tree[rt].r) return tree[rt].sum;
int mid = (tree[rt].l + tree[rt].r) >> 1;
ll res = 0;
if (l <= mid) res += query(rt<<1, l, r);
if (r > mid) res += query(rt<<1|1, l, r);
return res;
}
int main()
{
while (~scanf("%d", &n)) {
for (int i = 1; i <= n; ++i) scanf("%lld", &a[i]);
build(1, 1, n);
scanf("%d", &m);
printf("Case #%d:\n", ++cas);
int t, x, y;
while (m--) {
scanf("%d%d%d", &t, &x, &y);
if (x > y) swap(x, y);
if (t) printf("%lld\n", query(1, x, y));
else update(1, x, y);
}
puts("");
}
return 0;
}
题意:n 个地道,m 个操作,D x
: 炸掉第 x 个地道;Q x
: 查询第 x 个地道所在的最大区间长度;R x: 重建上一次被炸的地道。
??法一:线段树维护三个信息,ll: 左端点开始最大连续长度,rl: 右端点开始最大连续长度,ml: 区间中最大连续长度。
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>
using namespace std;
#define debug(x) cout << #x << " is " << x << endl
#define inc(i, a, b) for (int i = a; i <= b; ++i)
typedef long long ll;
const int INF = 0x3f3f3f3f, N = 5e4 + 5;
struct Node {
int l, r;
int ll, rl, ml;
}tree[N<<2];
int n, m;
int sta[N];
char op[3];
void push_up(int rt) {
tree[rt].ll = tree[rt<<1].ll, tree[rt].rl = tree[rt<<1|1].rl;
tree[rt].ml = max(tree[rt<<1].ml, tree[rt<<1|1].ml);
tree[rt].ml = max(tree[rt].ml, tree[rt<<1].rl + tree[rt<<1|1].ll);
if (tree[rt].ll == tree[rt<<1].r - tree[rt<<1].l + 1) tree[rt].ll += tree[rt<<1|1].ll;
if (tree[rt].rl == tree[rt<<1|1].r - tree[rt<<1|1].l + 1) tree[rt].rl += tree[rt<<1].rl;
}
void build(int rt, int l, int r) {
tree[rt].l = l, tree[rt].r = r;
tree[rt].ll = tree[rt].rl = tree[rt].ml = r - l + 1;
if (l == r) return;
int mid = (l + r) >> 1;
build(rt<<1, l, mid);
build(rt<<1|1, mid + 1, r);
}
void update(int rt, int x, int v) {
if (tree[rt].l == tree[rt].r) {
tree[rt].ll = tree[rt].rl = tree[rt].ml = v;
return;
}
int mid = (tree[rt].l + tree[rt].r) >> 1;
if (x <= mid) update(rt<<1, x, v);
else update(rt<<1|1, x, v);
push_up(rt);
}
int query(int rt, int x) {
if (tree[rt].l == tree[rt].r || !tree[rt].ml || tree[rt].ml == tree[rt].r - tree[rt].l + 1) return tree[rt].ml;
int mid = (tree[rt].l + tree[rt].r) >> 1;
if (x <= mid) {
if (x >= mid - tree[rt<<1].rl + 1)
return tree[rt<<1].rl + tree[rt<<1|1].ll;
else return query(rt<<1, x);
}
else {
if (x <= mid + tree[rt<<1|1].ll)
return tree[rt<<1|1].ll + tree[rt<<1].rl;
else return query(rt<<1|1, x);
}
}
int main()
{
while (~scanf("%d%d", &n, &m)) {
build(1, 1, n);
int top = 0, x;
while (m--) {
scanf("%s", op);
if (op[0] == ‘D‘) {
scanf("%d", &x);
sta[++top] = x;
update(1, x, 0);
}
else if (op[0] == ‘Q‘) {
scanf("%d", &x);
printf("%d\n", query(1, x));
}
else if (op[0] == ‘R‘) {
if (!top) continue;
x = sta[top--];
update(1, x, 1);
}
}
}
return 0;
}
??法二:线段树维护区间中被摧毁村庄编号的最值。
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>
using namespace std;
#define debug(x) cout << #x << " is " << x << endl
#define inc(i, a, b) for (int i = a; i <= b; ++i)
typedef long long ll;
const int INF = 0x3f3f3f3f, N = 5e4 + 5;
struct Node {
int l, r;
int mi, ma;
}tree[N<<2];
int n, m;
int sta[N];
char op[3];
void push_up(int rt) {
tree[rt].mi = min(tree[rt<<1].mi, tree[rt<<1|1].mi);
tree[rt].ma = max(tree[rt<<1].ma, tree[rt<<1|1].ma);
}
void build(int rt, int l, int r) {
tree[rt].l = l, tree[rt].r = r;
