cdq 分治

Author: Clouder0

Luogu/ShengXuan/P3157(2).cpp

@@ -0,0 +1,42 @@
+#include <cstdio>
+#include <algorithm>
+#include <ctype.h>
+const int bufSize = 1e6;
+inline char nc()
+{
+    #ifdef DEBUG
+    return getchar();
+    #endif
+    static char buf[bufSize], *p1 = buf, *p2 = buf;
+    return p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, bufSize, stdin), p1 == p2) ? EOF : *p1++;
+}
+inline void read(char *s)
+{
+    static char c;
+    for (; !isalpha(c); c = nc());
+    for (; isalpha(c); c = nc()) *s++ = c;
+    *s = '\0';
+}
+template<typename T>
+inline T read(T &r)
+{
+    static char c;
+    static int flag;
+    flag = 1, r = 0;
+    for (c = nc(); !isdigit(c); c = nc()) if (c == '-') flag = -1;
+    for (; isdigit(c); c = nc()) r = r * 10 + c - 48;
+    return r *= flag;
+}
+const int maxn = 5e5 + 100;
+int n, m, a[maxn];
+struct node
+{
+    int t, p, v, type;
+} A[maxn], B[maxn];
+int main()
+{
+    read(n), read(m);
+    for (int i = 1; i <= n; ++i) read(a[i]);
+
+    return 0;
+}

Luogu/ShengXuan/P3810(2).cpp

@@ -1,62 +1,66 @@
-#include <cstdio>
 #include <algorithm>
-template<typename T>
-void read(T &r)
+#include <cstdio>
+
+template <typename T>
+void read(T& r)
 {
-    static char c;r=0;
-    for(c=getchar();c>'9'||c<'0';c=getchar());
-    for(;c>='0'&&c<='9';r=(r<<1)+(r<<3)+(c^48),c=getchar());
+    static char c;
+    r = 0;
+    for (c = getchar(); c > '9' || c < '0'; c = getchar())
+        ;
+    for (; c >= '0' && c <= '9'; r = (r << 1) + (r << 3) + (c ^ 48), c = getchar())
+        ;
 }
 const int maxn = 2e5 + 100;
 struct node
 {
-    int a,b,c,d,cnt,id;
-}A[maxn],B[maxn],C[maxn];
-int n,maxk,tot;
-bool cmp(const node &x,const node &y)
+    int a, b, c, d, cnt, id;
+} A[maxn], B[maxn], C[maxn];
+int n, maxk, tot;
+bool cmp(const node& x, const node& y)
 {
-    if(x.a != y.a) return x.a < y.a;
-    if(x.b != y.b) return x.b < y.b;
+    if (x.a != y.a) return x.a < y.a;
+    if (x.b != y.b) return x.b < y.b;
     return x.c < y.c;
 }
 int ans[maxn];
 
-void cdq2(int l,int r)
+void cdq2(int l, int r)
 {
-    if(l == r) return;
+    if (l == r) return;
     int mid = l + r >> 1;
-    cdq2(l,mid),cdq2(mid + 1,r);
-    int p = l,q = mid + 1,k = l,sum = 0;
-    while(p <= mid && q <= r)
+    cdq2(l, mid), cdq2(mid + 1, r);
+    int p = l, q = mid + 1, k = l, sum = 0;
+    while (p <= mid && q <= r)
     {
-        if(B[p].c <= B[q].c)
+        if (B[p].c <= B[q].c)
         {
             sum += B[p].d;
             C[k++] = B[p++];
         }
         else
         {
-            if(!B[q].d) ans[B[q].id] += sum;
+            if (!B[q].d) ans[B[q].id] += sum;
             C[k++] = B[q++];
         }
     }
-    while(p <= mid) C[k++] = B[p++];
-    while(q <= r) 
+    while (p <= mid) C[k++] = B[p++];
+    while (q <= r)
     {
-        if(!B[q].d) ans[B[q].id] += sum;
+        if (!B[q].d) ans[B[q].id] += sum;
         C[k++] = B[q++];
     }
-    for(int i = l;i<=r;++i) B[i] = C[i];
+    for (int i = l; i <= r; ++i) B[i] = C[i];
 }
-void cdq(int l,int r)
+void cdq(int l, int r)
 {
-    if(l == r) return;
+    if (l == r) return;
     int mid = l + r >> 1;
-    cdq(l,mid),cdq(mid + 1,r);
-    int p = l,q = mid + 1,k = l;
-    while(p <= mid && q <= r)
+    cdq(l, mid), cdq(mid + 1, r);
+    int p = l, q = mid + 1, k = l;
+    while (p <= mid && q <= r)
     {
-        if(A[p].b <= A[q].b)
+        if (A[p].b <= A[q].b)
         {
             A[p].d = A[p].cnt;
             B[k++] = A[p++];
@@ -67,25 +71,26 @@ void cdq(int l,int r)
             B[k++] = A[q++];
         }
     }
-    while(p <= mid) A[p].d = A[p].cnt,B[k++] = A[p++];
-    while(q <= r) A[q].d = 0,B[k++] = A[q++];
-    for(int i = l;i<=r;++i) A[i] = B[i];
-    cdq2(l,r);
+    while (p <= mid) A[p].d = A[p].cnt, B[k++] = A[p++];
+    while (q <= r) A[q].d = 0, B[k++] = A[q++];
+    for (int i = l; i <= r; ++i) A[i] = B[i];
+    cdq2(l, r);
 }
 int d[maxn];
 int main()
 {
-    read(n),read(maxk);
-    for(int i = 1;i<=n;++i) read(B[i].a),read(B[i].b),read(B[i].c),B[i].cnt = 1,B[i].id = i;
-    std::sort(B + 1,B + 1 + n,cmp);
-    for(int i = 1;i<=n;++i)
+    read(n), read(maxk);
+    for (int i = 1; i <= n; ++i) read(B[i].a), read(B[i].b), read(B[i].c), B[i].cnt = 1, B[i].id = i;
+    std::sort(B + 1, B + 1 + n, cmp);
+    for (int i = 1; i <= n; ++i)
     {
-        if(B[i].a == B[i+1].a && B[i].b == B[i+1].b && B[i].c == B[i+1].c)
-            B[i+1].cnt += B[i].cnt;
-        else A[++tot] = B[i];
+        if (B[i].a == B[i + 1].a && B[i].b == B[i + 1].b && B[i].c == B[i + 1].c)
+            B[i + 1].cnt += B[i].cnt;
+        else
+            A[++tot] = B[i];
     }
-    cdq(1,tot);
-    for(int i = 1;i<=tot;++i) d[ans[A[i].id] + A[i].cnt] += A[i].cnt;
-    for(int i = 1;i<=n;++i) printf("%d\n",d[i]);
+    cdq(1, tot);
+    for (int i = 1; i <= tot; ++i) d[ans[A[i].id] + A[i].cnt] += A[i].cnt;
+    for (int i = 1; i <= n; ++i) printf("%d\n", d[i]);
     return 0;
 }

