几道偏序问题（数据结构）

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lifehappy 2021-08-26 17:10:19 博主文章分类：数据结构-主席树 ©著作权

文章标签 i++ ios #include c++ 三维偏序 文章分类 数据结构与算法人工智能

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P3157 [CQOI2011]动态逆序对

#include <bits/stdc++.h>

using namespace std;

typedef long long ll;

const int N = 1e5 + 10;

int root[N], ls[N << 8], rs[N << 8], sum[N << 8], cnt;

int n, m, pos[N];

inline int lowbit(int x) {
  return x & (-x);
}

void update(int &rt, int l, int r, int x, int v) {
  if (!rt) {
    rt = ++cnt;
  }
  sum[rt] += v;
  if (l == r) {
    return ;
  }
  int mid = l + r >> 1;
  if (x <= mid) {
    update(ls[rt], l, mid, x, v);
  }
  else {
    update(rs[rt], mid + 1, r, x, v);
  }
}

int A[50], B[50], cnt1, cnt2;

int query_sum(int l, int r, int L, int R) {
  if (l >= L && r <= R) {
    int ans = 0;
    for (int i = 1; i <= cnt1; i++) {
      ans -= sum[A[i]];
    }
    for (int i = 1; i <= cnt2; i++) {
      ans += sum[B[i]];
    }
    return ans;
  }
  int A1[50], B1[50];
  int mid = l + r >> 1, ans = 0;
  if (L <= mid) {
    for (int i = 1; i <= cnt1; i++) {
      A1[i] = A[i];
      A[i] = ls[A[i]];
    }
    for (int i = 1; i <= cnt2; i++) {
      B1[i] = B[i];
      B[i] = ls[B[i]];
    }
    ans += query_sum(l, mid, L, R);
    for (int i = 1; i <= cnt1; i++) {
      A[i] = A1[i];
    }
    for (int i = 1; i <= cnt2; i++) {
      B[i] = B1[i];
    }
  }
  if (R > mid) {
    for (int i = 1; i <= cnt1; i++) {
      A1[i] = A[i];
      A[i] = rs[A[i]];
    }
    for (int i = 1; i <= cnt2; i++) {
      B1[i] = B[i];
      B[i] = rs[B[i]];
    }
    ans += query_sum(mid + 1, r, L, R);
    for (int i = 1; i <= cnt1; i++) {
      A[i] = A1[i];
    }
    for (int i = 1; i <= cnt2; i++) {
      B[i] = B1[i];
    }
  }
  return ans;
}

int get_sum(int l, int r, int L, int R) {
  if (L > R || l > r) {
    return 0;
  }
  cnt1 = cnt2 = 0;
  for (int j = l - 1; j; j -= lowbit(j)) {
    A[++cnt1] = root[j];
  }
  for (int j = r; j; j -= lowbit(j)) {
    B[++cnt2] = root[j];
  }
  return query_sum(1, n, L, R);
}

int main() {
  // freopen("in.txt", "r", stdin);
  // freopen("out.txt", "w", stdout);
  // ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
  scanf("%d %d", &n, &m);
  for (int i = 1, x; i <= n; i++) {
    scanf("%d", &x);
    pos[x] = i;
    for (int j = i; j <= n; j += lowbit(j)) {
      update(root[j], 1, n, x, 1);
    }
  }
  ll ans = 0;
  for (int i = 1; i <= n; i++) {
    int p = pos[i];
    ans += get_sum(1, p - 1, i + 1, n);
    ans += get_sum(p + 1, n, 1, i - 1);
  }
  ans >>= 1;
  for (int i = 1, x; i <= m; i++) {
    scanf("%d", &x);
    printf("%lld\n", ans);
    int p = pos[x];
    for (int j = p; j <= n; j += lowbit(j)) {
      update(root[j], 1, n, x, -1);
    }
    ans -= get_sum(1, p - 1, x + 1, n);
    ans -= get_sum(p + 1, n, 1, x - 1);
  }
  return 0;
}

P3810 三维偏序（陌上花开）

#include <bits/stdc++.h>

using namespace std;

const int N = 1e5 + 10;

struct Res {
  int x, y, z;

  Res(int _x = 0, int _y = 0, int _z = 0) : x(_x), y(_y), z(_z) {}
}a[N << 1];

int n, m, ans[N];

int root[N << 2], ls[N << 9], rs[N << 9], sum[N << 9], cnt;

int A[50], cnt1;

bool cmp(Res a, Res b) {
  return a.x < b.x;
}

inline int lowbit(int x) {
  return x & (-x);
}

void update(int &rt, int l, int r, int x, int v) {
  if (!rt) {
    rt = ++cnt;
  }
  sum[rt] += v;
  if (l == r) {
    return ;
  }
  int mid = l + r >> 1;
  if (x <= mid) {
    update(ls[rt], l, mid, x, v);
  }
  else {
    update(rs[rt], mid + 1, r, x, v);
  }
}

