BZOJ 1588 营业额统计 Splay

主要操作为Splay中插入节点，查找前驱和后继节点。

   1:  #include <cstdio>

   2:  #include <iostream>

   3:  #include <cmath>

   4:  using namespace std;

   5:  #define MaxL 100005

   6:  #define INF 0x7ffffff

   7:  #define keyTree   sp[sp[root].child[1]].child[0]

   8:   

   9:  struct SplayTreeNode

  10:  {

  11:      int parent, child[2];   // parent and child[0] left child[1] right

  12:      int sz, val;  // sz 表示当前节点为根的子树总节点个数.  val表示当前节点的键值。

  13:      int lazy;     //  延迟标记

  14:      long long sum;   // 以x为根节点的子树的所有的和

  15:  };

  16:   

  17:  int num[MaxL];

  18:  struct SpalyTree

  19:  {

  20:      SplayTreeNode sp[MaxL];   // save space

  21:      int gc[MaxL];   // Garbage Collection idx

  22:      int root;  // root idx

  23:      int idx;   // Forward allocate tree

  24:      int idxrev; // garbage allocated nodes used for next allocation priority

  25:   

  26:      /*

  27:           A                        B

  28:         /   \    R(B,RR)->       /   \

  29:        B     C    <-R(A,LL)     D     A

  30:       / \                            /  \

  31:      D   E                          E    C

  32:      */

  33:      void Rotate(int x,int f)   // f ==0 l rot,1 r rot

  34:      {

  35:          int y = sp[x].parent;

  36:          PushDown(y);

  37:          PushDown(x);

  38:          sp[y].child[!f] = sp[x].child[f];

  39:          sp[sp[x].child[f]].parent = y;

  40:          sp[x].parent = sp[y].parent;

  41:          if(sp[x].parent)

  42:              sp[sp[y].parent].child[ sp[sp[y].parent].child[1] == y]= x;

  43:          sp[x].child[f] = y;

  44:          sp[y].parent = x;

  45:          PushUp(y);

  46:      }

  47:   

  48:      // x to be the child of goal, x and goal are key

  49:      void Splay(int x, int goal)

  50:      {

  51:          PushDown(x);

  52:          while(sp[x].parent != goal)

  53:          {

  54:              if(sp[sp[x].parent].parent == goal)

  55:                  Rotate(x, sp[sp[x].parent].child[0] == x);

  56:              else

  57:              {

  58:                  int y = sp[x].parent, z = sp[y].parent;

  59:                  int f = sp[z].child[0] == y;

  60:                  if(sp[y].child[f] == x)

  61:                      Rotate(x,!f), Rotate(x,f);

  62:                  else

  63:                      Rotate(y,f), Rotate(x,f);

  64:              }

  65:          }

  66:          PushUp(x);

  67:          if(goal == 0) root = x;

  68:      }

  69:   

  70:      //  把第k个的数转到goal下边，一般用来调整区间, 返回其key 键

  71:      int RotateTo(int k, int goal)

  72:      {

  73:          int x = root;

  74:          PushDown(x);

  75:          while(sp[sp[x].child[0]].sz !=k)

  76:          {

  77:              if( k< sp [ sp[x].child[0] ].sz)

  78:                  x = sp[x].child[0];

  79:              else

  80:              {

  81:                  k -= sp[sp[x].child[0]].sz +1;

  82:                  x = sp[x].child[1];

  83:              }

  84:              PushDown(x);

  85:          }

  86:          cout<<"Rotate "<<x<<" goal "<<goal<<endl;

  87:          Splay(x, goal);

  88:          return x;

  89:      }

  90:   

  91:      // insert a value, return the key

  92:      // first find the key, then insert a value.

  93:      // 不重复插入

  94:      pair<int,bool> Insert(int val)

  95:      {

  96:          int p = root;

  97:          while( sp[p].val == val || sp[p].child[ sp[p].val < val ])

  98:          {

  99:              if(sp[p].val == val)

 100:              {

 101:                  Splay(p, 0);

 102:                  return make_pair(p,false);

 103:              }

 104:              p = sp[p].child[sp[p].val < val];

 105:          }

 106:          int x = NewNode(sp[p].child[sp[p].val < val], val);

 107:          sp[x].parent = p;

 108:          Splay(x, 0);

 109:          return make_pair(x, true);

 110:      }

 111:   

 112:      int findPrefix(int x)

 113:      {

 114:          Splay(x,0);

 115:          int p = sp[x].child[0];

 116:          if(p)

 117:          {

 118:              while(sp[p].child[1])

 119:                  p = sp[p].child[1];

 120:          }

 121:          return p;

 122:      }

 123:   

 124:      int findSuffix(int x)

 125:      {

 126:          Splay(x, 0);

 127:          int p = sp[x].child[1];

 128:          if(p)

 129:          {

 130:              while(sp[p].child[0])

 131:                  p = sp[p].child[0];

 132:          }

 133:          return p;

 134:      }

 135:   

 136:   

 137:      int NewNode(int &x, int c)

 138:      {

 139:          if( idxrev) x = gc[--idxrev];

 140:          else  x = ++idx;

 141:          sp[x].child[1] = 0, sp[x].child[0] = 0, sp[x].parent = 0;

