火星商店问题 题解

Solution

线段树套 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 midint 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;
}