Distance(2019年牛客多校第八场D题+CDQ+树状数组)
题目链接
思路
这个题在\(BZOJ\)上有个二维平面的版本(\(BZOJ2716\)天使玩偶)，不过是权限题因此就不附带链接了，我也只是在算法进阶指南上看到过，那个题的写法是\(CDQ\)，然后比赛开始半个小时我就开始写\(CDQ\)，\(T\)了之后冷静分析发现复杂度我少算了个\(log\)，\(CDQ\)写这题的复杂度是\(nlog^3(n)\)，然后就没思路了。
赛后看\(qls\)说用三维\(bit\)可以过后试了一下\(T\)了，然后发现\(qls\)的代码当时跑了\(937ms\)应该是卡过去的，感觉是\(vector\)常数大，但是想不出除\(vector\)的其他动态开全局数组大小的方法，最后疯狂交在\(T\)了一页后成功卡过去了，下面贴一下三维\(bit\)的代码和\(CDQ\)写法(对拍了很久貌似没问题，就当过了吧~)的代码。
这两份代码的主体思路就是拆绝对值符号，然后查询时(拿\(x_1\leq x2,y_1\leq y2,z_1\leq z_2\)举例，下标为\(2\)的是查询的点)\(|x_2-x_1|+|y_2-y_1|+|z_2-z_1|=(x_2+y_2+z_2)-(x_1+y_1+z_1)\)，然后就是要查询\(x_1+y_1+z_1\)的最大值用树状数组维护即可，其他情况分别移动坐标即可。
update:发现题解里面贴的那份代码的三维\(bit\)写法贼牛逼，贴的代码就改成看了那个队的代码之后写的了。
代码
//三维bit
#include <set>
#include <map>
#include <deque>
#include <queue>
#include <stack>
#include <cmath>
#include <ctime>
#include <bitset>
#include <cstdio>
#include <string>
#include <vector>
#include <cassert>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
typedef long long LL;
typedef pair<LL, LL> pLL;
typedef pair<LL, int> pLi;
typedef pair<int, LL> pil;;
typedef pair<int, int> pii;
typedef unsigned long long uLL;
#define lson rt<<1
#define rson rt<<1|1
#define lowbit(x) x&(-x)
#define name2str(name) (#name)
#define bug printf("*********\n")
#define debug(x) cout<<#x"=["<<x<<"]" <<endl
#define FIN freopen("/home/dillonh/CLionProjects/Dillonh/in.txt","r",stdin)
#define IO ios::sync_with_stdio(false),cin.tie(0)
const double eps = 1e-8;
const int mod = 1000000007;
const int maxn = 800000 + 7;
const double pi = acos(-1);
const int inf = 0x3f3f3f3f;
const LL INF = 0x3f3f3f3f3f3f3f3fLL;
int n, m, h, q, op, x, y, z;
struct BIT {
int a[maxn];
int gethash(int x, int y, int z) {
return x * h * m + y * h + z;
}
void init() {
for(int i = 0; i <= n; ++i) {
for(int j = 0; j <= m; ++j) {
for(int k = 0; k <= h; ++k) {
a[gethash(i, j, k)] = 0;
}
}
}
}
void update(int x, int y, int z) {
for(int i = x; i <= n; i += lowbit(i)) {
for(int j = y; j <= m; j += lowbit(j)) {
for(int k = z; k <= h; k += lowbit(k)) {
int num = gethash(i, j, k);
a[num] = max(a[num], x + y + z);
}
}
}
}
int query(int x, int y, int z) {
int ans = 0;
for(int i = x; i > 0; i -= lowbit(i)) {
for(int j = y; j > 0; j -= lowbit(j)) {
for(int k = z; k > 0; k -= lowbit(k)) {
ans = max(ans, a[gethash(i, j, k)]);
}
}
}
if(ans == 0) return inf;
return x + y + z - ans;
}
}bit[8];
int main() {
scanf("%d%d%d%d", &n, &m, &h, &q);
n += 1, m += 1, h += 1;
for(int i = 0; i < 8; ++i) bit[i].init();
for(int i = 1; i <= q; ++i) {
scanf("%d%d%d%d", &op, &x, &y, &z);
if(op == 1) {
bit[1].update(x, y, z);
bit[2].update(x, y, h - z);
bit[3].update(x, m - y, z);
