ACM模板——各种各样的线段树
线段树模板(Powered By HC TECH - Kiritow)
include
/// General includes
#include
#include
#include
#include
using namespace std; 最基础的线段树
/// 最基础的线段树: 单点更新,区间运算(求和)
namespace SegmentTree
{
const int MAXN = 1000100;
const int MAXTREENODE = MAXN<<2;
struct node
{
int lt,rt;
int val;
};
node tree[MAXTREENODE];
/// _internal_v is a indexer of SegmentTree. It guides the procedure to the right node.
void build(int L,int R,int _internal_v=1) /// Build a tree, _internal_v is 1 by default.
{
tree[_internal_v].lt=L;
tree[_internal_v].rt=R;
if(L==R)
{
scanf("%d",&tree[_internal_v].val);
/// Or: tree[_internal].val = VAL_BY_DEFAULT
return;
}
int mid=(L+R)>>1;
build(L,mid,_internal_v<<1);
build(mid+1,R,_internal_v<<1|1);/// x<<1 == x*2; x<<1|1 == x*2+1; (faster == slower)
/// SegmentTree Main Algorithm
tree[_internal_v].val=tree[_internal_v<<1].val+tree[_internal_v<<1|1].val;
}
void update(int Pos,int Val,int _internal_v=1)/// Update a position, _internal_v is 1 by default.
{
if(tree[_internal_v].lt==tree[_internal_v].rt)
{
tree[_internal_v].val=Val;
return;
}
/// Update Deep-Loop
if(Pos <= tree[_internal_v<<1].rt) update(Pos,Val,_internal_v<<1);
if(Pos >= tree[_internal_v<<1|1].lt) update(Pos,Val,_internal_v<<1|1);
/// SegmentTree Main Algorithm
tree[_internal_v].val = tree[_internal_v<<1].val+tree[_internal_v<<1|1].val;
}
int _internal_ans;
inline void _internal_clear_ans()
{
_internal_ans=0;
}
inline int _internal_get_ans()
{
return _internal_ans;
}
void basic_query(int L,int R,int _internal_v=1)/// Query A Segment [L,R] , _internal_v is 1 by default.
{
if(tree[_internal_v].lt >= L && tree[_internal_v].rt <= R)
{
_internal_ans+=tree[_internal_v].val;
return;
}
if(L <= tree[_internal_v<<1].rt) basic_query(L,R,_internal_v<<1);
if(R >= tree[_internal_v<<1|1].lt) basic_query(L,R,_internal_v<<1|1);
}
int query(int L,int R)
{
_internal_clear_ans();
basic_query(L,R);
return _internal_get_ans();
}
}/// End of namespace SegmentTree属性线段树
/// 延迟更新: 区间赋值更新, 区间运算(求和)
namespace AttributeSegmentTree
{
const int MAXN = 100100;
const int MAXTREENODE = MAXN << 2;
const int ATTR_BY_DEFAULT=1;///默认初始化属性
struct node
{
int lt,rt;
int attr;
};
node tree[MAXTREENODE];
void build(int L,int R,int _indexer=1)
{
tree[_indexer].lt=L;
tree[_indexer].rt=R;
tree[_indexer].attr=ATTR_BY_DEFAULT;
if(L!=R)
{
int mid=(L+R)>>1;
build(L,mid,_indexer<<1);
build(mid+1,R,_indexer<<1|1);
}
}
void update(int L,int R,int NewAttr,int _indexer=1)
{
if(tree[_indexer].attr==NewAttr) return; /// Same Attribute. Don't Need Change.
if(tree[_indexer].lt==L&&tree[_indexer].rt==R)
{
/// Right this segment. Update.
tree[_indexer].attr=NewAttr;
return;
}
/// This segment has only 1 attribute. New attribute is different.
