参考:https://www.luogu.org/blog/Owencodeisking/post-xue-xi-bi-ji-cdq-fen-zhi-hu-zheng-ti-er-fen
前置技能：树状数组，线段树，分治、归并排序
CDQ分治：
据说是OI大佬陈丹琦发明的
1.三维偏序
思路：
第一维排序，第二维分治，第三维树状数组上查询
考虑分治时区间 [l, m] 对区间 [m+1, r] 的贡献，因为第一维已经排好序，所以区间 [l, m] 的第一维小于区间 [m+1, r]的第一维
然后对于区间 [m+1, r]中的某个元素x，将区间 [l, m] 的第二维小于x的元素的按第三维的权值加入树状数组，
最后区间 [l, m] 对区间 x 的贡献就是查询树状数组中小于x第三维的个数
可以边进行分治边进行归并排序，树状数组要及时清空
通过画图我们可以发现，对于每个位置，我们在分治时，它之前的位置对它的贡献都计算过了，所以这种方法是正确的。
因为递归的层数是log(n)层，再加上树状数组，所以时间复杂度是O(n*log(n)^2)
代码：
#pragma GCC optimize(2) #pragma GCC optimize(3) #pragma GCC optimize(4) #include<bits/stdc++.h> using namespace std; #define y1 y11 #define fi first #define se second #define pi acos(-1.0) #define LL long long #define ls rt<<1, l, m #define rs rt<<1|1, m+1, r //#define mp make_pair #define pb push_back #define ULL unsigned LL #define pll pair<LL, LL> #define pli pair<LL, int> #define pii pair<int, int> #define piii pair<pii, int> #define pdi pair<double, int> #define pdd pair<double, double> #define mem(a, b) memset(a, b, sizeof(a)) #define debug(x) cerr << #x << " = " << x << "\n"; #define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0); //head const int N = 1e5 + 5, M = 2e5 + 5; struct Node { int x, y, z; int ans, cnt; bool operator < (const Node & rhs) const { if(x == rhs.x) { if(y == rhs.y) return z < rhs.z; else return y < rhs.y; } else return x < rhs.x; } }a[N], tmp[N]; int bit[M], res[N], n, k, cnt = 0; void add(int x, int a) { while(x <= k) bit[x] += a, x += x&-x; } int sum(int x) { int res = 0; while(x) res += bit[x], x -= x&-x; return res; } void cdq(int l, int r) { if(l == r) { a[l].ans += a[l].cnt-1; return ; } int m = l+r >> 1; cdq(l, m); cdq(m+1, r); int p = l, q = m+1, tp = l; while(q <= r) { while(p <= m && a[p].y <= a[q].y) add(a[p].z, a[p].cnt), tmp[tp++] = a[p], ++p; a[q].ans += sum(a[q].z); tmp[tp++] = a[q]; ++q; } for (int i = l; i < p; ++i) add(a[i].z, -a[i].cnt); while(p <= m) tmp[tp++] = a[p], ++p; for (int i = l; i <= r; ++i) a[i] = tmp[i]; } int main() { scanf("%d %d", &n, &k); for (int i = 1; i <= n; ++i) scanf("%d %d %d", &a[i].x, &a[i].y, &a[i].z); sort(a+1, a+1+n); int now = 1; for (int i = 2; i <= n; ++i) { if(a[i].x == a[i-1].x && a[i].y == a[i-1].y && a[i].z == a[i-1].z) ++now; else { a[++cnt] = a[i-1]; a[cnt].cnt = now; a[cnt].ans = 0; now = 1; } } a[++cnt] = a[n]; a[cnt].cnt = now; a[cnt].ans = 0; cdq(1, cnt); for (int i = 1; i <= cnt; ++i) res[a[i].ans] += a[i].cnt; for (int i = 0; i < n; ++i) printf("%d\n", res[i]); return 0; }
思路：时间看成一个维度就转换成了三维偏序了
代码：
#pragma GCC optimize(2) #pragma GCC optimize(3) #pragma GCC optimize(4) #include<bits/stdc++.h> using namespace std; #define y1 y11 #define fi first #define se second #define pi acos(-1.0) #define LL long long #define ls rt<<1, l, m #define rs rt<<1|1, m+1, r //#define mp make_pair #define pb push_back #define ULL unsigned LL #define pll pair<LL, LL> #define pli pair<LL, int> #define pii pair<int, int> #define piii pair<pii, int> #define pdi pair<double, int> #define pdd pair<double, double> #define mem(a, b) memset(a, b, sizeof(a)) #define debug(x) cerr << #x << " = " << x << "\n"; #define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0); //head const int N = 1e5 + 5; struct node { int a, t, x, ans, id; bool operator < (const node & rhs) const { return id < rhs.id; } }a[N], tmp[N]; int n; map<int, int> cnt; void cdq(int l, int r) { if(l == r) return ; int m = l+r >> 1; cdq(l, m); cdq(m+1, r); int p = l, q = m+1, tp = l; while(q <= r) { while(p <= m && a[p].t <= a[q].t) { if(a[p].a == 1) cnt[a[p].x]++; else if(a[p].a == 2) cnt[a[p].x]--; tmp[tp++] = a[p], ++p; } if(a[q].a == 3) a[q].ans += cnt[a[q].x]; tmp[tp++] = a[q]; ++q; } for (int i = l; i < p; ++i) { if(a[i].a == 1) cnt[a[i].x]--; else if(a[i].a == 2) cnt[a[i].x]++; } while(p <= m) tmp[tp++] = a[p], ++p; for (int i = l; i <= r; ++i) a[i] = tmp[i]; } int main() { scanf("%d", &n); for (int i = 1; i <= n; ++i) scanf("%d %d %d", &a[i].a, &a[i].t, &a[i].x), a[i].ans = 0, a[i].id = i; cdq(1, n); sort(a+1, a+1+n); for (int i = 1; i <= n; ++i) if(a[i].a == 3) printf("%d\n", a[i].ans); return 0; }