int query_sum(int l, int r, int L, int R) {
  if (l >= L && r <= R) {
    int ans = 0;
    for (int i = 1; i <= cnt1; i++) {
      ans += sum[A[i]];
    }
    return ans;
  }
  int mid = l + r >> 1, ans = 0, A1[50];
  if (L <= mid) {
    for (int i = 1; i <= cnt1; i++) {
      A1[i] = A[i];
      A[i] = ls[A[i]];
    }
    ans += query_sum(l, mid, L, R);
    for (int i = 1; i <= cnt1; i++) {
      A[i] = A1[i];
    }
  }
  if (R > mid) {
    for (int i = 1; i <= cnt1; i++) {
      A1[i] = A[i];
      A[i] = rs[A[i]];
    }
    ans += query_sum(mid + 1, r, L, R);
    for (int i = 1; i <= cnt1; i++) {
      A[i] = A1[i];
    }
  }
  return ans;
}

int main() {
  // freopen("in.txt", "r", stdin);
  // freopen("out.txt", "w", stdout);
  // ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
  scanf("%d %d", &n, &m);
  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, cmp);
  int last = 1;
  for (int i = 1; i <= n; i++) {
    for (int j = a[i].y; j <= m; j += lowbit(j)) {
      update(root[j], 1, m, a[i].z, 1);
    }
    if (i == n || a[i].x != a[i + 1].x) {
      for (int j = last; j <= i; j++) {
        cnt1 = 0;
        for (int k = a[j].y; k; k -= lowbit(k)) {
          A[++cnt1] = root[k];
        }
        int res = query_sum(1, m, 1, a[j].z);
        ans[res - 1]++;
      }
      last = i + 1;
    }
  }
  for (int i = 0; i < n; i++) {
    printf("%d\n", ans[i]);
  }
  return 0;
}

P3658 [USACO17FEB]Why Did the Cow Cross the Road III P

#include <bits/stdc++.h>

using namespace std;

const int N = 1e5 + 10;

struct Res {
  int x, y, z;

  Res(int _x = 0, int _y = 0, int _z = 0) : x(_x), y(_y), z(_z) {}

  bool operator < (const Res &t) const {
    return x < t.x;
  }
}a[N];

int l[N], r[N], n, k;

int root[N], ls[N << 8], rs[N << 8], sum[N << 8], cnt;

int A[50], B[50], cnt1, cnt2;

inline int lowbit(int x) {
  return x & (-x);
}

void update(int &rt, int l, int r, int x, int v) {
  if (!rt) {
    rt = ++cnt;
  }
  sum[rt] += v;
  if (l == r) {
    return ;
  }
  int mid = l + r >> 1;
  if (x <= mid) {
    update(ls[rt], l, mid, x, v);
  }
  if (x > mid) {
    update(rs[rt], mid + 1, r, x, v);
  }
}

int query_sum(int l, int r, int L, int R) {
  if (l >= L && r <= R) {
    int ans = 0;
    for (int i = 1; i <= cnt1; i++) {
      ans -= sum[A[i]];
    }
    for (int i = 1; i <= cnt2; i++) {
      ans += sum[B[i]];
    }
    return ans;
  }
  int mid = l + r >> 1, ans = 0, A1[50], B1[50];
  if (L <= mid) {
    for (int i = 1; i <= cnt1; i++) {
      A1[i] = A[i];
      A[i] = ls[A[i]];
    }
    for (int i = 1; i <= cnt2; i++) {
      B1[i] = B[i];
      B[i] = ls[B[i]];
    }
    ans += query_sum(l, mid, L, R);
    for (int i = 1; i <= cnt1; i++) {
      A[i] = A1[i];
    }
    for (int i = 1; i <= cnt2; i++) {
      B[i] = B1[i];
    }
  }
  if (R > mid) {
    for (int i = 1; i <= cnt1; i++) {
      A1[i] = A[i];
      A[i] = rs[A[i]];
    }
    for (int i = 1; i <= cnt2; i++) {
      B1[i] = B[i];
      B[i] = rs[B[i]];
    }
    ans += query_sum(mid + 1, r, L, R);
    for (int i = 1; i <= cnt1; i++) {
      A[i] = A1[i];
    }
    for (int i = 1; i <= cnt2; i++) {
      B[i] = B1[i];
    }
  }
  return ans;
}

int get_sum(int l, int r, int L, int R) {
  if (l > r || L > R) {
    return 0;
  }
  cnt1 = cnt2 = 0;
  for (int i = l - 1; i; i -= lowbit(i)) {
    A[++cnt1] = root[i];
  }
  for (int i = r; i; i -= lowbit(i)) {
    B[++cnt2] = root[i];
  }
  return query_sum(1, n, L, R);
}

int main() {
  // freopen("in.txt", "r", stdin);
  // freopen("out.txt", "w", stdout);
  // ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
  scanf("%d %d", &n, &k);
  for (int i = 1, x; i <= n; i++) {
    scanf("%d", &x);
    l[x] = i;
  }
  for (int i = 1, x; i <= n; i++) {
    scanf("%d", &x);
    r[x] = i;
  }
  for (int i = 1; i <= n; i++) {
    a[i] = Res(l[i], r[i], i);
  }
  sort(a + 1, a + 1 + n);
  long long ans = 0;
  for (int i = 1; i <= n; i++) {
    ans += get_sum(a[i].y + 1, n, k + a[i].z + 1, n);
    ans += get_sum(a[i].y + 1, n, 1, a[i].z - k - 1);
    for (int j = a[i].y; j <= n; j += lowbit(j)) {
      update(root[j], 1, n, a[i].z, 1);
    }
  }
  printf("%lld\n", ans);
  return 0;
}