/// So change this segment's manager's attribute to -1 ( Different Attribute in this segment )
if(tree[_indexer].attr!=-1)
{
tree[_indexer<<1].attr=tree[_indexer<<1|1].attr=tree[_indexer].attr;
tree[_indexer].attr=-1;
}
/// If This segment has already had several attributes, operate its subtree by Deep-Loop.
int mid=(tree[_indexer].lt+tree[_indexer].rt)>>1;
if(L>mid)
{
update(L,R,NewAttr,_indexer<<1|1);
}
else if(R<=mid)
{
update(L,R,NewAttr,_indexer<<1);
}
else
{
update(L,mid,NewAttr,_indexer<<1);
update(mid+1,R,NewAttr,_indexer<<1|1);
}
}
#define ValueOfAttr(Attr) (Attr)
int AttrSumUp(int _indexer=1)
{
if(tree[_indexer].attr!=-1)
{
return ValueOfAttr(tree[_indexer].attr)*(tree[_indexer].rt-tree[_indexer].lt+1);
}
else
{
return AttrSumUp(_indexer<<1)+AttrSumUp(_indexer<<1|1);
}
}
}/// End of namespace AttributeSegmentTree成段更新的线段树(LAZY思想)
/// 延迟更新: 区间运算更新(加法), 区间运算(求和)
namespace LazySegmentTree
{
const int MAXN = 100100;
const int MAXTREENODE = MAXN << 2;
struct node
{
int lt,rt;
int val;
int add;
};
node tree[MAXTREENODE];
void _internal_PushUp(int _indexer)
{
tree[_indexer].val=tree[_indexer<<1].val+tree[_indexer<<1|1].val;
}
void _internal_PushDown(int _indexer)
{
if(tree[_indexer].add!=0)
{
/// Broadcast this add value to Left and Right sub-tree node.
tree[_indexer<<1].add+=tree[_indexer].add;
tree[_indexer<<1|1].add+=tree[_indexer].add;
/// Confirm this change by calculate and add changes to sub-trees.
tree[_indexer<<1].val+=tree[_indexer].add * (tree[_indexer<<1].rt-tree[_indexer<<1].lt+1);
tree[_indexer<<1|1].val+=tree[_indexer].add *(tree[_indexer<<1|1].rt-tree[_indexer<<1|1].lt+1);
/// Now Clear this node's add value.
tree[_indexer].add=0;
}
}
void build(int L,int R,int _indexer=1)
{
tree[_indexer].lt=L;
tree[_indexer].rt=R;
tree[_indexer].add=0;/// This must be set to 0.
if(L==R)
{
//scanf("%d",&tree[_indexer].val);
tree[_indexer].val = 0;
return;
}
int mid=(L+R)>>1;
build(L,mid,_indexer<<1);
build(mid+1,R,_indexer<<1|1);
/// Update this val from down to up. (>.<)
_internal_PushUp(_indexer);
}
void update(int L,int R,int ValToAdd,int _indexer=1)
{
/// Return when L or R exceeds range. So smart !
if(Rtree[_indexer].rt) return;
if(L<=tree[_indexer].lt&&R>=tree[_indexer].rt)
{
/// This range is covered. So just add the 'add' value, which is called "LAZY"
tree[_indexer].add+=ValToAdd;
tree[_indexer].val+=ValToAdd*(tree[_indexer].rt-tree[_indexer].lt+1);
return;
}
_internal_PushDown(_indexer);
/// This ... Hum.. Seems not so clever...
update(L,R,ValToAdd,_indexer<<1);
update(L,R,ValToAdd,_indexer<<1|1);
_internal_PushUp(_indexer);
}
int ans;
void basic_query(int L,int R,int _indexer=1)
{
/// Data to find is not in this range.
if(Rtree[_indexer].rt) return;
/// Data to find is right in this range , or covers this range.
