火星商店問題 題解

Solution

線段樹套 trie，秒了！

\(O(n\log^2 n)\)

Code

#include <bits/stdc++.h>
using namespace std;
#define rep(i, j, k) for (int i = (j); i <= (k); ++i)
#define reo(i, j, k) for (int i = (j); i >= (k); --i)
typedef long long ll;
const int N = 1e5 + 10;
struct Operation {
	int op, l, r, x, d;
} Oper[N];
int n, m;

#define lc (u << 1)
#define rc ((u << 1) | 1)
#define mid ((l + r) >> 1)

struct BinaryTrie {
	int tot;
	vector<array<int, 2>> ch;
	vector<int> Time;
	BinaryTrie() {
		tot = 1, ch.assign(2, {0, 0}), Time.assign(2, 0);
	}
	void Ins(int x, int d) {
		int pos = 1;
		reo(p, 16, 0) {
			int now = (x >> p) & 1;
			if (!ch[pos][now]) ch[pos][now] = ++tot, ch.push_back({0, 0}), Time.push_back(0);
			pos = ch[pos][now];
			Time[pos] = max(Time[pos], d);
		}
	}
} Trie[N << 2];

void Upd(int u, int l, int r, int x, int v, int d) {
	if (x < l || r < x) return;
	Trie[u].Ins(v, d);
	if (l == r) return;
	Upd(lc, l, mid, x, v, d), Upd(rc, mid + 1, r, x, v, d);
}
vector<array<int, 2>> nodes;
void Get(int u, int l, int r, int x, int y) {
	if (y < l || r < x || x > y) return;
	if (x <= l && r <= y) return nodes.push_back({u, 1});
	Get(lc, l, mid, x, y), Get(rc, mid + 1, r, x, y);
}

#undef lc
#undef rc
#undef mid

int main() {
	ios::sync_with_stdio(false), cin.tie(nullptr);
	cin >> n >> m;
	rep(i, 1, n) {
		int x;
		cin >> x, Upd(1, 1, n, i, x, 100001);
	}
	rep(i, 1, m) {
		cin >> Oper[i].op;
		if (Oper[i].op == 0) {
			cin >> Oper[i].l >> Oper[i].x;
		} else {
			cin >> Oper[i].l >> Oper[i].r >> Oper[i].x >> Oper[i].d;
		}
	}
	for (int day = 1, i = 1; i <= m; ++day) {
		if (Oper[i].op == 0)
			Upd(1, 1, n, Oper[i].l, Oper[i].x, day), ++i;
		for (; i <= m && Oper[i].op == 1; ++i) {
			int l = Oper[i].l, r = Oper[i].r, x = Oper[i].x, d = day - Oper[i].d + 1, ans = 0;
			Get(1, 1, n, l, r);
			reo(t, 16, 0) {
				int now = !((x >> t) & 1), ok = 0;
				for (auto p : nodes) {
					int v = Trie[p[0]].ch[p[1]][now];
					if (v && Trie[p[0]].Time[v] >= d) {
						ok = 1;
						break;
					}
				}
				if (ok) {
					ans |= (1 << t);
					for (auto & p : nodes) {
						int v = Trie[p[0]].ch[p[1]][now];
						if (v && Trie[p[0]].Time[v] >= d) {
							p[1] = v;
						} else {
							p[1] = 0;
						}
					}
				} else {
					now = !now;
					for (auto & p : nodes) {
						int v = Trie[p[0]].ch[p[1]][now];
						if (v && Trie[p[0]].Time[v] >= d) {
							p[1] = v;
						} else {
							p[1] = 0;
						}
					}
				}
			}
			nodes.clear();
			cout << ans << '\n';
		}
	}
	return 0;
}