tree[rt].mi = n + 1, tree[rt].ma = 0;
if (l == r) return;
int mid = (l + r) >> 1;
build(rt<<1, l, mid);
build(rt<<1|1, mid + 1, r);
}
void update(int rt, int x, int v) {
if (tree[rt].l == tree[rt].r) {
if (v) { tree[rt].mi = n + 1; tree[rt].ma = 0; }
else tree[rt].mi = tree[rt].ma = x;
return;
}
int mid = (tree[rt].l + tree[rt].r) >> 1;
if (x <= mid) update(rt<<1, x, v);
else update(rt<<1|1, x, v);
push_up(rt);
}
int query(int rt, int x, int f) {
int mid = (tree[rt].l + tree[rt].r) >> 1, res;
if (f) {
if (tree[rt].r <= x || tree[rt].l == tree[rt].r) {
return tree[rt].ma;
}
res = 0;
res = max(res, query(rt<<1, x, 1));
if (mid < x) res = max(res, query(rt<<1|1, x, 1));
return res;
}
else {
if (tree[rt].l >= x || tree[rt].l == tree[rt].r) {
return tree[rt].mi;
}
res = n + 1;
res = min(res, query(rt<<1|1, x, 0));
if (x <= mid) res = min(res, query(rt<<1, x, 0));
return res;
}
}
int main()
{
while (~scanf("%d%d", &n, &m)) {
build(1, 1, n);
int top = 0, x;
while (m--) {
scanf("%s", op);
if (op[0] == ‘D‘) {
scanf("%d", &x);
sta[++top] = x;
update(1, x, 0);
}
else if (op[0] == ‘Q‘) {
scanf("%d", &x);
int r = query(1, x, 0);
int l = query(1, x, 1);
if (l == r) puts("0");
else printf("%d\n", r - l - 1);
}
else if (op[0] == ‘R‘) {
if (!top) continue;
x = sta[top--];
update(1, x, 1);
}
}
}
return 0;
}
??法三:类似法二的思想,模拟来做。
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>
#include <set>
using namespace std;
#define debug(x) cout << #x << " is " << x << endl
#define inc(i, a, b) for (int i = a; i <= b; ++i)
typedef long long ll;
const int INF = 0x3f3f3f3f, N = 5e4 + 5;
int n, m;
int sta[N];
char op[3];
set<int> s;
int main()
{
while (~scanf("%d%d", &n, &m)) {
s.clear();
int top = 0, x;
while (m--) {
scanf("%s", op);
if (op[0] == ‘D‘) {
scanf("%d", &x);
sta[++top] = x;
s.insert(x);
}
else if (op[0] == ‘Q‘) {
scanf("%d", &x);
set<int>::iterator it = s.lower_bound(x);
int l, r;
if (it == s.end()) r = n + 1;
else r = *it;
if (it == s.begin()) l = 0;
else l = *(--it);
if (r == x) puts("0");
else printf("%d\n", r - l - 1);
}
else if (op[0] == ‘R‘) {
s.erase(sta[top--]);
}
}
}
return 0;
}
题意:n 个结点,n-1 个关系,所有结点初始值为 -1,给出 m 个操作,C x: 查询 x 结点的值,T x y: 以 x 为根的子树上所有结点值变成 y。
??dfs 找出树的 dfs 序,找出每个数字左右两边出现的位置,子结点必在两个位置之间,之后用线段树即可。
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>
using namespace std;
#define debug(x) cout << #x << " is " << x << endl
#define inc(i, a, b) for (int i = a; i <= b; ++i)
typedef long long ll;
const int INF = 0x3f3f3f3f, N = 5e4 + 5;
struct Node {
int l, r, dat, lazy;
}tree[N<<2];
int t, n, m, tot, root;
int head[N], L[N], R[N];
int ver[N], nxt[N];
char op[3];
void add(int x, int y) {
ver[++tot] = y;
nxt[tot] = head[x];
head[x] = tot;
}
void dfs(int x) {
L[x] = ++tot;
for (int i = head[x]; i; i = nxt[i]) {
dfs(ver[i]);
}
R[x] = ++tot;
}
void push_down(int rt) {
if (tree[rt].lazy) {
tree[rt<<1].dat = tree[rt<<1|1].dat = tree[rt].lazy;
tree[rt<<1].lazy = tree[rt<<1|1].lazy = tree[rt].lazy;
tree[rt].lazy = 0;
}
}
void build(int rt, int l, int r) {
tree[rt].l = l, tree[rt].r = r, tree[rt].lazy = 0;
if (l == r) { tree[rt].dat = -1; return; }
int mid = (l + r) >> 1;
