不妨考虑已知一个区间[l,r]的k=1、k=2....k=r-l+1这些数的答案ans(只是这一个区间,不包含子区间)
那么如果加入一个新的数字a[i](i = r+1)
则新区间[l, i]的答案为ans + (c+1)*a[i] + s ,c为[l,r]中小于等于a[i]的数的个数,s为大于它的树的和
接下来考虑一个区间组,区间组i表示的是以i为结尾的所有区间
另dp[i]表示[1,i], [2,i] .... [i-1, i],[i, i]这些区间的答案和
那么dp[i+1] = dp[i] + ∑(j*a[j])(if a[j] >= a[i]) + ∑k*a[i](if a[k] < a[i]) + i*a[i]
这样的话,最后只需要把dp[1~n]加起来就构成了答案
上面的值可以使用树状数组或者线段树维护
这里还使用了hashmap来进行离散化
(线段树日常卡常数,优化很久才过)
#include <iostream> #include <cstdio> #include <cstring> #include <vector> #include <algorithm> #include <ext/hash_map> #define pb push_back #define fi first #define se second #define mp make_pair using namespace std; using namespace __gnu_cxx; const int maxn = 1e6 + 100; typedef long long LL; typedef pair<int, int> PII; vector<int> V(maxn, 0); const int MOD = (1e9 + 7) + 0.5; hash_map <int, int> H; PII tree[maxn*4]; PII v; int k, L, R; inline PII Add(PII a, PII b){ return {(a.fi + b.fi)%MOD, (a.se + b.se)%MOD}; } void Insert(int o, int l, int r){ if(l == r){ tree[o] = Add(tree[o], {v.fi, (LL)v.fi*v.se%MOD}); return; } int mid = (l+r)>>1; if(k <= mid) Insert(o<<1, l, mid); else Insert((o<<1)+1, mid+1, r); tree[o] = Add(tree[o<<1], tree[(o<<1)+1]); } PII Query(int o, int l, int r){ if(tree[o].fi == 0) return mp(0, 0); if(L <= l && r <= R){ return tree[o]; } int mid = (l+r)>>1; return Add((L <= mid ? Query(o*2, l, mid) : mp(0, 0)), (R > mid ? Query(o*2+1, mid+1, r) : mp(0, 0))); } int a[maxn], A, B, C; int n; void I_AM_ANGRY(){ for(int i = 2; i <= n; i++){ a[i] = ((LL)a[i-1]*A + B)%C; V[i] = a[i]; } /* for(int i = 2; i <= n; i += 2){ a[i] = ((LL)a[i-1]*A + B)%C; a[i+1] = ((LL)a[i]*A + B)%C; V[i] = a[i]; V[i+1] = a[i+1]; } */ /* for(int i = 2; i <= n; i += 4){ a[i] = ((LL)a[i-1]*A + B)%C; a[i+1] = ((LL)a[i]*A + B)%C; a[i+2] = ((LL)a[i+1]*A + B)%C; a[i+3] = ((LL)a[i+2]*A + B)%C; V[i] = a[i]; V[i+1] = a[i+1]; V[i+2] = a[i+2]; V[i+3] = a[i+3]; }*/ V[1] = a[1]; } int main() { cin>>n>>a[1]>>A>>B>>C; I_AM_ANGRY(); sort(V.begin(), V.end()); int tot = 0; for(auto x : V) if(!H[x]) H[x] = ++tot; LL dp = a[1], ans = dp; int N = n; n = tot; v = {1, a[1]}; k = H[a[1]]; Insert(1, 1, n); for(int i = 2; i <= N; i++){ int t = H[a[i]]; L = t; R = n; PII x = Query(1, 1, n); dp = (dp + x.se + (LL)(tree[1].fi - x.fi+i)*a[i])%MOD; v = {i, a[i]}; k = t; Insert(1, 1, n); ans += dp; } cout<<(ans%MOD + MOD)%MOD<<endl; return 0; }