Problem A?華華教奕奕寫幾何

https://ac.nowcoder.com/acm/contest/894/A

題意：

題解：思維+數學

C++版本一

/* *@Author: STZG *@Language: C++ */ #include <bits/stdc++.h> #include<iostream> #include<algorithm> #include<cstdlib> #include<cstring> #include<cstdio> #include<string> #include<vector> #include<bitset> #include<queue> #include<deque> #include<stack> #include<cmath> #include<list> #include<map> #include<set> //#define DEBUG #define RI register int #define endl "\n" using namespace std; typedef long long ll; //typedef __int128 lll; const int N=100000+10; const int M=100000+10; const int MOD=1e9+7; const double PI = acos(-1.0); const double EXP = 1E-8; const int INF = 0x3f3f3f3f; int t,n,m,k,p,l,r,u,v; int ans,cnt,flag,temp,sum; int a[N]; char str; struct node{}; int main() { #ifdef DEBUGfreopen("input.in", "r", stdin);//freopen("output.out", "w", stdout); #endif//ios::sync_with_stdio(false);//cin.tie(0);//cout.tie(0);//scanf("%d",&t);//while(t--){scanf("%d",&n);printf("%.3f\n",2*sqrt(n/PI));//}#ifdef DEBUGprintf("Time cost : %lf s\n",(double)clock()/CLOCKS_PER_SEC); #endif//cout << "Hello world!" << endl;return 0; }

Problem B?華華送奕奕小禮物

https://ac.nowcoder.com/acm/contest/894/B

題意：

題解：前綴和+二分

C++版本一

/* *@Author: STZG *@Language: C++ */ #include <bits/stdc++.h> #include<iostream> #include<algorithm> #include<cstdlib> #include<cstring> #include<cstdio> #include<string> #include<vector> #include<bitset> #include<queue> #include<deque> #include<stack> #include<cmath> #include<list> #include<map> #include<set> //#define DEBUG #define RI register int #define endl "\n" using namespace std; typedef long long ll; //typedef __int128 lll; const int N=1000+10; const int M=1000000+10; const int MOD=1e9+7; const double PI = acos(-1.0); const double EXP = 1E-8; const int INF = 0x3f3f3f3f; int t,n,m,k,p; ll l,r,u,v; ll ans,cnt,flag,temp,sum[2][N]; int a[N],b[N]; ll A[M]; char str; struct node{}; int main() { #ifdef DEBUGfreopen("input.in", "r", stdin);//freopen("output.out", "w", stdout); #endif//ios::sync_with_stdio(false);//cin.tie(0);//cout.tie(0);//scanf("%d",&t);//while(t--){scanf("%d%d%lld%lld",&n,&m,&l,&r);for(int i=1;i<=n;i++)scanf("%d",&a[i]),sum[0][i]=sum[0][i-1]+a[i];for(int i=1;i<=m;i++)scanf("%d",&b[i]),sum[1][i]=sum[1][i-1]+b[i];for(int i=1;i<=n;i++){for(int j=0;j<i;j++){A[++cnt]=sum[0][i]-sum[0][j];}}sort(A+1,A+cnt+1);for(int i=1;i<=m;i++){for(int j=0;j<i;j++){temp=sum[1][i]-sum[1][j];ans+=(upper_bound(A+1,A+cnt+1,(double)r/temp)-lower_bound(A+1,A+cnt+1,(double)l/temp));}}cout<<ans<<endl;//}#ifdef DEBUGprintf("Time cost : %lf s\n",(double)clock()/CLOCKS_PER_SEC); #endif//cout << "Hello world!" << endl;return 0; }