templates/cdq.cpp

@@ -0,0 +1,108 @@
+#include <algorithm>
+#include <cstdio>
+const int maxn = 1e5 + 100;
+namespace cdq
+{
+int n;
+struct node
+{
+    int a, b, c, id, cnt;
+    int atag, btag;
+} A[maxn], B[maxn], C[maxn];
+int res[maxn];
+bool cmpa(const node& x, const node& y)
+{
+    if (x.a != y.a) return x.a < y.a;
+    if (x.b != y.b) return x.b < y.b;
+    return x.c < y.c;
+}
+void init()
+{
+    for (int i = 1; i <= n; ++i) A[i].id = i, A[i].cnt = 1;
+    for (int i = 1; i <= n; ++i) res[i] = 0;
+    std::sort(A + 1, A + 1 + n, cmpa);
+    int tot = 0;
+    for (int i = 2; i <= n; ++i)
+        if (A[i].a == A[i - 1].a && A[i].b == A[i - 1].b && A[i].c == A[i - 1].c)
+            A[i].cnt = A[i - 1].cnt + 1;
+        else
+            B[++tot] = A[i - 1];
+    B[++tot] = A[n];
+    n = tot;
+    for (int i = 1; i <= n; ++i) A[i] = B[i];
+}
+void cdq2(int l, int r)
+{
+    if(l == r) return;
+    int mid = (l + r) >> 1;
+    cdq2(l, mid), cdq2(mid + 1, r);
+    // sort according to c
+    for (int i = l; i <= mid; ++i) B[i].btag = 0;
+    for (int i = mid + 1; i <= r; ++i) B[i].btag = 1;
+    int p = l, q = mid + 1, k = l;
+    while (p <= mid && q <= r)
+    {
+        if (B[p].c <= B[q].c)
+            C[k++] = B[p++];
+        else
+            C[k++] = B[q++];
+    }
+    while (p <= mid) C[k++] = B[p++];
+    while (q <= r) C[k++] = B[q++];
+    for (int i = l; i <= r; ++i) B[i] = C[i];
+    // now count the answer
+    int num = 0;
+    for (int i = l; i <= r; ++i)
+    {
+        if (B[i].atag && B[i].btag)
+            res[B[i].id] += num;
+        else if (!B[i].atag && !B[i].btag)
+            num += B[i].cnt;
+    }
+}
+void cdq(int l, int r)
+{
+    if (l == r) return;
+    int mid = (l + r) >> 1;
+    cdq(l, mid), cdq(mid + 1, r);
+    // now [l,mid] [mid+1,r] has been sorted according to b
+    for (int i = l; i <= mid; ++i) A[i].atag = 0;
+    for (int i = mid + 1; i <= r; ++i) A[i].atag = 1;
+    // merge sort to get [l,r] sorted by b
+    int p = l, q = mid + 1, k = l;
+    while (p <= mid && q <= r)
+    {
+        if (A[p].b <= A[q].b)
+            B[k++] = A[p++];
+        else
+            B[k++] = A[q++];
+    }
+    while (p <= mid) B[k++] = A[p++];
+    while (q <= r) B[k++] = A[q++];
+    // A should be sorted by b
+    for(int i = l;i<=r;++i) A[i] = B[i];
+    // now [l,r] sorted by b, cdq2 to get the answer 
+    cdq2(l, r);
+}
+}  // namespace cdq
+int ans[maxn];
+int main()
+{
+    int _n, k;
+    using namespace cdq;
+    scanf("%d%d", &cdq::n, &k);
+    _n = n;
+    for (int i = 1; i <= cdq::n; ++i)
+    {
+        int a, b, c;
+        scanf("%d%d%d", &a, &b, &c);
+        A[i].a = a, A[i].b = b, A[i].c = c;
+    }
+    cdq::init();
+    cdq::cdq(1, cdq::n);
+//    for(int i = 1;i<=cdq::n;++i) 
+//        printf("[%d]%d %d %d %d:%d\n",A[i].id,A[i].a,A[i].b,A[i].c,A[i].cnt, res[A[i].id] + A[i].cnt - 1);
+    for (int i = 1; i <= cdq::n; ++i) ans[res[A[i].id] + A[i].cnt] += A[i].cnt;
+    for (int i = 1; i <= _n; ++i) printf("%d\n", ans[i]);
+    return 0;
+}