build(rt<<1, l, mid);
build(rt<<1|1, mid + 1, r);
}
void update(int rt, int l, int r, int v) {
if (l <= tree[rt].l && r >= tree[rt].r) {
tree[rt].dat = v;
tree[rt].lazy = v;
return;
}
push_down(rt);
int mid = (tree[rt].l + tree[rt].r) >> 1;
if (l <= mid) update(rt<<1, l, r, v);
if (r > mid) update(rt<<1|1, l, r, v);
}
int query(int rt, int x) {
if (tree[rt].l == tree[rt].r) {
return tree[rt].dat;
}
push_down(rt);
int mid = (tree[rt].l + tree[rt].r) >> 1;
if (x <= mid) return query(rt<<1, x);
else return query(rt<<1|1, x);
}
int main()
{
scanf("%d", &t);
for (int cas = 1; cas <= t; ++cas) {
scanf("%d", &n);
tot = 0, root = n * (n + 1) / 2;
for (int i = 1; i <= n; ++i) {
head[i] = 0;
}
int x, y;
for (int i = 1; i < n; ++i) {
scanf("%d%d", &x, &y);
root -= x;
add(y, x);
}
tot = 0;
dfs(root);
build(1, 1, n<<1);
scanf("%d", &m);
printf("Case #%d:\n", cas);
while (m--) {
scanf("%s%d", op, &x);
if (op[0] == ‘C‘) {
printf("%d\n", query(1, L[x]));
}
else if (op[0] == ‘T‘) {
scanf("%d", &y);
update(1, L[x], R[x], y);
}
}
}
return 0;
}
题意:给定一个长度为 n 的序列,有 4 种操作:
1 x y c
[x, y] 上的值全部加 c2 x y c
[x, y] 上的值全部乘 c3 x y c
[x, y] 上的值全部赋为 c4 x y p
[x, y] 上的值的 p 次方和??线段树维护延迟标记 加(add), 乘(mul),以及 sum[i] 表示 i 次方的和,更新时考虑 add、mul 对 sum[i] 的影响
乘法:
加法
其中 len 为当前区间的长度。
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>
using namespace std;
#define debug(x) cout << #x << " is " << x << endl
#define inc(i, a, b) for (int i = a; i <= b; ++i)
typedef long long ll;
const int INF = 0x3f3f3f3f, MOD = 1e4 + 7, N = 1e5 + 5;
struct Node {
int l, r, add, mul;
int sum[4];
void _mul(int v) {
mul = (mul * v) % MOD;
add = (add * v) % MOD;
for (int i = 1; i <= 3; ++i) {
for (int p = 1; p <= i; ++p) {
sum[i] = (sum[i] * v) % MOD;
}
}
}
void _add(int v) {
add = (add + v) % MOD;
int len = r - l + 1;
sum[3] = (sum[3] + 3 * v % MOD * v % MOD * sum[1] % MOD) % MOD;
sum[3] = (sum[3] + 3 * v % MOD * sum[2] % MOD) % MOD;
sum[3] = (sum[3] + len * v % MOD * v % MOD * v % MOD) % MOD;
sum[2] = (sum[2] + 2 * v % MOD * sum[1] % MOD) % MOD;
sum[2] = (sum[2] + len * v % MOD * v % MOD) % MOD;
sum[1] = (sum[1] + len * v % MOD) % MOD;
}
void calc(int MUL, int ADD) {
_mul(MUL);
_add(ADD);
}
}tree[N<<2];
int n, m;
void push_up(int rt) {
for (int i = 1; i <= 3; ++i) {
tree[rt].sum[i] = (tree[rt<<1].sum[i] + tree[rt<<1|1].sum[i]) % MOD;
}
}
void push_down(int rt) {
if (tree[rt].add || tree[rt].mul != 1) {
tree[rt<<1].calc(tree[rt].mul, tree[rt].add);
tree[rt<<1|1].calc(tree[rt].mul, tree[rt].add);
tree[rt].add = 0, tree[rt].mul = 1;
}
}
void build(int rt, int l, int r) {
tree[rt].l = l, tree[rt].r = r;
tree[rt].add = 0, tree[rt].mul = 1;
for (int i = 1; i <= 3; ++i) tree[rt].sum[i] = 0;
if (l == r) return;
int mid = (l + r) >> 1;
build(rt<<1, l, mid);
build(rt<<1|1, mid + 1, r);
}
void update(int rt, int l, int r, int v, int op) {
if (l <= tree[rt].l && r >= tree[rt].r) {
if (op == 1) tree[rt].calc(1, v);
else if (op == 2) tree[rt].calc(v, 0);
else if (op == 3) tree[rt].calc(0, v);
return;
}
push_down(rt);
int mid = (tree[rt].l + tree[rt].r) >> 1;
if (l <= mid) update(rt<<1, l, r, v, op);
if (r > mid) update(rt<<1|1, l, r, v, op);
push_up(rt);
