【模板】分块

题意简述

已知一个数列，你需要进行下面两种操作：
1.将某区间每一个数加上x
2.求出某区间每一个数的和

题解思路

对于一个长度为n的序列，我们可以讲其中的元素分为\( \sqrt{n} \) 个连续的子序列，每块的长度自然就为\( \sqrt{n} \)。
我们更新一段区间[l,r]，可以先更新l到l所在块的右端点，r到r所在块的右端点到r和中间的整个区间。

代码

#include <cmath>
#include <cstdio>
using namespace std;
typedef long long ll;
struct Point{ll w, num;
};
struct K{ll l, r, tot, sum;ll len(){return r - l + 1;} 
};
ll n, m, s, len;
Point p[100001];
K k[501];
void add(ll x, ll y, ll t)
{if (p[x].num == p[y].num){for (register ll i = x; i <= y; ++i)p[i].w += t;k[p[x].num].tot += (y - x + 1) * t;return;}for (register ll i = x; i <= k[p[x].num].r; ++i)p[i].w += t;k[p[x].num].tot += (k[p[x].num].r - x + 1) * t;for (register ll i = k[p[y].num].l; i <= y; ++i)p[i].w += t;k[p[y].num].tot += (y - k[p[y].num].l + 1) * t;for (register ll i = p[x].num + 1; i <= p[y].num - 1; ++i){k[i].tot += t * k[i].len();k[i].sum += t;}
}
ll query(ll x, ll y)
{ll ans = 0;if (p[x].num == p[y].num){for (register ll i = x; i <= y; ++i)ans += p[i].w;return ans;}for (register ll i = x; i <= k[p[x].num].r; ++i)ans += p[i].w + k[p[x].num].sum;for (register ll i = k[p[y].num].l; i <= y; ++i)ans += p[i].w + k[p[y].num].sum;for (register ll i = p[x].num + 1; i <= p[y].num - 1; ++i)ans += k[i].tot;return ans;
}
int main()
{scanf("%lld%lld", &n, &m);len = sqrt(n);s = n / len + (bool)(n % len);for (register ll i = 1; i <= s; ++i){k[i].l = (i - 1) * len + 1;k[i].r = i * len;}k[s].r = n;for (register ll i = 1; i <= n; ++i){scanf("%lld", &p[i].w);p[i].num = (i - 1) / len + 1;k[p[i].num].tot += p[i].w;}for (register ll i = 1; i <= m; ++i){ll op, x, y, t;scanf("%lld", &op);if (op == 1){scanf("%lld%lld%lld", &x, &y, &t);add(x, y, t);}else{scanf("%lld%lld", &x, &y);printf("%lld\n", query(x, y));}}return 0;
}