SPOJ 4487 Splay 基本操作

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2024-07-01 23:39:20 225人阅读

插入操作，删除操作和置换操作都是单点的，所以不需要lazy标记。这个很简单，都是两次RotateTo，一次Splay操作就搞定。

求最大连续字段和的操作和线段树的题目类似，只需要保存最左边的连续最大字段和，最右边的连续最大字段和，整个子树的连续最大字段和就OK，整个子树的和就OK。

注意PushUp函数的写法就OK

//Problem Specific Function
    void PushUp(int x )
    {
        int ll = sp[x].child[0], rr = sp[x].child[1];
        // sz, lsum , rsum , msum, sum
        sp[x].sz = 1 + sp[sp[x].child[0]].sz + sp[sp[x].child[1]].sz;
        sp[x].sum =  sp[x].val + sp[sp[x].child[0]].sum + sp[sp[x].child[1]].sum;
        sp[x].lsum = max(sp[ll].lsum, sp[ll].sum + sp[x].val + max(sp[rr].lsum, 0));
        sp[x].rsum = max(sp[rr].rsum, sp[rr].sum + sp[x].val + max(sp[ll].rsum , 0));
        // 这里类似于线段树的
        sp[x].msum = max(max(sp[ll].msum, sp[rr].msum), sp[x].val + max(sp[ll].rsum, 0) + max(sp[rr].lsum, 0));
    }

这个题目的代码

1:

   2:  #include <cstdio>

   3:  #include <iostream>

4:

   5:  using namespace std;

   6:  #define INF 10009

   7:  #define MaxL 222222

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

9:

  10:  struct SplayTreeNode

  11:  {

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

  13:      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。

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

  15:      int lsum;   // 以该点为根的子树的左子树最大的连续和 [left, x)

  16:      int rsum;   // 以该点为根的子树的右子树 最大的连续和 (x, right]

  17:      int msum;   // 以该点为根的子树中的连续最大字段和

  18:  };

19:

  20:  int num[MaxL];

  21:  struct SpalyTree

  22:  {

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

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

  25:      int root;  // root idx

  26:      int idx;   // Forward allocate tree

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

28:

  29:      /*

  30:           A                        B

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

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

  33:       / \                            /  \

  34:      D   E                          E    C

  35:      */

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

  37:      {

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

  39:          //PushDown(y);

  40:          //PushDown(x);

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

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

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

  44:          if(sp[x].parent)

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

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

  47:          sp[y].parent = x;

  48:          PushUp(y);

  49:      }

50:

  51:      void Splay(int x, int goal)

  52:      {

  53:          //PushDown(x);

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

  55:          {

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

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

  58:              else

  59:              {

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

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

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

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

  64:                  else

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

66:

  67:              }

  68:          }

  69:          PushUp(x);

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

  71:      }

  72:      //  把第k个的数转到goal下边，一般用来调整区间

  73:      int RotateTo(int k, int goal)

  74:      {

  75:          int x = root;

  76:          //PushDown(x);

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

  78:          {

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

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

  81:              else

  82:              {

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

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

  85:              }

  86:  //            PushDown(x);

  87:          }

  88:  //        cout<<"Rotate "<<x<<" goal "<<goal<<endl;

  89:          Splay(x, goal);

  90:          return x;

  91:      }

92:

  93:      void NewNode(int &x, int c)

  94:      {

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

  96:          else  x = ++idx;

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

  98:          sp[x].sz = 1;

  99:          sp[x].val = sp[x].sum = sp[x].lsum = sp[x].rsum  = sp[x].msum = c;

 100:          //sp[x].lazy = 0;

 101:      }

 102:

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

 104:      void eraseSubTree(int x)

 105:      {

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

 107:          int head = idxrev , tail = idxrev;

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

 109:          {

 110:              idxrev++;

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

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

 113:          }

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

 115:          PushUp(father);

 116:      }

 117:

 118:

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

 120:      {

 121:          if(l > r) return ;

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

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

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

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

 126:          sp[x].parent = parent;

 127:          PushUp(x);

 128:      }

 129:      void Init(int n)

 130:      {

 131:          idx = idxrev =  0;

