Codeforces Round #163 (Div. 2) E. More Queries to Array...

题意：有N个数，M个操作。（1）"= l r k"，表示把区间[l,r]的数全部变成k。（2）"? l r k"，查询区间[l,r]范围里。

k比较小，将式子拆开成多项式，一项一项加。数学的东西感觉多些。。

#include <iostream>#include <cstdio>#include <cstring>using namespace std;typedef long long LL;#define LL(x) (x<<1)#define RR(x) (x<<1|1)#define MID(a,b) (a+((b-a)>>1))const LL mod=1000000007;const int N=100005;const int K=10;LL C[K][K],S[N][K],a[N];LL pow(int x,int y){LL res=1;for(int i=0;i<y;i++) res=(res*(LL)x)%mod;return res;}struct node{int lft,rht;LL valu[K],flag;int mid(){return MID(lft,rht);}void fun(int tmp){flag=tmp;for(int i=0;i<K;i++){valu[i]=((((S[rht][i]-S[lft-1][i])%mod+mod)%mod)*flag)%mod;}}void init(){flag=-1;memset(valu,0,sizeof(valu));}};struct Seg{node tree[N*4];void PushUp(int ind){for(int i=0;i<K;i++)tree[ind].valu[i]=(tree[LL(ind)].valu[i]+tree[RR(ind)].valu[i])%mod;}void PushDown(int ind){if(tree[ind].flag==-1) return;tree[LL(ind)].fun(tree[ind].flag);tree[RR(ind)].fun(tree[ind].flag);tree[ind].flag=-1;}void build(int lft,int rht,int ind){tree[ind].lft=lft;tree[ind].rht=rht;tree[ind].init();if(lft==rht){for(int i=0;i<K;i++)tree[ind].valu[i]=(a[lft]*pow(lft,i))%mod;}else{int mid=tree[ind].mid();build(lft,mid,LL(ind));build(mid+1,rht,RR(ind));PushUp(ind);}}void updata(int st,int ed,int ind,int flag){int lft=tree[ind].lft,rht=tree[ind].rht;if(st<=lft&&rht<=ed) tree[ind].fun(flag);else{PushDown(ind);int mid=tree[ind].mid();if(st<=mid) updata(st,ed,LL(ind),flag);if(ed> mid) updata(st,ed,RR(ind),flag);PushUp(ind);}}LL query(int st,int ed,int ind,int k){int lft=tree[ind].lft,rht=tree[ind].rht;if(st<=lft&&rht<=ed) return tree[ind].valu[k];else{PushDown(ind);LL sum=0;int mid=tree[ind].mid();if(st<=mid) sum=(sum+query(st,ed,LL(ind),k))%mod;if(ed> mid) sum=(sum+query(st,ed,RR(ind),k))%mod;PushUp(ind);return sum%mod;}}}seg;void pre_calu(int n){for(int i=0;i<=K;i++) C[i][i]=C[i][0]=1;for(int i=2;i<K;i++)for(int j=1;j<i;j++)C[i][j]=(C[i-1][j-1]+C[i-1][j])%mod;for(int i=1;i<=n;i++)for(int j=0;j<K;j++)S[i][j]=(S[i-1][j]+pow(i,j))%mod;}int main(){int n,m;while(scanf("%d%d",&n,&m)!=EOF){pre_calu(n);for(int i=1;i<=n;i++) scanf("%I64d",&a[i]);seg.build(1,n,1);while(m--){char str[5];int l,r,k;scanf("%s%d%d%d",str,&l,&r,&k);if(str[0]=='=') seg.updata(l,r,1,k);else{LL res=0,t=1;for(int i=0;i<=k;i++){res=(res+((seg.query(l,r,1,k-i)*C[k][i])%mod*t)%mod)%mod;res=(res+mod)%mod;t=(t*(1-l))%mod;}printf("%I64d\n",res);}}}return 0;}