if(L<=tree[_indexer].lt&&R>=tree[_indexer].rt)
{
ans+=tree[_indexer].val;
return ;
}
_internal_PushDown(_indexer);
int mid=(tree[_indexer].lt+tree[_indexer].rt)>>1;
if(R<=mid)
basic_query(L,R,_indexer<<1);
else if(L>mid)
basic_query(L,R,_indexer<<1|1);
else
{
basic_query(L,mid,_indexer<<1);
basic_query(mid+1,R,_indexer<<1|1);
}
}
int query(int L,int R)
{
ans=0;
basic_query(L,R);
return ans;
}
}/// End of namespace LazySegmentTree 成段更新，区间合并的线段树
/// 区间赋值更新, 区间合并, 查找左端
namespace AttributeMergeSegmentTree
{
const int MAXN = 100100;
const int MAXTREENODE = MAXN << 3;
const int ATTR_BY_DEFAULT=-1;///默认初始化属性 -1 无需操作 0 子树有住户离开 1 子树有住户进入 (来自POJ 3667)
struct node
{
int lt,rt;
int lsum,rsum,sum;
int attr;
};
node tree[MAXTREENODE];
void build(int L,int R,int _indexer=1)
{
tree[_indexer].lt=L;
tree[_indexer].rt=R;
tree[_indexer].attr=ATTR_BY_DEFAULT;
tree[_indexer].lsum=tree[_indexer].rsum=tree[_indexer].sum=R-L+1;
if(L!=R)
{
int mid=(L+R)>>1;
build(L,mid,_indexer<<1);
build(mid+1,R,_indexer<<1|1);
}
}
void update(int L,int R,int NewAttr,int _indexer=1)
{
if(L==tree[_indexer].lt&&R==tree[_indexer].rt)
{
tree[_indexer].lsum=tree[_indexer].rsum=tree[_indexer].sum=
NewAttr==1 ? 0 : tree[_indexer].rt-tree[_indexer].lt+1 ; /// Same as R-L+1
tree[_indexer].attr=NewAttr;
return;
}
/// Push Down (updated)
if(tree[_indexer].attr!=-1)
{
/// Sync the Attribute to sub-tree
tree[_indexer<<1].attr=tree[_indexer<<1|1].attr=tree[_indexer].attr;
tree[_indexer].attr=-1;
tree[_indexer<<1].rsum=tree[_indexer<<1].lsum=tree[_indexer<<1].sum= tree[_indexer<<1].attr==1 ? 0 : tree[_indexer<<1].rt-tree[_indexer<<1].lt+1;
tree[_indexer<<1|1].rsum=tree[_indexer<<1|1].lsum=tree[_indexer<<1|1].sum= tree[_indexer<<1|1].attr==1 ? 0 : tree[_indexer<<1|1].rt-tree[_indexer<<1|1].lt+1;
}
int mid=(tree[_indexer].lt+tree[_indexer].rt)>>1;
if(R<=mid)
{
update(L,R,NewAttr,_indexer<<1);
}
else if(L>mid)
{
update(L,R,NewAttr,_indexer<<1|1);
}
else
{
update(L,mid,NewAttr,_indexer<<1);
update(mid+1,R,NewAttr,_indexer<<1|1);
}
/// Push Up (updated)
tree[_indexer].lsum=tree[_indexer<<1].lsum; /// left & left
tree[_indexer].rsum=tree[_indexer<<1|1].rsum; /// right & right
if(tree[_indexer<<1].lsum == tree[_indexer<<1].rt-tree[_indexer].lt+1)
{
/// Father.LeftSum == RightSon.LeftSum + LeftSon.LeftSum
tree[_indexer].lsum+=tree[_indexer<<1|1].lsum;
}
/// Why tree[_indexer].rsum but not tree[_indexer<<1|1].rsum ???
