Submission #1157380

#	Time	Username	Problem	Language	Result	Execution time	Memory
1157380		OI_Account	Circle selection (APIO18_circle_selection)	C++17	49 / 100	3116 ms	1016164 KiB

circle_selection

#pragma GCC optimize("O2,unroll-loops,Ofast")
#include <bits/stdc++.h>
using namespace std;

typedef long long ll;

const int N = 600'000;

int n, x[N / 2 + 10], y[N / 2 + 10], r[N / 2 + 10];
int ans[N / 2 + 10],  sizeVecX, cntPnt[N / 2 + 10];
bool mark[N / 2 + 10];
vector<int> vecX, good, nxt[4 * N + 10], lst[4 * N + 10], par[4 * N + 10];
vector<pair<int, int>> vec[4 * N + 10], pnt[N / 2 + 10];
pair<int, int> p[N + 10];

void calcVecX() {
    for (int i = 1; i <= n; i++) {
        vecX.push_back(x[i] - r[i]);
        vecX.push_back(x[i] + r[i]);
    }
    sort(vecX.begin(), vecX.end());
    vecX.resize(unique(vecX.begin(), vecX.end()) - vecX.begin());
    sizeVecX = (int) vecX.size();
}

int getIdx(int x) {
    return lower_bound(vecX.begin(), vecX.end(), x) - vecX.begin();
}

void addToSeg(int idx, pair<int, int> p, int id = 1, int l = 0, int r = sizeVecX) {
    if (idx < l || r <= idx)
        return;
    if (l + 1 == r) {
        vec[id].push_back(p);
        return;
    }
    int mid = (l + r) >> 1;
    addToSeg(idx, p, id << 1, l, mid);
    addToSeg(idx, p, id << 1 | 1, mid, r);
}

void calcVecId(int id, vector<pair<int, int>> &x, vector<pair<int, int>> &y) {
    vec[id].resize((int) (x.size() + y.size()));
    merge(x.begin(), x.end(), y.begin(), y.end(), vec[id].begin());
}

void calcPnt(int id) {
    for (int i = 0; i < vec[id].size(); i++)
        cntPnt[vec[id][i].second]++;
}

void buildFen(int id = 1, int l = 0, int r = sizeVecX) {
    if (l + 1 == r) {
        sort(vec[id].begin(), vec[id].end());
        vec[id].shrink_to_fit();
        nxt[id].resize((int) vec[id].size() + 1);
        lst[id].resize((int) vec[id].size() + 1);
        par[id].resize((int) vec[id].size() + 1);
        for (int i = 1; i <= (int) vec[id].size(); i++) {
            par[id][i] = i;
            lst[id][i] = i - 1;
            nxt[id][i] = (i < (int) vec[id].size()? i + 1: 0);
        }
        calcPnt(id);
        return;
    }
    int mid = (l + r) >> 1;
    buildFen(id << 1, l, mid);
    buildFen(id << 1 | 1, mid, r);
    calcVecId(id, vec[id << 1], vec[id << 1 | 1]);
    nxt[id].resize((int) vec[id].size() + 1);
    lst[id].resize((int) vec[id].size() + 1);
    par[id].resize((int) vec[id].size() + 1);
    for (int i = 1; i <= (int) vec[id].size(); i++) {
        par[id][i] = i;
        lst[id][i] = i - 1;
        nxt[id][i] = (i < (int) vec[id].size()? i + 1: 0);
    }
    calcPnt(id);
}

void initSeg() {
    for (int idx = 1; idx <= n; idx++) {
        for (int i = -1; i <= 1; i += 2)
            for (int j = -1; j <= 1; j += 2) {
                int nx = x[idx] + r[idx] * i;
                int ny = y[idx] + r[idx] * j;
                addToSeg(getIdx(nx), {ny, idx});
            }
    }
    buildFen();
    for (int i = 1; i <= n; i++)
        pnt[i].reserve(cntPnt[i]);
    for (int id = 1; id <= 4 * sizeVecX - 5; id++)
        for (int i = 0; i < vec[id].size(); i++)
            pnt[vec[id][i].second].push_back({id, i + 1});
}

void delPoint(int idx) {
    for (auto [id, x]: pnt[idx]) {
        int f = lst[id][x], g = nxt[id][x];
        if (f)
            nxt[id][f] = g;
        if (g)
            lst[id][g] = f;
        par[id][x] = nxt[id][x];
    }
}

int getPar(int id, int u) {
    auto p = par[id];
    int pnt = u, last;
    while (p[pnt] != pnt)
        pnt = p[pnt];
    while (u != pnt) {
        last = p[u];
        p[u] = pnt;
        u = last;
    }
    return pnt;
}

void check(int id, int l, int r) {
    int x = lower_bound(vec[id].begin(), vec[id].end(), make_pair(l, 0)) - vec[id].begin() + 1;
    if (x > (int) vec[id].size())
        return;
    x = getPar(id, x);
    auto nx = nxt[id];
    for(; x && vec[id][x - 1].first <= r; x = nx[x])
        good.push_back(vec[id][x - 1].second);
}

void get(int st, int en, int x, int y, int id = 1, int l = 0, int r = sizeVecX) {
    if (en <= l || r <= st)
        return;
    if (st <= l && r <= en) {
        check(id, x, y);
        return;
    }
    int mid = (l + r) >> 1;
    get(st, en, x, y, id << 1, l, mid);
    get(st, en, x, y, id << 1 | 1, mid, r);
}

bool isGood(int &i, int &j) {
    ll dx = x[i] - x[j], dy = y[i] - y[j];
    return dx * dx + dy * dy <= (ll) (r[i] + r[j]) * (r[i] + r[j]);
}

void newPoint(int idx) {
    good.clear();
    get(getIdx(x[idx] - r[idx]), getIdx(x[idx] + r[idx]) + 1, y[idx] - r[idx], y[idx] + r[idx]);
    for (auto x: good)
        if (!mark[x]) {
            if (isGood(x, idx)) {
                ans[x] = idx;
                delPoint(x);
            }
            mark[x] = true;
        }
    for (auto x: good)
        mark[x] = false;
}

void solve() {
    for (int i = 1; i <= n; i++) {
        int x = p[i].second;
        if (!ans[x])
            newPoint(x);
    }
}

void writeOutput() {
    for (int i = 1; i <= n; i++)
        cout << ans[i] << ' ';
    cout.flush();
}

void readInput() {
    cin >> n;
    for (int i = 1; i <= n; i++) {
        cin >> x[i] >> y[i] >> r[i];
        p[i] = {-r[i], i};
    }
    sort(p + 1, p + n + 1);
}

void readInput2() {
    n = N / 2;
    for (int i = 1; i <= n; i++) {
        x[i] = i;
        y[i] = i + 1;
        r[i] = 1;
        p[i] = {-r[i], i};
    }
    sort(p + 1, p + n + 1);
}

int main() {
    ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
    readInput();
    calcVecX();
    initSeg();
    solve();
    writeOutput();
    //cout << clock() << endl;
    return 0;
}

/*
11
9 9 2
13 2 1
11 8 2
3 3 2
3 12 1
12 14 1
9 8 5
2 8 2
5 2 1
14 4 2
14 14 1
*/

• Subtask 1: 7 / 7
• Subtask 2: 12 / 12
• Subtask 3: 0 / 15
• Subtask 4: 0 / 23
• Subtask 5: 30 / 30
• Subtask 6: 0 / 13