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Algorithm

线段树 Segment Tree

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线段树（Segment Tree）是一种数据结构，它支持区间最大值、最小值以及区间和的查询的修改操作，时间复杂度O（nlogn）。

C++
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#include <cstdio>
#include <iostream>
#include <cstring>
#include <algorithm>
 
using namespace std;
 
typedef long long LL;
 
const int maxn = 100005;
 
int n, m, x, y, opt = 0;
LL z;
LL a[maxn];
 
struct Segment_Tree
{
LL l, r, sum, max_val, min_val, tag;
} tree[maxn << 4];
 
inline int getint()
{
int r = 0, k = 1;
char c = getchar();
for(; c < '0' || c > '9'; c = getchar())
if(c == '-') k = -1;
for(; c >= '0' && c <= '9'; c = getchar())
r = r * 10 + c - '0';
return r * k;
}
 
inline LL getll()
{
LL r = 0, k = 1;
char c = getchar();
for(; c < '0' || c > '9'; c = getchar())
if(c == '-') k = -1;
for(; c >= '0' && c <= '9'; c = getchar())
r = r * 10 + c - '0';
return r * k;
}
 
void push_up(int now)
{
tree[now].sum = tree[now << 1].sum + tree[now << 1 | 1].sum;
tree[now].max_val = max(tree[now << 1].max_val, tree[now << 1 | 1].max_val);
tree[now].min_val = min(tree[now << 1].min_val, tree[now << 1 | 1].min_val);
return;
}
 
void push_down(int now)
{
tree[now << 1].tag += tree[now].tag;
tree[now << 1].sum += tree[now].tag * (tree[now << 1].r - tree[now << 1].l + 1);
tree[now << 1].max_val += tree[now].tag;
tree[now << 1].min_val += tree[now].tag;
 
tree[now << 1 | 1].tag += tree[now].tag;
tree[now << 1 | 1].sum += tree[now].tag * (tree[now << 1 | 1].r - tree[now << 1 | 1].l + 1);
tree[now << 1 | 1].max_val += tree[now].tag;
tree[now << 1 | 1].min_val += tree[now].tag;
 
tree[now].tag = 0;
 
return;
}
 
void build(int now, int l, int r)
{
tree[now].l = l;
tree[now].r = r;
tree[now].tag = 0;
 
if(l == r)
{
tree[now].sum = tree[now].max_val = tree[now].min_val = a[l];
return;
}
 
int mid = (tree[now].l + tree[now].r) >> 1;
build(now << 1, l, mid);
build(now << 1 | 1, mid + 1, r);
 
push_up(now);
return;
}
 
void update(int now, int ll, int rr, LL x)
{
if(ll <= tree[now].l && tree[now].r <= rr)
{
tree[now].tag += x;
tree[now].sum += x * (tree[now].r - tree[now].l + 1);
tree[now].max_val += x;
tree[now].min_val += x;
return;
}
 
push_down(now);
 
int mid = (tree[now].l + tree[now].r) >> 1;
if(rr <= mid) update(now << 1, ll, rr, x);
else if(ll > mid) update(now << 1 | 1, ll, rr, x);
else
{
update(now << 1, ll, mid, x);
update(now << 1 | 1, mid + 1, rr, x);
}
 
push_up(now);
return;
}
 
LL query_sum(int now, int ll, int rr)
{
if(ll <= tree[now].l && tree[now].r <= rr) return tree[now].sum;
push_down(now);
 
int mid = (tree[now].l + tree[now].r) >> 1;
if(rr <= mid) return query_sum(now << 1, ll, rr);
else if(ll > mid) return query_sum(now << 1 | 1, ll, rr);
else return (query_sum(now << 1, ll, mid) + query_sum(now << 1 | 1, mid + 1, rr));
}
 
LL query_max(int now, int ll, int rr)
{
if(ll <= tree[now].l && tree[now].r <= rr) return tree[now].max_val;
push_down(now);
 
int mid = (tree[now].l + tree[now].r) >> 1;
if(rr <= mid) return query_max(now << 1, ll, rr);
else if(ll > mid) return query_max(now << 1 | 1, ll, rr);
else return max(query_max(now << 1, ll, mid), query_max(now << 1 | 1, mid + 1, rr));
}
 
LL query_min(int now, int ll, int rr)
{
if(ll <= tree[now].l && tree[now].r <= rr) return tree[now].max_val;
push_down(now);
 
int mid = (tree[now].l + tree[now].r) >> 1;
if(rr <= mid) return query_min(now << 1, ll, rr);
else if(ll > mid) return query_min(now << 1 | 1, ll, rr);
else return min(query_min(now << 1, ll, mid), query_min(now << 1 | 1, mid + 1, rr));
}
 
int main(int argc, char const * argv[])
{
ios :: sync_with_stdio(false);
 
n = getint();
m = getint();
 
for(int i = 1; i <= n; i++) a[i] = getll();
 
build(1, 1, n);
 
while(m--)
{
opt = getint();
x = getint();
y = getint();
 
if(opt == 1)
{
z = getll();
update(1, x, y, z);
}
 
else if(opt == 2)
{
printf("%lld\n", query_sum(1, x, y));
}
}
 
return 0;
}

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