}
int query(int rt, int l, int r, int p) {
if (l <= tree[rt].l && r >= tree[rt].r) return tree[rt].sum[p];
push_down(rt);
int mid = (tree[rt].l + tree[rt].r) >> 1;
int res = 0;
if (l <= mid) res = (res + query(rt<<1, l, r, p)) % MOD;
if (r > mid) res = (res + query(rt<<1|1, l, r, p)) % MOD;
return res;
}
int main()
{
while (scanf("%d%d", &n, &m), n || m) {
build(1, 1, n);
int op, x, y, z;
while (m--) {
scanf("%d%d%d%d", &op, &x, &y, &z);
if (op == 4) {
printf("%d\n", query(1, x, y, z) % MOD);
}
else update(1, x, y, z, op);
}
}
return 0;
}
题意:有 n 个空花瓶 \(0\sim n-1\),m 个操作:1 x y
: 从 x 位置插 y 多花,有花的花瓶跳过,到最后一个花瓶还有剩余,丢弃剩余花;2 x y
: 将区间 \([x,y]\)的花瓶清空。对 1 操作,输出第一个和最后一个插花的位置,如果一朵花都插不了,输出 ‘Can not put any one.‘;对 2 操作,输出区间 \([x,y]\) 内被清空的花瓶数量。
??线段树维护区间空花瓶数 num 和一个延迟标记 tag,对操作 1,判断所求区间空花瓶数大于 0,区间空花瓶递增,可二分找到第一个和最后一个插花位置,将两个位置间 num 置 0;对操作 2,输出总数减空花瓶数,之后区间 num 置为区间长度。
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>
using namespace std;
#define debug(x) cout << #x << " is " << x << endl
#define inc(i, a, b) for (int i = a; i <= b; ++i)
typedef long long ll;
const int INF = 0x3f3f3f3f, N = 5e4 + 5;
struct Node {
int l, r;
int num, tag;
}tree[N<<2];
int t, n, m;
void push_up(int rt) {
tree[rt].num = tree[rt<<1].num + tree[rt<<1|1].num;
}
void push_down(int rt) {
if (~tree[rt].tag) {
tree[rt<<1].tag = tree[rt<<1|1].tag = tree[rt].tag;
int mid = (tree[rt].l + tree[rt].r) >> 1;
tree[rt<<1].num = (mid - tree[rt].l + 1) * tree[rt].tag;
tree[rt<<1|1].num = (tree[rt].r - mid) * tree[rt].tag;
tree[rt].tag = -1;
}
}
void build(int rt, int l, int r) {
tree[rt].l = l, tree[rt].r = r;
tree[rt].num = r - l + 1, tree[rt].tag = -1;
if (l == r) return;
int mid = (l + r) >> 1;
build(rt<<1, l, mid);
build(rt<<1|1, mid + 1, r);
}
void update(int rt, int l, int r, int f) {
if (l <= tree[rt].l && r >= tree[rt].r) {
tree[rt].num = (tree[rt].r - tree[rt].l + 1) * f;
tree[rt].tag = f;
return;
}
push_down(rt);
int mid = (tree[rt].l + tree[rt].r) >> 1;
if (l <= mid) update(rt<<1, l, r, f);
if (r > mid) update(rt<<1|1, l, r, f);
push_up(rt);
}
int query(int rt, int l, int r) {
if (l <= tree[rt].l && r >= tree[rt].r) return tree[rt].num;
push_down(rt);
int mid = (tree[rt].l + tree[rt].r) >> 1;
int res = 0;
if (l <= mid) res += query(rt<<1, l, r);
if (r > mid) res += query(rt<<1|1, l, r);
return res;
}
int search(int x, int num) {
int l = x, r = n;
while (l < r) {
int mid = (l + r) >> 1;
if (query(1, x, mid) >= num) r = mid;
else l = mid + 1;
}
return l;
}
int main()
{
scanf("%d", &t);
while (t--) {
scanf("%d%d", &n, &m);
build(1, 1, n);
int op, x, y;
while (m--) {
scanf("%d%d%d", &op, &x, &y);
x++;
if (op == 1) {
int cnt = query(1, x, n);
if (!cnt) puts("Can not put any one.");
else {
int l = search(x, 1);
int r = search(x, min(cnt, y));
update(1, l, r, 0);
printf("%d %d\n", l - 1, r - 1);
}
}
else if (op == 2) {
y++;
printf("%d\n", y - x + 1 - query(1, x, y));
update(1, x, y, 1);
}
}
puts("");
}
return 0;
}
题意:长度为 n 的区间,m 个操作:D x
: 请求占用长度为 x 的连续区间,返回区间开始位置;N x
: 请求占用长度为 x 的连续区间,如果没找到,可以忽略 D 的请求再寻找;S x y
: 清空 [x, y] 占用部分。
??建 2 棵线段树维护最长连续区间,分别表示只有女神,以及既可以屌丝又可以女神,函数增加表示线段树的参数,注意输出标点符号是英文的。
