# 【BZOJ2752】【Luogu P2221】 [HAOI2012]高速公路

#include <bits/stdc++.h>
using namespace std;

const int N = 100000 + 5;

#define ls (p << 1)
#define rs (p << 1 | 1)
#define mid ((l + r) >> 1)
#define int long long

int n, m, sum1, sum2, sum3;

struct Segment_Tree {
int tag[N << 2], s1[N << 2], s2[N << 2], s3[N << 2];

Segment_Tree () {
memset (s1, 0, sizeof (s1));
memset (s2, 0, sizeof (s2));
memset (s3, 0, sizeof (s3));
memset (tag, 0, sizeof (tag));
}

void push_up (int p) {
s1[p] = s1[ls] + s1[rs];
s2[p] = s2[ls] + s2[rs];
s3[p] = s3[ls] + s3[rs];
}

int F1 (int x, int y) {return y - x + 1;}  // \sum_{i = x} ^ {y} i ^ 0
int F2 (int x, int y) {return (x + y) * (y - x + 1) / 2;} // \sum_{i = x} ^ {y} i ^ 1
int F3 (int x, int y) {
x = x - 1;
int w1 = x * (x + 1) * (2 * x + 1) / 6;
int w2 = y * (y + 1) * (2 * y + 1) / 6;
return w2 - w1;
} // \sum_{i = x} ^ {y} i ^ 2

void work (int p, int l, int r, int val) {
s1[p] += F1 (l, r) * val;
s2[p] += F2 (l, r) * val;
s3[p] += F3 (l, r) * val;
tag[p] += val;
}

void push_down (int p, int l, int r) {
work (ls, l, mid + 0, tag[p]);
work (rs, mid + 1, r, tag[p]);
tag[p] = 0;
}

void modify (int nl, int nr, int w, int l = 1, int r = n, int p = 1) {
if (nl <= l && r <= nr) {
work (p, l, r, w);
return;
}
push_down (p, l, r);
if (nl <= mid) modify (nl, nr, w, l, mid, ls);
if (mid < nr) modify (nl, nr, w, mid + 1, r, rs);
push_up (p); return;
}

void query (int nl, int nr, int l = 1, int r = n, int p = 1) {
if (nl <= l && r <= nr) {
sum1 += s1[p];
sum2 += s2[p];
sum3 += s3[p];
return;
}
push_down (p, l, r);
if (nl <= mid) query (nl, nr, l, mid, ls);
if (mid < nr) query (nl, nr, mid + 1, r, rs);
push_up (p); return;
}
}tr; // 维护 \sum_{x = L}^{R} sumd(x)

int gcd (int x, int y) {
return y ? gcd (y, x % y) : x;
}

signed main () {
freopen ("data.in", "r", stdin);
cin >> n >> m;
for (int i = 1; i <= m; ++i) {
char opt; int l, r, v;
cin >> opt;
if (opt == 'C') {
cin >> l >> r >> v; r--;
tr.modify (l, r, v);
} else {
cin >> l >> r; r--;
sum1 = sum2 = sum3 = 0;
tr.query (l, r);
int w1 = (r - l + 1 - r * l);
int w2 = l + r;
int w3 = -1;
int upp = w1 * sum1 + w2 * sum2 + w3 * sum3;
int dwn = (r - l + 2) * (r - l + 1) / 2;
int d = gcd (upp, dwn); upp /= d, dwn /= d;
cout << upp << "/" << dwn << endl;
}
}
}

posted @ 2019-05-28 20:15  maomao9173  阅读(82)  评论(0编辑  收藏  举报