 132:          root = 0;

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

 134:          sp[0].sz = sp[0].sum = 0;

 135:          sp[0].val = sp[0].lsum = sp[0].rsum = sp[0].msum = -INF;

 136:          NewNode(root, -INF);

 137:          NewNode(sp[root].child[1], -INF);

 138:          sp[idx].parent = root;

 139:          sp[root].sz = 2;

 140:          makeTree( sp [sp[root].child[1] ].child[0] , 1, n, sp[root].child[1]);

 141:          PushUp(sp[root].child[1]);

 142:          PushUp(root);

 143:      }

 144:

 145:      void Travel(int x)

 146:      {

 147:          if(x)

 148:          {

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

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

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

 152:          }

 153:      }

 154:

 155:      //Problem Specific Function

 156:      void PushUp(int x )

 157:      {

 158:          int ll = sp[x].child[0], rr = sp[x].child[1];

 159:          // sz, lsum , rsum , msum, sum

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

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

 162:          sp[x].lsum = max(sp[ll].lsum, sp[ll].sum + sp[x].val + max(sp[rr].lsum, 0));

 163:          sp[x].rsum = max(sp[rr].rsum, sp[rr].sum + sp[x].val + max(sp[ll].rsum , 0));

 164:          // 这里类似于线段树的

 165:          sp[x].msum = max(max(sp[ll].msum, sp[rr].msum), sp[x].val + max(sp[ll].rsum, 0) + max(sp[rr].lsum, 0));

 166:      }

 167:

 168:      void Insert(int pos, int m)

 169:      {

 170:          RotateTo(pos - 1, 0);

 171:          RotateTo(pos, root);

 172:          int p = 0;

 173:          NewNode(p, m);

 174:          keyTree = p;

 175:          sp[p].parent = sp[root].child[1];

 176:          Splay(p,0);

 177:      }

 178:

 179:      void Delete(int pos)

 180:      {

 181:          RotateTo(pos-1, 0);

 182:          RotateTo(pos+1, root);

 183:          eraseSubTree(keyTree);

 184:          Splay(sp[root].child[1], 0);

 185:      }

 186:

 187:      void Replace(int pos, int m)

 188:      {

 189:          RotateTo(pos-1, 0);

 190:          RotateTo(pos+1, root);

 191:          int x = keyTree;

 192:          sp[x].val = sp[x].sum = sp[x].lsum = sp[x].rsum  = sp[x].msum = m;

 193:          Splay(keyTree,0);

 194:      }

 195:

 196:      int Query(int l, int r)

 197:      {

 198:          RotateTo(l -1, 0);

 199:          RotateTo(r+1, root);

 200:

 201:          int ret =  sp[keyTree].msum;

 202:          Splay(keyTree,0);

 203:          return ret;

 204:      }

 205:  } spt;

 206:

 207:

 208:  int main()

 209:  {

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

 211:      int n;

 212:      while(scanf("%d",&n)!=EOF)

 213:      {

 214:          for(int i=1; i<=n; i++)

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

 216:          spt.Init(n);

 217:          int q;

 218:          scanf("%d", &q);

 219:          while(q--)

 220:          {

 221:              char op[2];

 222:              scanf("%s",op);

 223:              int pos,m;

 224:              if(op[0]==‘I‘)

 225:              {

 226:                  n++;

 227:                  scanf("%d%d",&pos, &m);

 228:                  spt.Insert(pos,m);

 229:              }

 230:              else if(op[0]==‘D‘)

 231:              {

 232:                  n--;

 233:  //                scanf_(pos);

 234:                  scanf("%d", & pos);

 235:                  spt.Delete(pos);

 236:              }

 237:              else if(op[0]==‘R‘)

 238:              {

 239:                  scanf("%d%d",&pos, &m);

 240:                  spt.Replace(pos,m);

 241:              }

 242:              else if(op[0]==‘Q‘)

 243:              {

 244:                  scanf("%d%d", &pos, &m);

 245:                  printf("%d\n", spt.Query(pos,m));

 246:              }

 247:          }

 248:      }

 249:      return 0;

 250:  }

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SPOJ 4487 Splay 基本操作

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