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>
using namespace std;
#define debug(x) cout << #x << " is " << x << endl
#define inc(i, a, b) for (int i = a; i <= b; ++i)
typedef long long ll;
const int INF = 0x3f3f3f3f, N = 1e5 + 5;
struct Node {
int l, r;
int ll, rl, ml, tag;
inline int length() { return r - l + 1; }
}ds[N<<2], ns[N<<2];
int t, n, m;
char str[10];
void push_up(Node tree[], int rt) {
tree[rt].ll = tree[rt<<1].ll, tree[rt].rl = tree[rt<<1|1].rl;
if (tree[rt].ll == tree[rt<<1].length()) tree[rt].ll += tree[rt<<1|1].ll;
if (tree[rt].rl == tree[rt<<1|1].length()) tree[rt].rl += tree[rt<<1].rl;
tree[rt].ml = max(tree[rt<<1].rl + tree[rt<<1|1].ll, max(tree[rt<<1].ml, tree[rt<<1|1].ml));
}
void push_down(Node tree[], int rt) {
if (~tree[rt].tag) {
tree[rt<<1].tag = tree[rt<<1|1].tag = tree[rt].tag;
tree[rt<<1].ll = tree[rt<<1].rl = tree[rt<<1].ml = tree[rt].tag ? 0 : tree[rt<<1].length();
tree[rt<<1|1].ll = tree[rt<<1|1].rl = tree[rt<<1|1].ml = tree[rt].tag ? 0 : tree[rt<<1|1].length();
tree[rt].tag = -1;
}
}
void build(Node tree[], int rt, int l, int r) {
tree[rt].l = l, tree[rt].r = r;
tree[rt].ll = tree[rt].rl = tree[rt].ml = r - l + 1;
tree[rt].tag = -1;
if (l == r) return;
int mid = (l + r) >> 1;
build(tree, rt<<1, l, mid);
build(tree, rt<<1|1, mid + 1, r);
}
void update(Node tree[], int rt, int l, int r, int v) {
if (l <= tree[rt].l && r >= tree[rt].r) {
tree[rt].tag = v;
tree[rt].ll = tree[rt].rl = tree[rt].ml = v ? 0 : tree[rt].length();
return;
}
push_down(tree, rt);
int mid = (tree[rt].l + tree[rt].r) >> 1;
if (l <= mid) update(tree, rt<<1, l, r, v);
if (r > mid) update(tree, rt<<1|1, l, r, v);
push_up(tree, rt);
}
int query(Node tree[], int rt, int v) {
if (tree[rt].ml < v) return 0;
if (tree[rt].l == tree[rt].r) return tree[rt].l;
push_down(tree, rt);
if (tree[rt<<1].ml >= v) return query(tree, rt<<1, v);
if (tree[rt<<1].rl + tree[rt<<1|1].ll >= v) return tree[rt<<1].r - tree[rt<<1].rl + 1;
return query(tree, rt<<1|1, v);
}
int main()
{
scanf("%d", &t);
for (int cas = 1; cas <= t; ++cas) {
scanf("%d%d", &n, &m);
build(ds, 1, 1, n);
build(ns, 1, 1, n);
printf("Case %d:\n", cas);
int x, y;
while (m--) {
scanf("%s%d", str, &x);
if (str[0] == ‘D‘) {
y = query(ds, 1, x);
if (y) {
printf("%d,let‘s fly\n", y);
update(ds, 1, y, y + x - 1, 1);
}
else puts("fly with yourself");
}
else if (str[0] == ‘N‘) {
y = query(ds, 1, x);
if (y) {
printf("%d,don‘t put my gezi\n", y);
update(ds, 1, y, y + x - 1, 1);
update(ns, 1, y, y + x - 1, 1);
}
else {
y = query(ns, 1, x);
if (y) {
printf("%d,don‘t put my gezi\n", y);
update(ds, 1, y, y + x - 1, 1);
update(ns, 1, y, y + x - 1, 1);
}
else puts("wait for me");
}
}
else if (str[0] == ‘S‘) {
scanf("%d", &y);
update(ds, 1, x, y, 0);
update(ns, 1, x, y, 0);
puts("I am the hope of chinese chengxuyuan!!");
}
}
}
return 0;
}
接下来几题会涉及到扫描线,建议先学习 OIWiki-扫描线
题意:求 n 个矩形的周长并。
??扫描线经典题。线段按 y 升序排序,按照 x 轴建立线段树,线段树维护区间完全覆盖次数 cnt,连续区间个数 num,覆盖长度 len,左右端点是否覆盖 lf、rf。
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>
#include <map>
using namespace std;
#define debug(x) cout << #x << " is " << x << endl
#define inc(i, a, b) for (int i = a; i <= b; ++i)