templates/cdq2.cpp

@@ -0,0 +1,102 @@
+#include <algorithm>
+#include <cstdio>
+const int maxn = 2e5 + 100;
+namespace BitTree
+{
+int n;
+int sum[maxn], tag[maxn], now;
+inline void clear() { ++now; }
+inline void check(int x)
+{
+    if (tag[x] != now) sum[x] = 0, tag[x] = now;
+}
+void add(int x, int k)
+{
+    for (; x <= n; x += (x & -x)) check(x), sum[x] += k;
+}
+int ask(int x)
+{
+    int res = 0;
+    for (; x > 0; x -= (x & -x)) check(x), res += sum[x];
+    return res;
+}
+}  // namespace BitTree
+namespace cdq
+{
+int n;
+struct node
+{
+    int a, b, c, id, cnt;
+} A[maxn], B[maxn], C[maxn];
+int res[maxn];
+bool cmpa(const node& x, const node& y)
+{
+    if (x.a != y.a) return x.a < y.a;
+    if (x.b != y.b) return x.b < y.b;
+    return x.c < y.c;
+}
+void init()
+{
+    for (int i = 1; i <= n; ++i) A[i].id = i, A[i].cnt = 1;
+    for (int i = 1; i <= n; ++i) res[i] = 0;
+    std::sort(A + 1, A + 1 + n, cmpa);
+    int tot = 0;
+    for (int i = 2; i <= n; ++i)
+        if (A[i].a == A[i - 1].a && A[i].b == A[i - 1].b && A[i].c == A[i - 1].c)
+            A[i].cnt = A[i - 1].cnt + 1;
+        else
+            B[++tot] = A[i - 1];
+    B[++tot] = A[n];
+    n = tot;
+    for (int i = 1; i <= n; ++i) A[i] = B[i];
+}
+void cdq(int l, int r)
+{
+    if (l == r) return;
+    int mid = (l + r) >> 1;
+    cdq(l, mid), cdq(mid + 1, r);
+    // now [l,mid] [mid+1,r] has been sorted according to b
+    // merge sort to get [l,r] sorted by b
+    int p = l, q = mid + 1, k = l;
+    while (p <= mid && q <= r)
+    {
+        if (A[p].b <= A[q].b)
+        {
+            BitTree::add(A[p].c, A[p].cnt);
+            B[k++] = A[p++];
+        }
+        else
+        {
+            res[A[q].id] += BitTree::ask(A[q].c);
+            B[k++] = A[q++];
+        }
+    }
+    while (p <= mid) B[k++] = A[p++];
+    while (q <= r) res[A[q].id] += BitTree::ask(A[q].c), B[k++] = A[q++];
+    BitTree::clear();
+    // A should be sorted by b
+    for (int i = l; i <= r; ++i) A[i] = B[i];
+}
+}  // namespace cdq
+int ans[maxn];
+int main()
+{
+    int _n, k;
+    using namespace cdq;
+    scanf("%d%d", &cdq::n, &k);
+    _n = n;
+    BitTree::n = k;
+    for (int i = 1; i <= cdq::n; ++i)
+    {
+        int a, b, c;
+        scanf("%d%d%d", &a, &b, &c);
+        A[i].a = a, A[i].b = b, A[i].c = c;
+    }
+    cdq::init();
+    cdq::cdq(1, cdq::n);
+    //    for(int i = 1;i<=cdq::n;++i)
+    //        printf("[%d]%d %d %d %d:%d\n",A[i].id,A[i].a,A[i].b,A[i].c,A[i].cnt, res[A[i].id] + A[i].cnt - 1);
+    for (int i = 1; i <= cdq::n; ++i) ans[res[A[i].id] + A[i].cnt] += A[i].cnt;
+    for (int i = 1; i <= _n; ++i) printf("%d\n", ans[i]);
+    return 0;
+}