bit[4].update(n - x, y, z);
bit[5].update(n - x, m - y, z);
bit[6].update(n - x, y, h - z);
bit[7].update(x, m - y, h - z);
bit[0].update(n - x, m - y, h - z);
} else {
int ans = inf;
ans = min(ans, bit[1].query(x, y, z));
ans = min(ans, bit[2].query(x, y, h - z));
ans = min(ans, bit[3].query(x, m - y, z));
ans = min(ans, bit[4].query(n - x, y, z));
ans = min(ans, bit[5].query(n - x, m - y, z));
ans = min(ans, bit[6].query(n - x, y, h - z));
ans = min(ans, bit[7].query(x, m - y, h - z));
ans = min(ans, bit[0].query(n - x, m - y, h - z));
printf("%d\n", ans);
}
}
return 0;
}
//CDQ
#include <set>
#include <map>
#include <deque>
#include <queue>
#include <stack>
#include <cmath>
#include <ctime>
#include <bitset>
#include <cstdio>
#include <string>
#include <vector>
#include <cassert>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
typedef long long LL;
typedef pair<LL, LL> pLL;
typedef pair<LL, int> pLi;
typedef pair<int, LL> pil;;
typedef pair<int, int> pii;
typedef unsigned long long uLL;
#define lson rt<<1
#define rson rt<<1|1
#define lowbit(x) x&(-x)
#define name2str(name) (#name)
#define bug printf("*********\n")
#define debug(x) cout<<#x"=["<<x<<"]" <<endl
#define FIN freopen("/home/dillonh/CLionProjects/Dillonh/in.txt","r",stdin)
#define IO ios::sync_with_stdio(false),cin.tie(0)
const double eps = 1e-8;
const int mod = 1000000007;
const int maxn = 100001;
const double pi = acos(-1);
const int inf = 0x3f3f3f3f;
const LL INF = 0x3f3f3f3f3f3f3f3fLL;
int n, m, h, q, op, x, y, z;
int tree[maxn], ans[maxn];
struct node {
int id, x, y, z, op, val, flag;
bool operator < (const node& a) const {
return id < a.id;
}
}a[maxn], tmp[maxn], pp[maxn];
void add(int x, int val) {
while(x <= h) {
tree[x] = max(tree[x], val);
x += lowbit(x);
}
}
int query(int x) {
int ans = 0;
while(x) {
ans = max(ans, tree[x]);
x -= lowbit(x);
}
if(ans == 0) ans = -inf;
return ans;
}
void del(int x) {
while(x <= h + 1) {
tree[x] = 0;
x += lowbit(x);
}
}
void cdq2(int l, int r) {
if(l == r) return;
int mid = (l + r) >> 1;
cdq2(l, mid), cdq2(mid + 1, r);
int ls = l, rs = mid + 1, cnt = l;
for(; rs <= r; ++rs) {
for(; ls <= mid && tmp[ls].y <= tmp[rs].y; ++ls) {
if(tmp[ls].op == 1 && tmp[ls].flag) {
add(tmp[ls].z, tmp[ls].val);
}
}
if(!tmp[rs].flag && tmp[rs].op == 2) ans[tmp[rs].id] = min(ans[tmp[rs].id], tmp[rs].val - query(tmp[rs].z));
}
--ls;
while(ls >= l) {
if(tmp[ls].op == 1 && tmp[ls].flag) {
del(tmp[ls].z);
}
--ls;
}
ls = l, rs = mid + 1;
while(ls <= mid && rs <= r) {
if(tmp[ls].y < tmp[rs].y) {
pp[cnt++] = tmp[ls++];
} else if(tmp[ls].y > tmp[rs].y) {
pp[cnt++] = tmp[rs++];
