2019牛客暑期多校訓練營(第八場) Distance
題意: 給你一個 的空間,每次插入一個點,或者詢問空間中點到這一點的最小曼哈頓距離。
題解:
1.HASH+三維BIT
三維BIT,對於這種寫法,太巨了, 特麼直接用三維BIT 存一下就可以了,枚舉八個方向,把絕對值去掉,然後最牛的還是hash
處理,把三維壓縮成一維,削常數,我特麼卡常卡成這樣也是少見。
這種hash
將維度,枚舉八個方向去絕對值,數組數組模擬空間,還是挺6的
#include "bits/stdc++.h"
using namespace std;
typedef long long LL;
typedef unsigned long long uLL;
typedef pair<int, int> P;
#define VNAME(value) (#value)
#define bug printf("*********\n");
#define debug(x) cout<<"["<<VNAME(x)<<" = "<<x<<"]"<<endl;
#define mid ((l + r) >> 1)
#define chl 2 * k + 1
#define chr 2 * k + 2
#define lson l, mid, chl
#define rson mid + 1, r, chr
#define eb(x) emplace_back(x)
#define pb(x) emplace_back(x)
#define mem(a, b) memset(a, b, sizeof(a));
const LL mod = (LL) 1e9 + 7;
const int maxn = (int) 1e6 + 5;
const LL INF = 0x7fffffff;
const LL inf = 0x3f3f3f3f;
const double eps = 1e-8;
#ifndef ONLINE_JUDGE
clock_t prostart = clock();
#endif
void f() {
#ifndef ONLINE_JUDGE
freopen("../data.in", "r", stdin);
#endif
}
//typedef __int128 LLL;
template<typename T>
void read(T &w) {//讀入
char c;
while (!isdigit(c = getchar()));
w = c & 15;
while (isdigit(c = getchar()))
w = w * 10 + (c & 15);
}
template<typename T>
void output(T x) {
if (x < 0)
putchar('-'), x = -x;
int ss[55], sp = 0;
do
ss[++sp] = x % 10;
while (x /= 10);
while (sp)
putchar(48 + ss[sp--]);
}
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<VVI> VVVI;
struct BIT {
int n, m, h;
int a[maxn];
void init(int n, int m, int h) {
this->n = n;
this->m = m;
this->h = h;
mem(a, -inf);
}
int get(int x, int y, int z) {
return x * h * m + y * h + z;
}
int lowbit(int &x) {
return x & (-x);
}
void add(int x, int y, int z, int t) {
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)) a[get(i, j, k)] = max(a[get(i, j, k)], t);
}
int sum(int x, int y, int z) {
int res = -inf;
for (int i = x; i; i -= lowbit(i))
for (int j = y; j; j -= lowbit(j))
for (int k = z; k; k -= lowbit(k))
res = max(a[get(i, j, k)], res);
return res;
}
} b[8];
int get_pos(int x, int pos) {
return (x >> pos) & 1;
}
int main() {
f();
int n, m, h, q;
int op;
read(n);
read(m);
read(h);
read(q);
for (int i = 0; i < 8; i++) {
b[i].init(n, m, h);
}
int d[] = {n + 1, m + 1, h + 1};
int a[3], c[3];
while (q--) {
read(op);
read(a[0]);
read(a[1]);
read(a[2]);
if (op == 1) {
for (int i = 0; i < 8; i++) {
c[0] = get_pos(i, 0) ? d[0] - a[0] : a[0];
c[1] = get_pos(i, 1) ? d[1] - a[1] : a[1];
c[2] = get_pos(i, 2) ? d[2] - a[2] : a[2];
b[i].add(c[0], c[1], c[2], c[1] + c[2] + c[0]);
}
} else {
int ans = inf;
for (int i = 0; i < 8; i++) {
c[0] = get_pos(i, 0) ? d[0] - a[0] : a[0];
c[1] = get_pos(i, 1) ? d[1] - a[1] : a[1];
c[2] = get_pos(i, 2) ? d[2] - a[2] : a[2];
ans = min(ans, c[0] + c[1] + c[2] - b[i].sum(c[0], c[1], c[2]));
}
output(ans);
puts("");
}
}
#ifndef ONLINE_JUDGE
cout << "運行時間:" << 1.0 * (clock() - prostart) / CLOCKS_PER_SEC << " s" << endl;
#endif
return 0;
}
2.分塊+bfs
第二種寫法就更騷了Orz,對於 組查詢,分成 塊,每次插入一個點,先判斷有沒有個,少於這個數量,直接暴力找,假設就算每次都是滿的都是 的複雜度,然後如果滿了,直接空間中bfs
,比如說你插入了兩個點,0,0,1
0,0,2
,直接暴力bfs
,枚舉6
個方向,找離這個點最近的距離是多少。暴力枚舉空間複雜度是.總複雜度就是 .
