Fire in the City

二分答案， 用掃描先加線段樹去check

#include<bits/stdc++.h>
#define LL long long
#define LD long double
#define ull unsigned long long
#define fi first
#define se second
#define mk make_pair
#define PLL pair<LL, LL>
#define PLI pair<LL, int>
#define PII pair<int, int>
#define
 
 SZ(x) ((int)x.size())
#define ALL(x) (x).begin(), (x).end()
#define fio ios::sync_with_stdio(false); cin.tie(0);

using namespace std;

const int N = 2e5 + 7;
const int inf = 0x3f3f3f3f;
const LL INF = 0x3f3f3f3f3f3f3f3f;
const int mod = 998244353;
const double eps = 1e-8;
const double PI = acos(-1
 
);

template<class T, class S> inline void add(T& a, S b) {a += b; if(a >= mod) a -= mod;}
template<class T, class S> inline void sub(T& a, S b) {a -= b; if(a < 0) a += mod;}
template<class T, class S> inline bool chkmax(T& a, S b) {return a < b ? a = b, true
 
 : false;}
template<class T, class S> inline bool chkmin(T& a, S b) {return a > b ? a = b, true : false;}

vector<int> oo, gg;

int getPos(int x) {
    return lower_bound(ALL(oo), x) - oo.begin() + 1;
}

namespace SGT {
#define lson l, mid, rt << 1
#define rson mid + 1, r, rt << 1 | 1
    int a[N << 2], lazy[N << 2];
    inline void push(int rt) {
        if(lazy[rt]) {
            a[rt << 1] += lazy[rt];
            a[rt << 1 | 1] += lazy[rt];
            lazy[rt << 1] += lazy[rt];
            lazy[rt << 1 | 1] += lazy[rt];
            lazy[rt] = 0;
        }
    }
    void build(int l, int r, int rt) {
        a[rt] = lazy[rt] = 0;
        if(l == r) return;
        int mid = l + r >> 1;
        build(lson); build(rson);
    }
    void update(int L, int R, int v, int l, int r, int rt) {
        if(R < l || r < L) return;
        if(L <= l && r <= R) {
            a[rt] += v;
            lazy[rt] += v;
            return;
        }
        push(rt);
        int mid = l + r >> 1;
        update(L, R, v, lson);
        update(L, R, v, rson);
        a[rt] = min(a[rt << 1], a[rt << 1 | 1]);
    }
    int getMinId(int l, int r, int rt) {
        if(a[rt] > 0) return -1;
        if(l == r) return oo[l - 1];
        push(rt);
        int mid = l + r >> 1;
        if(a[rt << 1] == 0) return getMinId(lson);
        else return getMinId(rson);
    }
    int getMaxId(int l, int r, int rt) {
        if(a[rt] > 0) return -1;
        if(l == r) return oo[l] - 1;
        push(rt);
        int mid = l + r >> 1;
        if(a[rt << 1 | 1] == 0) return getMaxId(rson);
        else return getMaxId(lson);
    }
}


struct Point {
    Point(int x = 0, int y = 0) : x(x), y(y) {}
    int x, y;
};

struct Rec {
    Point a, b;
};

Rec mergeRec(const Rec& lhs, const Rec& rhs) {
    Rec ans;
    ans.a.x = max(lhs.a.x, rhs.a.x);
    ans.a.y = max(lhs.a.y, rhs.a.y);
    ans.b.x = min(lhs.b.x, rhs.b.x);
    ans.b.y = min(lhs.b.y, rhs.b.y);
    return ans;
}
inline bool ok(const Rec& r) {
    return r.a.x <= r.b.x && r.a.y <= r.b.y;
}

int n, m, k;
Point a[N];
vector<Rec> vc, tmp;

inline void go(Rec& now, Point p, int T) {
    now = mergeRec(now, Rec{Point(p.x - T, p.y - T), Point(p.x + T, p.y + T)});
}

bool check(int T) {
    oo.clear(); gg.clear();
    gg.push_back(1); gg.push_back(m + 1);
    oo.push_back(1); oo.push_back(n + 1);
    for(int i = 1; i <= k; i++) {
        oo.push_back(max(1, a[i].x - T));
        oo.push_back(min(n + 1, a[i].x + T + 1));
        gg.push_back(max(1, a[i].y - T));
        gg.push_back(min(m + 1, a[i].y + T + 1));
    }
    sort(oo.begin(), oo.end());
    oo.erase(unique(ALL(oo)), oo.end());
    sort(gg.begin(), gg.end());
    gg.erase(unique(ALL(gg)), gg.end());
    SGT::build(1, SZ(oo) - 1, 1);
    Rec now = Rec{Point(1, 1), Point(n, m)};
    for(int i = 0; i < SZ(gg); i++) {
        if(i > 0) {
            int mnx = SGT::getMinId(1, SZ(oo) - 1, 1);
            int mxx = SGT::getMaxId(1, SZ(oo) - 1, 1);
            if(~mnx) {
                go(now, Point(mnx, gg[i - 1]), T);
                go(now, Point(mnx, gg[i] - 1), T);
                go(now, Point(mxx, gg[i - 1]), T);
                go(now, Point(mxx, gg[i] - 1), T);
            }
        }
        if(i == SZ(gg) - 1) break;
        for(int j = 1; j <= k; j++) {
            if(max(1, a[j].y - T) == gg[i]) {
                SGT::update(getPos(max(1, a[j].x - T)), getPos(min(n + 1, a[j].x + T + 1)) - 1, 1, 1, SZ(oo) - 1, 1);
            }
            if(min(m + 1, a[j].y + T + 1) == gg[i]) {
                SGT::update(getPos(max(1, a[j].x - T)), getPos(min(n + 1, a[j].x + T + 1)) - 1, -1, 1, SZ(oo) - 1, 1);
            }
        }
    }
    return ok(now);
}

int main() {
    scanf("%d%d%d", &n, &m, &k);
    for(int i = 1; i <= k; i++) scanf("%d%d", &a[i].x, &a[i].y);
    int low = 0, high = max(n, m), ans = high;
    while(low <= high) {
        int mid = low + high >> 1;
        if(check(mid)) high = mid - 1, ans = mid;
        else low = mid + 1;
    }
    printf("%d\n", ans);
    return 0;
}

/*
*/

Codeforces 845E Fire in the City 線段樹