} else if(tmp[ls].z <= tmp[rs].z) {
pp[cnt++] = tmp[ls++];
} else {
pp[cnt++] = tmp[rs++];
}
}
while(ls <= mid) pp[cnt++] = tmp[ls++];
while(rs <= r) pp[cnt++] = tmp[rs++];
for(int i = l; i <= r; ++i) tmp[i] = pp[i];
}
void cdq1(int l, int r) {
if(l == r) return;
int mid = (l + r) >> 1;
cdq1(l, mid), cdq1(mid + 1, r);
int ls = l, rs = mid + 1, cnt = l;
while(ls <= mid && rs <= r) {
if(a[ls].x < a[rs].x) {
tmp[cnt] = a[ls++];
tmp[cnt++].flag = 1;
} else if(a[ls].x > a[rs].x) {
tmp[cnt] = a[rs++];
tmp[cnt++].flag = 0;
} else if(a[ls].y < a[rs].y) {
tmp[cnt] = a[ls++];
tmp[cnt++].flag = 1;
} else if(a[ls].y > a[rs].y) {
tmp[cnt] = a[rs++];
tmp[cnt++].flag = 0;
} else if(a[ls].z <= a[rs].z) {
tmp[cnt] = a[ls++];
tmp[cnt++].flag = 1;
} else {
tmp[cnt] = a[rs++];
tmp[cnt++].flag = 0;
}
}
while(ls <= mid) {
tmp[cnt] = a[ls++];
tmp[cnt++].flag = 1;
}
while(rs <= r) {
tmp[cnt] = a[rs++];
tmp[cnt++].flag = 0;
}
for(int i = l; i <= r; ++i) a[i] = tmp[i];
cdq2(l, r);
}
int main() {
#ifndef ONLINE_JUDGE
FIN;
#endif
scanf("%d%d%d%d", &n, &m, &h, &q);
n += 1, m += 1, h += 1;
for(int i = 1; i <= q; ++i) {
scanf("%d%d%d%d", &op, &x, &y, &z);
a[i] = {i, x, y, z, op, 0, 0};
}
//x,y,z
for(int i = 1; i <= q; ++i) {
ans[i] = inf;
a[i].val = a[i].x + a[i].y + a[i].z, a[i].flag = 0;
}
cdq1(1, q);
//x,y,-z
for(int i = 1; i <= q; ++i) {
a[i].z = h - a[i].z;
a[i].val = a[i].x + a[i].y + a[i].z, a[i].flag = 0;
}
sort(a + 1, a + q + 1);
cdq1(1, q);
//x,-y,z
for(int i = 1; i <= q; ++i) {
a[i].z = h - a[i].z;
a[i].y = m - a[i].y;
a[i].val = a[i].x + a[i].y + a[i].z, a[i].flag = 0;
}
sort(a + 1, a + q + 1);
cdq1(1, q);
//-x,y,z
for(int i = 1; i <= q; ++i) {
a[i].y = m - a[i].y;
a[i].x = n - a[i].x;
a[i].val = a[i].x + a[i].y + a[i].z, a[i].flag = 0;
}
sort(a + 1, a + q + 1);
cdq1(1, q);
//-x,-y,z
for(int i = 1; i <= q; ++i) {
a[i].y = m - a[i].y;
a[i].val = a[i].x + a[i].y + a[i].z, a[i].flag = 0;
}
sort(a + 1, a + q + 1);
cdq1(1, q);
//-x,y,-z
for(int i = 1; i <= q; ++i) {
a[i].y = m - a[i].y;
a[i].z = h - a[i].z;
a[i].val = a[i].x + a[i].y + a[i].z, a[i].flag = 0;
}
sort(a + 1, a + q + 1);
cdq1(1, q);
//x,-y,-z
for(int i = 1; i <= q; ++i) {
a[i].x = n - a[i].x;
a[i].y = m - a[i].y;
a[i].val = a[i].x + a[i].y + a[i].z, a[i].flag = 0;
}
sort(a + 1, a + q + 1);
cdq1(1, q);
//-x,-y,-z
for(int i = 1; i <= q; ++i) {
a[i].x = n - a[i].x;
a[i].val = a[i].x + a[i].y + a[i].z, a[i].flag = 0;
}
sort(a + 1, a + q + 1);
cdq1(1, q);
sort(a + 1, a + q + 1);
for(int i = 1; i <= q; ++i) {
if(a[i].op == 2) {
printf("%d\n", ans[i]);
}
}
return 0;
}
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