if(tree[_indexer].rsum==tree[_indexer<<1|1].rt-tree[_indexer<<1|1].lt+1)
{
/// Father.RightSum == LeftSon.RightSum + RightSon.RightSum
tree[_indexer].rsum+=tree[_indexer<<1].rsum;
}
tree[_indexer].sum=max(max(tree[_indexer<<1].sum,tree[_indexer<<1|1].sum),tree[_indexer<<1].rsum+tree[_indexer<<1|1].lsum);
}
int query(int Val,int _indexer=1)
{
if(tree[_indexer].lt==tree[_indexer].rt)
{
return tree[_indexer].lt;
}
/// Push Down (updated)
if(tree[_indexer].attr!=-1)
{
/// Sync the Attribute to sub-tree
tree[_indexer<<1].attr=tree[_indexer<<1|1].attr=tree[_indexer].attr;
tree[_indexer].attr=-1;
tree[_indexer<<1].rsum=tree[_indexer<<1].lsum=tree[_indexer<<1].sum= tree[_indexer<<1].attr==1 ? 0 : tree[_indexer<<1].rt-tree[_indexer<<1].lt+1;
tree[_indexer<<1|1].rsum=tree[_indexer<<1|1].lsum=tree[_indexer<<1|1].sum= tree[_indexer<<1|1].attr==1 ? 0 : tree[_indexer<<1|1].rt-tree[_indexer<<1|1].lt+1;
}
int Mid=(tree[_indexer].rt+tree[_indexer].lt)>>1;
/// Left
if(tree[_indexer<<1].sum>=Val)
{
return query(Val,_indexer<<1);
}
/// Both Left and Right
else if(tree[_indexer<<1].rsum+tree[_indexer<<1|1].lsum >= Val)
{
return Mid-tree[_indexer<<1].rsum+1;
}
else /// Right
{
return query(Val,_indexer<<1|1);
}
}
}/// End of namespace AttributeMergeSegmentTree最长连续上升子段(LCIS)与线段树结合(HDU 3308) 模板
/// 最长连续上升字串 与线段树结合
namespace LCISSegmentTree
{
const int MAXN = 1000100;
const int MAXTREENODE = MAXN<<2;
int seq[MAXN];
struct node
{
/// Be Sure That "BounderLen" always equal to "RightBounder - LeftBounder + 1"
/// And Bounder Never change in one single test.
int leftbounder,rightbounder,bounderlen;
int leftseqlen,rightseqlen,mergedseqlen; /// From HDU 3308
int leftvalue,rightvalue;
};
node tree[MAXTREENODE];
/// _internal_v is a indexer of SegmentTree. It guides the procedure to the right node.
void pushup(int _internal_v)
{
/// Left == Left.Left
tree[_internal_v].leftseqlen=tree[_internal_v<<1].leftseqlen;
tree[_internal_v].leftvalue=tree[_internal_v<<1].leftvalue;
/// Right == Right.Right
tree[_internal_v].rightseqlen=tree[_internal_v<<1|1].rightseqlen;
tree[_internal_v].rightvalue=tree[_internal_v<<1|1].rightvalue;
/// Merged SeqLen is the max one of two sub-tree.MergedSeqLen
tree[_internal_v].mergedseqlen=max(tree[_internal_v<<1].mergedseqlen,tree[_internal_v<<1|1].mergedseqlen);
/// If LeftSon.RightValue < RightSon.LeftValue, a longer Seq may exist.
if(tree[_internal_v<<1].rightvalue>1;
build(L,mid,_internal_v<<1);
build(mid+1,R,_internal_v<<1|1);/// x<<1 == x*2; x<<1|1 == x*2+1; (faster == slower)
/// Push Up
pushup(_internal_v);
}
void update(int Pos,int Val,int _internal_v=1)/// Update a position, _internal_v is 1 by default.
{
/// Reach a clearly node with same LeftBounder and RightBounder
if(tree[_internal_v].leftbounder==tree[_internal_v].rightbounder)
{
tree[_internal_v].leftvalue=tree[_internal_v].rightvalue=Val;
return;
}
/// Calculate Mid
int mid=(tree[_internal_v].leftbounder+tree[_internal_v].rightbounder)>>1;
/// If in left then try update in left
if(Pos <= mid)
update(Pos,Val,_internal_v<<1);
else /// Else try update in right
update(Pos,Val,_internal_v<<1|1);
/// And then push it up !
pushup(_internal_v);
}
int query(int L,int R,int _internal_v=1)
{
/// This Node ( and the segment which is under its control )
/// is included in query area.
if(L<=tree[_internal_v].leftbounder && tree[_internal_v].rightbounder <= R)
{
return tree[_internal_v].mergedseqlen;
}
/// Calculate Mid
int mid=(tree[_internal_v].leftbounder+tree[_internal_v].rightbounder)>>1;
/// Answer saved in 'ans'
int ans=0;
/// Query If Segment L~R has common area with ThisNode.LeftBounder~Mid
if(L<=mid)
{
ans=max(ans,query(L,R,_internal_v<<1));
}
/// Query If Segment L~R has common area with Mid+1 ~ ThisNode.RightBounder
if(mid