 142:          sp[x].sz = 1;

 143:          sp[x].val = sp[x].sum = c;

 144:          sp[x].lazy = 0;

 145:          return x;

 146:      }

 147:   

 148:      //把以x为祖先结点（x 也算）删掉放进内存池,回收内存

 149:      void eraseSubTree(int x)

 150:      {

 151:          int father = sp[x].parent;

 152:          int head = idxrev , tail = idxrev;

 153:          for (gc[tail++] = x ; head < tail ; head ++)

 154:          {

 155:              idxrev++;

 156:              if( sp[gc[head]].child[0]) gc[tail++] = sp[gc[head]].child[0];

 157:              if( sp[gc[head]].child[1]) gc[tail++] = sp[gc[head]].child[1];

 158:          }

 159:          sp[father].child[ sp[father].child[1] == x] = 0;

 160:          PushUp(father);

 161:      }

 162:   

 163:      void makeTree(int &x, int l, int r, int parent)

 164:      {

 165:          if(l > r) return ;

 166:          int m = (l+r)>>1;

 167:          NewNode(x,num[m]);

 168:          makeTree(sp[x].child[0], l, m-1, x);

 169:          makeTree(sp[x].child[1], m+1, r, x);

 170:          sp[x].parent = parent;

 171:          PushUp(x);

 172:      }

 173:      void Init(int n)

 174:      {

 175:          idx = idxrev =  0;

 176:          root = 0;

 177:          sp[0].child[0] = sp[0].child[1] = sp[0].parent  = 0;

 178:          sp[0].sz = sp[0].lazy = sp[0].sum = 0;

 179:      }

 180:   

 181:      void Travel(int x)

 182:      {

 183:          if(x)

 184:          {

 185:              Travel( sp[x].child[0]);

 186:              printf("结点%2d:左儿子 %2d 右儿子 %2d 父结点 %2d size = %2d ,val = %2d\n",x, sp[x].child[0],sp[x].child[1],sp[x].parent,sp[x].sz,sp[x].val);

 187:              Travel( sp[x].child[1]);

 188:          }

 189:      }

 190:   

 191:      //Problem Specific Function

 192:      void PushUp(int x )

 193:      {

 194:          sp[x].sz = 1 + sp[sp[x].child[0]].sz + sp[sp[x].child[1]].sz;

 195:          sp[x].sum = sp[x].lazy + sp[x].val + sp[sp[x].child[0]].sum + sp[sp[x].child[1]].sum;

 196:      }

 197:   

 198:      void PushDown(int x)

 199:      {

 200:          if(sp[x].lazy)

 201:          {

 202:              sp[x].val += sp[x].lazy;

 203:              sp[sp[x].child[0]].lazy += sp[x].lazy;

 204:              sp[sp[x].child[1]].lazy += sp[x].lazy;

 205:              sp[sp[x].child[0]].sum += (long long) sp[ sp[x].child[0]].sz * sp[x].lazy;

 206:              sp[sp[x].child[1]].sum += (long long) sp[ sp[x].child[1]].sz * sp[x].lazy;

 207:              sp[x].lazy = 0;

 208:          }

 209:      }

 210:   

 211:      void update(int l, int r, int c )

 212:      {

 213:          RotateTo(l-1,0);

 214:          RotateTo(r+1,root);

 215:          sp[keyTree].lazy += c;

 216:          sp[keyTree].sum += (long long) c * sp[keyTree].sz;

 217:      }

 218:   

 219:      // query for the interval [l,r]

 220:      void query(int l, int r)

 221:      {

 222:          RotateTo(l-1,0);

 223:          RotateTo(r+1,root);

 224:  //        int keyTree =  sp [sp[root].child[1] ].child[0];

 225:          printf("%lld\n",sp[keyTree].sum);

 226:      }

 227:  } spt;

 228:   

 229:  int abs(int x)

 230:  {

 231:      if(x < 0) return -x;

 232:      else return x;

 233:  }

 234:  int main()

 235:  {

 236:   

 237:      //freopen("1.txt","r",stdin);

 238:      int n,m;

 239:      cin>>n;

 240:      m = 0;

 241:      for(int i=0; i<n; i++)

 242:          scanf("%d",&num[i]);

 243:      spt.Init(0);

 244:      int ret = 0;

 245:      while(m!=n)

 246:      {

 247:          pair<int,bool> state = spt.Insert(num[m]);

 248:          if(state.second != 0)

 249:          {

 250:              int pre = spt.findPrefix(state.first);

 251:              int nxt = spt.findSuffix(state.first);

 252:              int ans = INF;

 253:              if(pre)

 254:                  ans = abs(num[m] - spt.sp[pre].val);

 255:              if(nxt)

 256:              {

 257:                  int x = abs(num[m] - spt.sp[nxt].val);

 258:                  ans = std::min(ans, x );

 259:              }

 260:   

 261:              if(pre == 0 && nxt == 0) ans = num[0];

 262:  //            cout<<num[m]<<" "<<pre<<" "<<nxt<<" "<<ans<<endl;

 263:              ret += ans;

 264:          }

 265:          m++;

 266:      }

 267:      cout<<ret<<endl;;

 268:      return 0;

 269:  }

 270:   

 271:   

 272:   

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