typedef long long ll;
const int INF = 0x3f3f3f3f, N = 2e4 + 5;
struct Line {
int h, l, r, f;
Line() {}
Line(int h, int l, int r, int f) : h(h), l(l), r(r), f(f) {}
bool operator < (const Line &b) const {
return h < b.h;
}
}line[N];
struct Node {
int l, r, cnt;
int num, len;
bool lf, rf;
}tree[N<<2];
int n, ans, pre;
int x[N];
map<int, int> mp;
void push_up(int rt) {
if (tree[rt].cnt) {
tree[rt].num = tree[rt].lf = tree[rt].rf = 1;
tree[rt].len = x[tree[rt].r+1] - x[tree[rt].l];
}
else if (tree[rt].l == tree[rt].r) tree[rt].len = tree[rt].num = tree[rt].lf = tree[rt].rf = 0;
else {
tree[rt].len = tree[rt<<1].len + tree[rt<<1|1].len;
tree[rt].num = tree[rt<<1].num + tree[rt<<1|1].num;
if (tree[rt<<1].rf && tree[rt<<1|1].lf) --tree[rt].num;
tree[rt].lf = tree[rt<<1].lf;
tree[rt].rf = tree[rt<<1|1].rf;
}
}
void build(int rt, int l, int r) {
tree[rt].l = l, tree[rt].r = r;
tree[rt].cnt = tree[rt].num = tree[rt].len = 0;
if (l == r) return;
int mid = (l + r) >> 1;
build(rt<<1, l, mid);
build(rt<<1|1, mid + 1, r);
}
void update(int rt, int l, int r, int k) {
if (l <= tree[rt].l && r >= tree[rt].r) {
tree[rt].cnt += k;
push_up(rt);
return;
}
int mid = (tree[rt].l + tree[rt].r) >> 1;
if (l <= mid) update(rt<<1, l, r, k);
if (r > mid) update(rt<<1|1, l, r, k);
push_up(rt);
}
int main()
{
scanf("%d", &n);
int x1, y1, x2, y2;
for (int i = 1; i <= n; ++i) {
scanf("%d%d%d%d", &x1, &y1, &x2, &y2);
line[i*2-1] = Line(y1, x1, x2, 1);
line[i*2] = Line(y2, x1, x2, -1);
x[2*i-1] = x1;
x[2*i] = x2;
}
n <<= 1;
sort(line + 1, line + n + 1);
sort(x + 1, x + n + 1);
int m = unique(x + 1, x + n + 1) - (x + 1);
for (int i = 1; i <= m; ++i) mp[x[i]] = i;
build(1, 1, m - 1);
for (int i = 1; i <= n; ++i) {
int l = mp[line[i].l], r = mp[line[i].r] - 1;
update(1, l, r, line[i].f);
ans += abs(tree[1].len - pre);
pre = tree[1].len;
ans += tree[1].num * (line[i+1].h - line[i].h) << 1; // 竖直周长
}
printf("%d\n", ans);
return 0;
}
题意:\(n(1\le n\le1000)\) 个矩形,求覆盖 2 次及以上的矩形面积并。
??稍微修改一下扫描线模板,维护结点被竖直线段完全覆盖次数 cnt,覆盖一次 x 方向长度 len1, 覆盖 2 次及以上 x 方向长度 len2。
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>
#include <map>
using namespace std;
#define debug(x) cout << #x << " is " << x << endl
#define inc(i, a, b) for (int i = a; i <= b; ++i)
typedef long long ll;
const int INF = 0x3f3f3f3f, N = 2005;
struct Line {
double h, l, r;
int f;
Line() {}
Line(double h, double l, double r, int f) : h(h), l(l), r(r), f(f) {}
bool operator < (const Line &b) const {
return h < b.h;
}
}line[N];
struct Node {
int l, r, cnt;
double len1, len2;
}tree[N<<2];
int t, n;
double x[N];
map<double, int> mp;
void push_up(int rt) {
if (tree[rt].cnt > 1) {
tree[rt].len1 = 0;
tree[rt].len2 = x[tree[rt].r+1] - x[tree[rt].l];
}
else if (tree[rt].cnt == 1) {
if (tree[rt].l == tree[rt].r) tree[rt].len2 = 0;
else tree[rt].len2 = tree[rt<<1].len2 + tree[rt<<1].len1 + tree[rt<<1|1].len2 + tree[rt<<1|1].len1;
tree[rt].len1 = (x[tree[rt].r+1] - x[tree[rt].l]) - tree[rt].len2;
}
else {
if (tree[rt].l == tree[rt].r) tree[rt].len1 = tree[rt].len2 = 0;
else {
tree[rt].len1 = tree[rt<<1].len1 + tree[rt<<1|1].len1;
tree[rt].len2 = tree[rt<<1].len2 + tree[rt<<1|1].len2;
