Submission #1157253

#	Time	Username	Problem	Language	Result	Execution time	Memory
1157253		OI_Account	Circle selection (APIO18_circle_selection)	C++17	0 / 100	3112 ms	530116 KiB

circle_selection

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

typedef long long ll;

const int N = 1'000'000;

int n, x[N + 10], y[N + 10], r[N + 10];
int ans[N + 10], id[N + 10], sizeVecX;
int mark[N + 10], cnt[N + 10];
vector<int> vecX, good, fen[4 * N + 10];
vector<pair<int, int>> vec[4 * N + 10];
pair<int, int> p[N + 10];

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

void calcId() {
    sort(p + 1, p + n + 1);
    for (int i = 1; i <= n; i++)
        id[i] = p[i].second;
}

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

void updateFen(int t, int idx, int val) {
    for (; idx <= (int) vec[t].size(); idx += idx & -idx)
        fen[t][idx] += val;
}

void buildFen(int id = 1, int l = 0, int r = sizeVecX) {
    sort(vec[id].begin(), vec[id].end());
    vec[id].resize(unique(vec[id].begin(), vec[id].end()) - vec[id].begin());
    vec[id].shrink_to_fit();
    fen[id].resize((int) vec[id].size() + 1);
    fen[id].shrink_to_fit();
    for (int i = 1; i <= (int) vec[id].size(); i++)
        updateFen(id, i, 1);
    if (l + 1 == r)
        return;
    int mid = (l + r) >> 1;
    buildFen(id << 1, l, mid);
    buildFen(id << 1 | 1, mid, r);
}

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();
}

void delSeg(int idx, pair<int, int> p, int d, int id = 1, int l = 0, int r = sizeVecX) {
    if (idx < l || r <= idx)
        return;
    int x = lower_bound(vec[id].begin(), vec[id].end(), p) - vec[id].begin();
    if (x + 1 < (int) vec[id].size() && vec[id][x + 1] == p && d == 1)
        x++;
    updateFen(id, x + 1, -1);
    if (l + 1 == r)
        return;
    int mid = (l + r) >> 1;
    delSeg(idx, p, d, id << 1, l, mid);
    delSeg(idx, p, d, id << 1 | 1, mid, r);
}

void delPoint(int 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;
            delSeg(getIdx(nx), {ny, idx}, i);
        }
}

int getFen(int t, int idx) {
    int res = 0;
    for (; idx; idx -= idx & -idx)
        res += fen[t][idx];
    return res;
}

int getIdxFen(int t, int k) {
    int idx = 0, m = 32 - __builtin_clz((int) vec[t].size());
    for (int j = m; j >= 0; j--)
        if (idx + (1 << j) <= (int) vec[t].size() && fen[t][idx + (1 << j)] < k) {
            idx += (1 << j);
            k -= fen[t][idx];
        }
    return idx + 1;
}

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;
    while (x <= (int) vec[id].size()) {
        x = getIdxFen(id, getFen(id, x - 1) + 1);
        if (x == (int) fen[id].size() || vec[id][x - 1].first > r)
            break;
        good.push_back(vec[id][x - 1].second);
        x++;
    }
}

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;
            cnt[x]++;
        }
    for (auto x: good)
        mark[x] = false;
}

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

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

int main() {
    ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
    readInput();
    calcId();
    calcVecX();
    initSeg();
    solve();
    writeOutput();
    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: 0 / 7
• Subtask 2: 0 / 12
• Subtask 3: 0 / 15
• Subtask 4: 0 / 23
• Subtask 5: 0 / 30
• Subtask 6: 0 / 13