区间修改
当我们要修改一个区间时,要保证 (ax+b) 的形式,即先乘后加的形式。当将区间乘以一个数 (k) 时,原来的区间和为 (ax+b) ,乘以 (k) 得 (k(ax+b)=kax+kb) 。
区间加一个数更加简单,原来的区间和为 (ax+b) ,加上一个 (k) 为 (ax+b+k) ,合并 (b) ,(k) 得 (ax+(b+k)) 。
标记下传
[a(a'x+b')+b = (aa')cdot x + (ab'+b)
]
#include<bits/stdc++.h>
using namespace std;
#define lson l, mid, root << 1
#define rson mid + 1, r, root << 1 | 1
const int maxn = 100005;
long long tree[maxn << 2];
int n, p, q;
struct L{
long long mul, add;
}label[maxn << 2];
inline void pushUp(int root)
{
tree[root] = (tree[root << 1] + tree[root << 1 | 1]) % p;
}
inline void pushDown(int root, int len)
{
if(label[root].add == 0 && label[root].mul == 1) return;
else{
tree[root << 1] = (label[root].mul * tree[root << 1] + label[root].add * (len - (len >> 1))) % p;/***长度划分***/
tree[root << 1 | 1] = (label[root].mul * tree[root << 1 | 1] + label[root].add * (len >> 1)) % p;
label[root << 1].add = (label[root].mul * label[root << 1].add + label[root].add) % p;
label[root << 1 | 1].add = (label[root].mul * label[root << 1 | 1].add + label[root].add) % p;
label[root << 1].mul = (label[root << 1].mul * label[root].mul) % p;
label[root << 1 | 1].mul = (label[root << 1 | 1].mul * label[root].mul) % p;
label[root].add = 0; label[root].mul = 1;
}
}
void build(int l, int r, int root)
{
label[root].add = 0; label[root].mul = 1;
if(l == r){
scanf("%lld", &tree[root]); return;
}
int mid = (l + r) >> 1;
build(lson); build(rson);
pushUp(root);
}
void update(int l, int r, int root, int L, int R, int tag, int c)
{
if(L == l && R == r){
if(tag == 1){
tree[root] = tree[root] * c % p;
label[root].add = label[root].add * c % p;
label[root].mul = label[root].mul * c % p;
}else{
tree[root] = (tree[root] + c * (r - l + 1)) % p;
label[root].add = (label[root].add + c) % p;
}
return;
}
pushDown(root, r - l + 1);
int mid = (l + r) >> 1;
if(L >= mid + 1) update(rson, L, R, tag, c);
else if(R <= mid) update(lson, L, R, tag, c);
else{
update(lson, L, mid, tag, c); update(rson, mid + 1, R, tag, c);
}
pushUp(root);
}
long long query(int l, int r, int root, int L, int R)
{
if(L == l && R == r){
return tree[root] % p;
}
pushDown(root, r - l + 1);
int mid = (l + r) >> 1;
if(L >= mid + 1) return (query(rson, L, R) % p);
else if(R <= mid) return (query(lson, L, R) % p);
else{
return ((query(lson, L, mid) + query(rson, mid + 1, R)) % p);
}
}
int main()
{
scanf("%d%d", &n, &p);
build(1, n, 1);
scanf("%d", &q);
for(int cas = 1; cas <= q; cas++){
int tag, t, g, c;
scanf("%d", &tag);
if(tag == 1){
scanf("%d%d%d", &t, &g, &c);
update(1, n, 1, t, g, 1, c);
}
else if(tag == 2){
scanf("%d%d%d", &t, &g, &c);
update(1, n, 1, t, g, 2, c);
}
else{
scanf("%d%d", &t, &g);
printf("%lld
", query(1, n, 1, t, g) % p);
}
}
return 0;
}