ZOJ 4009 And Another Data Structure Problem(ZOJ Monthly, March 2018 Problem F,发现循环节 + 线段树 + 永久标记)

题目链接  ZOJ Monthly, March 2018 Problem F

题意很明确

这个模数很奇妙,在$[0, mod)$的所有数满足任意一个数立方$48$次对$mod$取模之后会回到本身。

所以开$48$棵线段树,和一个永久标记。当对某个区间操作时对这个区间加一层永久标记。

即当前我要查找的第$x$层,实际找的是第$up[i] + x$层。

时间复杂度$O(48nlogn)$

#include <bits/stdc++.h>

using namespace std;

#define rep(i, a, b)	for (int i(a); i <= (b); ++i)
#define dec(i, a, b) for (int i(a); i >= (b); --i)
#define ls i << 1
#define rs i << 1 | 1
#define mid ((l + r) >> 1)
#define lson ls, l, mid
#define rson rs, mid + 1, r typedef long long LL; const int N = 1e5 + 10;
const int mod = 99971; int T;
int a[N], nxt[N], cal[N][49];
int t[N << 2][49], up[N << 2];
int n, m; void pushup(int i){
rep(j, 0, 47){
t[i][j] = t[ls][(j + up[ls] + 48) % 48] + t[rs][(j + up[rs] + 48) % 48];
t[i][j] %= mod;
}
} void build(int i, int l, int r){
up[i] = 0;
if (l == r){
rep(j, 0, 47) t[i][j] = cal[a[l]][j];
return;
} build(lson);
build(rson);
pushup(i);
} void update(int i, int l, int r, int L, int R){
if (L <= l && r <= R){
++up[i];
up[i] %= 48;
return;
} if (L <= mid) update(lson, L, R);
if (R > mid) update(rson, L, R);
pushup(i);
} int query(int i, int l, int r, int L, int R, int cnt){
if (L <= l && r <= R){
return t[i][(up[i] + cnt) % 48];
} int ret = 0;
int now = cnt + up[i];
if (L <= mid) ret += query(lson, L, R, now);
if (R > mid) ret += query(rson, L, R, now);
ret %= mod;
return ret;
} int main(){ scanf("%d", &T);
rep(i, 1, mod - 1) nxt[i] = 1ll * i * i * i % mod;
rep(i, 1, mod - 1){
cal[i][0] = i;
rep(j, 1, 47){
cal[i][j] = nxt[cal[i][j - 1]];
}
} while (T--){
scanf("%d%d", &n, &m);
rep(i, 1, n){
scanf("%d", a + i);
a[i] %= mod;
} build(1, 1, n); while (m--){
int op, l, r;
scanf("%d%d%d", &op, &l, &r);
if (op == 1) update(1, 1, n, l, r);
else printf("%d\n", query(1, 1, n, l, r, 0));
}
} return 0;
}

  

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