目录
线段树的结构关系:
int作为下标的:
long long作为下标的:
类的构造函数写在类最后了,本板子没有将左右下标封装到节点中,而是实时计算的。
建议阅读:线段树 - OI Wiki (oi-wiki.org)
// 1
// 2 3 2^1
// 4 5 6 7 2^2
// 8 9 2^3
//1 log1==0
//2 log2==1 log3==1
//4 log4==2 log5==log6==log7==2
//8
//log5 == 2, +1在第三层,0~3 共四层 4
//
//完全二叉树的总结点数就是:
//等比数列求和
//1*(2^ - 1)/(2-1)
//logn + 1层
//pow(2,(int)log2(n)+1)-1
//
template
class ST//segment tree
{
struct node
{
T val;
T t;//懒标记//服务后代
node(T v = 0) :val(v), t(0)
{}
};
int n = a.size();
vectora;
vectord;
public:
void build_tree(int i, int l, int r)
{
if (l == r)
{
d[i].val = a[l];
return;
}
int mid = l + (r - l) / 2;
build_tree(i * 2, l, mid);
build_tree(i * 2 + 1, mid + 1, r);
d[i].val = d[i * 2].val + d[i * 2 + 1].val;
}
void spread(int i, int l, int r, int aiml, int aimr)
{
int mid = l + (r - l) / 2;
if (d[i].t != 0 && l != r)
{
d[i * 2].val += d[i].t * (mid - l + 1);
d[i * 2 + 1].val += d[i].t * (r - mid);
d[i * 2].t += d[i].t;//可能上上次也没改
d[i * 2 + 1].t += d[i].t;
d[i].t = 0;
}
}
T getsum(int l, int r)
{
return _getsum(1, 1, n, l, r);
}
T _getsum(int i, int l, int r, int aiml, int aimr)
{
if (aiml <= l && r <= aimr)//查询区间的子集全部加起来
return d[i].val;
//访问
int mid = l + (r - l) / 2;
spread(i, l, r, aiml, aimr);
T ret = 0;
if (aiml <= mid)
ret += _getsum(i * 2, l, mid, aiml, aimr);
if (aimr >= mid + 1)
ret += _getsum(i * 2 + 1, mid + 1, r, aiml, aimr);
return ret;
}
void update(int l, int r, ll val)
{
_update(1, 1, n, l, r, val);//加并挂标记
}
void _update(int i, int l, int r, int aiml, int aimr, ll val)
{
if (aiml <= l && r <= aimr)
{
d[i].val += val * (r - l + 1);
d[i].t += val;
return;
}
int mid = l + (r - l) / 2;
spread(i, l, r, aiml, aimr);
if (aiml <= mid)
_update(i * 2, l, mid, aiml, aimr, val);
if (aimr >= mid + 1)
_update(i * 2 + 1, mid + 1, r, aiml, aimr, val);
//我们只对叶子更新了,(别多想懒标记)
d[i].val = d[i * 2].val + d[i * 2 + 1].val;
}
ST(vectorarr)
{
a = arr;
n = a.size() - 1;
d = vector(pow(2, (int)log2(n) + 1 + 1) - 1 + 1);
build_tree(1, 1, n);
}
};
#define ll long long
template
class ST//segment tree
{
struct node
{
T val;
T t;//懒标记//服务后代
node(T v = 0) :val(v), t(0)
{}
};
ll n = a.size();
vectora;
vectord;
public:
void build_tree(ll i, ll l, ll r)
{
if (l == r)
{
d[i].val = a[l];
return;
}
ll mid = l + (r - l) / 2;
build_tree(i * 2, l, mid);
build_tree(i * 2 + 1, mid + 1, r);
d[i].val = d[i * 2].val + d[i * 2 + 1].val;
}
void spread(ll i, ll l, ll r, ll aiml, ll aimr)
{
ll mid = l + (r - l) / 2;
if (d[i].t != 0 && l != r)
{
d[i * 2].val += d[i].t * (mid - l + 1);
d[i * 2 + 1].val += d[i].t * (r - mid);
d[i * 2].t += d[i].t;//可能上上次也没改
d[i * 2 + 1].t += d[i].t;
d[i].t = 0;
}
}
T getsum(ll l, ll r)
{
return _getsum(1, 1, n, l, r);
}
T _getsum(ll i, ll l, ll r, ll aiml, ll aimr)
{
if (aiml <= l && r <= aimr)//查询区间的子集全部加起来
return d[i].val;
//访问
ll mid = l + (r - l) / 2;
spread(i, l, r, aiml, aimr);
T ret = 0;
if (aiml <= mid)
ret += _getsum(i * 2, l, mid, aiml, aimr);
if (aimr >= mid + 1)
ret += _getsum(i * 2 + 1, mid + 1, r, aiml, aimr);
return ret;
}
void update(ll l, ll r, ll val)
{
_update(1, 1, n, l, r, val);//加并挂标记
}
void _update(ll i, ll l, ll r, ll aiml, ll aimr, ll val)
{
if (aiml <= l && r <= aimr)
{
d[i].val += val * (r - l + 1);
d[i].t += val;
return;
}
ll mid = l + (r - l) / 2;
spread(i, l, r, aiml, aimr);
if (aiml <= mid)
_update(i * 2, l, mid, aiml, aimr, val);
if (aimr >= mid + 1)
_update(i * 2 + 1, mid + 1, r, aiml, aimr, val);
//我们只对叶子更新了,(别多想懒标记)
d[i].val = d[i * 2].val + d[i * 2 + 1].val;
}
ST(vectorarr)
{
a = arr;
n = a.size() - 1;
d = vector(pow(2, (ll)log2(n) + 1 + 1) - 1 + 1);
build_tree(1, 1, n);
}
};