Codeforces 1109E 线段树

思路及博客：https://www.cnblogs.com/uid001/p/10507346.html

代码：

#include <bits/stdc++.h>
#define LL long long
#define ls(x) (x << 1)
#define rs(x) ((x << 1) | 1)
using namespace std;
const int maxn = 100010;
int m;
int p[20], b[maxn], tot, re[10];
LL Phi;
LL qpow(LL a, LL b) {
	LL ans = 1;
	for (; b; b >>= 1) {
		if(b & 1) ans = (ans * a) % m;
		a = a * a % m;
	}
	return ans;
}
LL phi(LL n) {
	LL ans = n;
	for (int i = 2; i * i <= n; i++) {
		if(n % i == 0) {
			ans = ans / i * (i - 1);
			p[tot++] = i;
			while(n % i == 0) n /= i; 
		}
	}
	if(n > 1) {
		p[tot++] = n;
		ans = ans / n * (n - 1);
	} 
	return ans;
}
struct SegmentTree {
	LL remain, rtag;
	LL tag, sum;
	LL a[10], flag[10];
};
SegmentTree tr[maxn * 4];
void pushup(int o) {
	tr[o].sum = (tr[ls(o)].sum + tr[rs(o)].sum) % m;
}
void pushdown(int o) {
	if(tr[o].rtag != 1) {
		tr[ls(o)].remain = (tr[ls(o)].remain * tr[o].rtag) % m;
		tr[ls(o)].rtag = (tr[ls(o)].rtag * tr[o].rtag) % m;
		tr[rs(o)].remain = (tr[rs(o)].remain * tr[o].rtag) % m;
		tr[rs(o)].rtag = (tr[rs(o)].rtag * tr[o].rtag) % m;
		tr[o].rtag = 1;
	}
	if(tr[o].tag != 1) {
		tr[ls(o)].sum = (tr[ls(o)].sum * tr[o].tag) % m;
		tr[ls(o)].tag = (tr[ls(o)].tag * tr[o].tag) % m;
		tr[rs(o)].sum = (tr[rs(o)].sum * tr[o].tag) % m;
		tr[rs(o)].tag = (tr[rs(o)].tag * tr[o].tag) % m;
		tr[o].tag = 1;
	}
	for (int i = 0; i < tot; i++) {
		tr[ls(o)].a[i] = (tr[ls(o)].a[i] + tr[o].flag[i]);
		tr[ls(o)].flag[i] = (tr[ls(o)].flag[i] + tr[o].flag[i]);
		tr[rs(o)].a[i] = (tr[rs(o)].a[i] + tr[o].flag[i]);
		tr[rs(o)].flag[i] = (tr[rs(o)].flag[i] + tr[o].flag[i]);
		tr[o].flag[i] = 0;
	}
}
void build(int o, int l, int r) {
	tr[o].remain = tr[o].tag = tr[o].sum = tr[o].rtag = 1;
	memset(tr[o].a, 0, sizeof(tr[o].a));
	memset(tr[o].flag, 0, sizeof(tr[o].flag));
	if(l == r) {
		tr[o].sum = b[l] % m;
		for (int i = 0; i < tot; i++) {
			while(b[l] % p[i] == 0) {
				b[l] /= p[i];
				tr[o].a[i]++;
			}
		}
		tr[o].remain = b[l] % m;
		return; 
	}
	int mid = (l + r) >> 1;
	build(ls(o), l, mid);
	build(rs(o), mid + 1, r);
	pushup(o);
}
void mul(int o, int l, int r, int ql, int qr, LL x, LL y) {
	if(l >= ql && r <= qr) {
		tr[o].sum = (tr[o].sum * x) % m;
		tr[o].tag = (tr[o].tag * x) % m;
		tr[o].remain = (tr[o].remain * y) % m;
		tr[o].rtag = (tr[o].rtag * y) % m;
		for (int i = 0; i < tot; i++) {
			tr[o].flag[i] += re[i];
			tr[o].a[i] += re[i];
		}
		return;
	}
	pushdown(o);
	int mid = (l + r) >> 1;
	if(ql <= mid) mul(ls(o), l, mid, ql, qr, x, y);
	if(qr > mid) mul(rs(o), mid + 1, r, ql, qr, x, y);
	pushup(o);
}
void div(int o, int l, int r, int pos, LL y) {
	if(l == r) {
		for (int i = 0; i < tot; i++) {
			while(y % p[i] == 0) y /= p[i], tr[o].a[i]--;
		}
		tr[o].remain = (tr[o].remain * qpow(y, Phi - 1)) % m;
		tr[o].sum = tr[o].remain;
		for (int i = 0; i < tot; i++)
			tr[o].sum = (tr[o].sum * qpow(p[i], tr[o].a[i])) % m;
		return;
	}
	pushdown(o);
	int mid = (l + r) >> 1;
	if(pos <= mid) div(ls(o), l, mid, pos, y);
	else div(rs(o), mid + 1, r, pos, y);
	pushup(o); 
}
LL query(int o, int l, int r, int ql, int qr) {
	if(l >= ql && r <= qr) return tr[o].sum;
	pushdown(o);
	int mid = (l + r) >> 1;
	LL ans = 0;
	if(ql <= mid) ans = (ans + query(ls(o), l, mid, ql, qr)) % m;
	if(qr > mid) ans = (ans + query(rs(o), mid + 1, r, ql, qr)) % m;
	return ans;
}
int main() {
	int n;
	scanf("%d%lld", &n, &m);
	Phi = phi(m);
	for (int i = 1; i <= n; i++) {
		scanf("%d", &b[i]);
	}
	int t, op, x, y, z;
	build(1, 1, n);
	scanf("%d", &t);
	while(t--) {
		scanf("%d", &op);
		if(op == 1) {
			scanf("%d%d%d", &x, &y, &z);
			int tmp = z;
			for (int i = 0; i < tot; i++) {
				re[i] = 0;
				while(tmp % p[i] == 0) {
					tmp /= p[i];
					re[i]++;
				}
			}
			mul(1, 1, n, x, y, z, tmp);
		} else if(op == 2) {
			scanf("%d%d", &x, &y);
			div(1, 1, n, x, y);
		} else {
			scanf("%d%d", &x, &y);
			printf("%lld
", query(1, 1, n, x, y));
		} 
	}
}