** 這種分塊更新的操作,學不來,學不來,根本學不來。 **
#include "bits/stdc++.h"
using namespace std;
typedef long long LL;
typedef unsigned long long uLL;
typedef pair<int, int> P;
#define VNAME(value) (#value)
#define bug printf("*********\n");
#define debug(x) cout<<"["<<VNAME(x)<<" = "<<x<<"]"<<endl;
#define mid ((l + r) >> 1)
#define chl 2 * k + 1
#define chr 2 * k + 2
#define lson l, mid, chl
#define rson mid + 1, r, chr
#define eb(x) emplace_back(x)
#define pb(x) emplace_back(x)
#define mem(a, b) memset(a, b, sizeof(a));
const LL mod = (LL) 1e9 + 7;
const int maxn = (int) 1e6 + 5;
const LL INF = 0x7fffffff;
const LL inf = 0x3f3f3f3f;
const double eps = 1e-8;
#ifndef ONLINE_JUDGE
clock_t prostart = clock();
#endif
void f() {
#ifndef ONLINE_JUDGE
freopen("../data.in", "r", stdin);
#endif
}
//typedef __int128 LLL;
template<typename T>
void read(T &w) {//讀入
char c;
while (!isdigit(c = getchar()));
w = c & 15;
while (isdigit(c = getchar()))
w = w * 10 + (c & 15);
}
template<typename T>
void output(T x) {
if (x < 0)
putchar('-'), x = -x;
int ss[55], sp = 0;
do
ss[++sp] = x % 10;
while (x /= 10);
while (sp)
putchar(48 + ss[sp--]);
}
int a[maxn];
int dir[6][3] = {{1, 0, 0},
{-1, 0, 0},
{0, 1, 0},
{0, -1, 0},
{0, 0, 1},
{0, 0, -1}};
int X[maxn], Y[maxn], Z[maxn];
int lx, ly, lz;
int n, m, h, q;
int get(int x, int y, int z) {
return x * h * m + y * h + z;
}
struct node {
int k, x, y, z;
node(int x, int y, int z) {
this->x = x;
this->y = y;
this->z = z;
this->k = get(x, y, z);
}
};
void rebuild() {
queue<node> que;
for (int i = 0; i < lx; i++) {
que.push(node(X[i], Y[i], Z[i]));
a[get(X[i], Y[i], Z[i])] = 0;
}
while (que.size()) {
node t = que.front();
que.pop();
for (int i = 0; i < 6; i++) {
int tox = t.x + dir[i][0], toy = t.y + dir[i][1],
toz = t.z + dir[i][2];
if (tox < 0 || tox >= n || toy < 0 || toy >= m || toz < 0 || toz >= h) continue;
int k = get(tox, toy, toz);
if (a[k] > a[t.k] + 1) {
a[k] = a[t.k] + 1;
que.push(node(tox, toy, toz));
}
}
}
lx = 0;
ly = 0;
lz = 0;
}
int op, x, y, z;
int main() {
f();
mem(a, inf);
read(n);
read(m);
read(h);
read(q);
while (q--) {
read(op);
read(x);
read(y);
read(z);
--x, --y, --z;
if (op == 1) {
X[lx++] = x;
Y[ly++] = y;
Z[lz++] = z;
} else {
int k = get(x, y, z);
int ans = a[k];
for (int i = 0; i < lx; i++) {
ans = min(ans, abs(x - X[i]) + abs(z - Z[i]) + abs(y - Y[i]));
}
output(ans);
puts("");
}
if (lx == 300) {
rebuild();
}
}
#ifndef ONLINE_JUDGE
cout << "運行時間:" << 1.0 * (clock() - prostart) / CLOCKS_PER_SEC << " s" << endl;
#endif
return 0;
}