}
}
}
void build(int rt, int l, int r) {
tree[rt].l = l, tree[rt].r = r, tree[rt].cnt = 0;
tree[rt].len1 = tree[rt].len2 = 0;
if (l == r) return;
int mid = (l + r) >> 1;
build(rt<<1, l, mid);
build(rt<<1|1, mid + 1, r);
}
void update(int rt, int l, int r, int k) {
if (l <= tree[rt].l && r >= tree[rt].r) {
tree[rt].cnt += k;
push_up(rt);
return;
}
int mid = (tree[rt].l + tree[rt].r) >> 1;
if (l <= mid) update(rt<<1, l, r, k);
if (r > mid) update(rt<<1|1, l, r, k);
push_up(rt);
}
int main()
{
scanf("%d", &t);
while (t--) {
scanf("%d", &n);
double x1, y1, x2, y2;
for (int i = 1; i <= n; ++i) {
scanf("%lf%lf%lf%lf", &x1, &y1, &x2, &y2);
line[i*2-1] = Line(y1, x1, x2, 1);
line[i*2] = Line(y2, x1, x2, -1);
x[i*2-1] = x1;
x[i*2] = x2;
}
n <<= 1;
sort(line + 1, line + n + 1);
sort(x + 1, x + n + 1);
int m = unique(x + 1, x + n + 1) - (x + 1);
for (int i = 1; i <= m; ++i) mp[x[i]] = i;
build(1, 1, m - 1);
double ans = 0;
for (int i = 1; i <= n; ++i) {
int l = mp[line[i].l], r = mp[line[i].r] - 1;
update(1, l, r, line[i].f);
ans += tree[1].len2 * (line[i+1].h - line[i].h);
}
printf("%.2lf\n", ans);
}
return 0;
}
题意:求 \(n(1\le n\le 100)\) 个矩形的面积并。
??看这张别人画的图就明白了
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>
#include <map>
using namespace std;
#define debug(x) cout << #x << " is " << x << endl
#define inc(i, a, b) for (int i = a; i <= b; ++i)
typedef long long ll;
const int INF = 0x3f3f3f3f, N = 105;
struct Line {
double h, l, r;
int f;
Line() {}
Line(double h, double l, double r, int f) : h(h), l(l), r(r), f(f) {}
bool operator < (const Line &b) const {
return h < b.h;
}
}line[N<<1];
struct Node {
int l, r, cnt;
double len;
}tree[N<<3];
int n, cas, tot;
double x[N<<1];
map<double, int> mp;
void push_up(int rt) {
if (tree[rt].cnt) tree[rt].len = x[tree[rt].r+1] - x[tree[rt].l];
else if (tree[rt].l == tree[rt].r) tree[rt].len = 0;
else tree[rt].len = tree[rt<<1].len + tree[rt<<1|1].len;
}
void build(int rt, int l, int r) {
tree[rt].l = l, tree[rt].r = r;
tree[rt].cnt = 0, tree[rt].len = 0;
if (l == r) return;
int mid = (l + r) >> 1;
build(rt<<1, l, mid);
build(rt<<1|1, mid + 1, r);
}
void update(int rt, int l, int r, int k) {
if (l <= tree[rt].l && r >= tree[rt].r) {
tree[rt].cnt += k;
push_up(rt);
return;
}
int mid = (tree[rt].l + tree[rt].r) >> 1;
if (l <= mid) update(rt<<1, l, r, k);
if (r > mid) update(rt<<1|1, l, r, k);
push_up(rt);
}
int main()
{
while (scanf("%d", &n), n) {
double x1, x2, y1, y2;
for (int i = 1; i <= n; ++i) {
scanf("%lf%lf%lf%lf", &x1, &y1, &x2, &y2);
line[i*2-1] = Line(y1, x1, x2, 1);
line[i*2] = Line(y2, x1, x2, -1);
x[2*i-1] = x1;
x[2*i] = x2;
}
n <<= 1;
sort(line + 1, line + n + 1);
sort(x + 1, x + n + 1);
int m = unique(x + 1, x + n + 1) - (x + 1);
for (int i = 1; i <= m; ++i) mp[x[i]] = i;
build(1, 1, m - 1);
double ans = 0;
for (int i = 1; i <= n; ++i) {
int l = mp[line[i].l], r = mp[line[i].r] - 1;
update(1, l, r, line[i].f);
ans += tree[1].len * (line[i+1].h - line[i].h);
}
printf("Test case #%d\nTotal explored area: %.2lf\n\n", ++cas, ans);
}
return 0;
}
题意:\(n(1\le n\le1000)\) 个长方体,求相交 3 次及以上部分的体积。
