SPOJ 4487 Splay 基本操作
时间：2014-04-29 21:11:43
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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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