??\(z\in[-500,500]\),枚举 \(z_i\) 在 \([z_i,z_{i+1})\) 用扫描线转化为二维。
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>
#include <map>
using namespace std;
#define debug(x) cout << #x << " is " << x << endl
#define inc(i, a, b) for (int i = a; i <= b; ++i)
typedef long long ll;
const int INF = 0x3f3f3f3f, N = 2005;
struct Plane {
int y, x1, z1, x2, z2, f;
Plane() {}
Plane(int y, int x1, int z1, int x2, int z2, int f) : y(y), x1(x1), z1(z1), x2(x2), z2(z2), f(f) {}
bool operator < (const Plane &b) const {
return y < b.y;
}
}plane[N], tmp[N];
struct Node {
int l, r, cnt;
int len1, len2, len3;
}tree[N<<2];
int t, n;
int x[N], z[N];
map<int, int> mp;
void push_up(int rt) {
if (tree[rt].cnt) tree[rt].len1 = x[tree[rt].r+1] - x[tree[rt].l];
else if (tree[rt].l == tree[rt].r) tree[rt].len1 = 0;
else tree[rt].len1 = tree[rt<<1].len1 + tree[rt<<1|1].len1;
if (tree[rt].cnt >= 2) tree[rt].len2 = x[tree[rt].r+1] - x[tree[rt].l];
else if (tree[rt].l == tree[rt].r) tree[rt].len2 = 0;
else if (tree[rt].cnt == 1) tree[rt].len2 = tree[rt<<1].len1 + tree[rt<<1|1].len1;
else if (!tree[rt].cnt) tree[rt].len2 = tree[rt<<1].len2 + tree[rt<<1|1].len2;
if (tree[rt].cnt >= 3) tree[rt].len3 = x[tree[rt].r+1] - x[tree[rt].l];
else if (tree[rt].l == tree[rt].r) tree[rt].len3 = 0;
else if (tree[rt].cnt == 2) tree[rt].len3 = tree[rt<<1].len1 + tree[rt<<1|1].len1;
else if (tree[rt].cnt == 1) tree[rt].len3 = tree[rt<<1].len2 + tree[rt<<1|1].len2;
else if (!tree[rt].cnt) tree[rt].len3 = tree[rt<<1].len3 + tree[rt<<1|1].len3;
}
void build(int rt, int l, int r) {
tree[rt].l = l, tree[rt].r = r, tree[rt].cnt = 0;
tree[rt].len1 = tree[rt].len2 = tree[rt].len3 = 0;
if (l == r) return;
int mid = (l + r) >> 1;
build(rt<<1, l, mid);
build(rt<<1|1, mid + 1, r);
}
void update(int rt, int l, int r, int k) {
if (l <= tree[rt].l && r >= tree[rt].r) {
tree[rt].cnt += k;
push_up(rt);
return;
}
int mid = (tree[rt].l + tree[rt].r) >> 1;
if (l <= mid) update(rt<<1, l, r, k);
if (r > mid) update(rt<<1|1, l, r, k);
push_up(rt);
}
int main()
{
scanf("%d", &t);
for (int cas = 1; cas <= t; ++cas) {
scanf("%d", &n);
int x1, x2, y1, y2, z1, z2;
for (int i = 1; i <= n; ++i) {
scanf("%d%d%d%d%d%d", &x1, &y1, &z1, &x2, &y2, &z2);
plane[i*2-1] = Plane(y1, x1, z1, x2, z2, 1);
plane[i*2] = Plane(y2, x1, z1, x2, z2, -1);
x[i*2-1] = x1;
x[i*2] = x2;
z[i*2-1] = z1;
z[i*2] = z2;
}
n <<= 1;
sort(x + 1, x + n + 1);
sort(z + 1, z + n + 1);
int m1 = unique(x + 1, x + n + 1) - (x + 1);
int m2 = unique(z + 1, z + n + 1) - (z + 1);
for (int i = 1; i <= m1; ++i) mp[x[i]] = i;
n >>= 1;
ll ans = 0;
for (int i = 1; i < m2; ++i) {
build(1, 1, m1 - 1);
int tot = 0;
for (int j = 1; j <= n; ++j) {
if (plane[j*2-1].z1 <= z[i] && plane[j*2-1].z2 > z[i]) {
tmp[++tot] = plane[j*2-1];
tmp[++tot] = plane[j*2];
}
}
sort(tmp + 1, tmp + tot + 1);
ll res = 0;
for (int j = 1; j < tot; ++j) {
int l = mp[tmp[j].x1], r = mp[tmp[j].x2] - 1;
update(1, l, r, tmp[j].f);
res += (ll)tree[1].len3 * (tmp[j+1].y - tmp[j].y);
}
ans += res * (z[i+1] - z[i]);
}
printf("Case %d: %lld\n", cas, ans);
}
return 0;
}
标签:初始 延迟标记 最大连续 之间 tin 端点 add geo algo
原文地址:https://www.cnblogs.com/2inf/p/13868482.html