Problem C?華華跟奕奕玩游戲

https://ac.nowcoder.com/acm/contest/894/C

題意：

C++版本一

題解：矩陣快速冪

/* *@Author: STZG *@Language: C++ */ #include <bits/stdc++.h> #include<iostream> #include<algorithm> #include<cstdlib> #include<cstring> #include<cstdio> #include<string> #include<vector> #include<bitset> #include<queue> #include<deque> #include<stack> #include<cmath> #include<list> #include<map> #include<set> //#define DEBUG #define RI register int #define endl "\n" using namespace std; typedef long long ll; //typedef __int128 lll; const int N=100+10; const int M=100000+10; const int MOD=1e9+7; const double PI = acos(-1.0); const double EXP = 1E-8; const int INF = 0x3f3f3f3f; int t,n,m,k; ll q,p,l,r,u,v; int cnt,flag,temp,sum; int a,b; char str; struct node{}; ll POW(ll a,ll b,ll c){ll res=1;ll base=a%c;while(b){if(b&1)res=(res*base)%c;base=(base*base)%c;b>>=1;}return res; } struct Matrix{int n;Matrix(int nn = 1):n(nn){ memset(a,0,sizeof(a));};long long a[N][N];void print(){for(int i = 0;i <= n; ++i)for(int j= 0;j <= n; ++j)printf("%lld%c",a[i][j]," \n"[j==n]);}Matrix operator*(const Matrix &b)const{Matrix c(n);for(int i = 0;i <= n; ++i){for(int j = 0;j <= n; ++j){for(int k = 0;k <= n; ++k){c.a[i][j] += a[i][k] * b.a[k][j];c.a[i][j] %= MOD;}}}//c.print();return c;} }; Matrix ans,fac; void MatrixPOW(ll k){while(k){if(k&1)ans=ans*fac;fac=fac*fac;k>>=1;//ans.print();} } void init(){ans.n = fac.n = 2;ans.a[0][0] = n;ans.a[0][1] = (p*q)%MOD;fac.a[0][0] = q;fac.a[1][0] = 1;fac.a[1][1] = 1; } int main() { #ifdef DEBUGfreopen("input.in", "r", stdin);//freopen("output.out", "w", stdout); #endif//ios::sync_with_stdio(false);//cin.tie(0);//cout.tie(0);//scanf("%d",&t);//while(t--){scanf("%d%d%d%d%d",&n,&m,&k,&a,&b);p=(a*POW(b,MOD-2,MOD))%MOD;q=((n+m)*POW(n+m+1,MOD-2,MOD))%MOD;init();MatrixPOW(k);cout<<ans.a[0][0]<<endl;//}#ifdef DEBUGprintf("Time cost : %lf s\n",(double)clock()/CLOCKS_PER_SEC); #endif//cout << "Hello world!" << endl;return 0; }

C++版本二?

題解：數學+數列

?

/* *@Author: STZG *@Language: C++ */ #include <bits/stdc++.h> #include<iostream> #include<algorithm> #include<cstdlib> #include<cstring> #include<cstdio> #include<string> #include<vector> #include<bitset> #include<queue> #include<deque> #include<stack> #include<cmath> #include<list> #include<map> #include<set> //#define DEBUG #define RI register int #define endl "\n" using namespace std; typedef long long ll; //typedef __int128 lll; const int N=100+10; const int M=100000+10; const int MOD=1e9+7; const double PI = acos(-1.0); const double EXP = 1E-8; const int INF = 0x3f3f3f3f; int t,n,m,k; ll q,p,l,r,u,v; ll ans,cnt,flag,temp,sum; int a,b; char str; struct node{}; ll POW(ll a,ll b,ll c){ll res=1;ll base=a%c;while(b){if(b&1)res=(res*base)%c;base=(base*base)%c;b>>=1;}return res; } int main() { #ifdef DEBUGfreopen("input.in", "r", stdin);//freopen("output.out", "w", stdout); #endif//ios::sync_with_stdio(false);//cin.tie(0);//cout.tie(0);//scanf("%d",&t);//while(t--){scanf("%d%d%d%d%d",&n,&m,&k,&a,&b);p=(a*POW(b,MOD-2,MOD))%MOD;q=((n+m)*POW(n+m+1,MOD-2,MOD))%MOD;ll qk=POW(q,k,MOD);ll tmp=(q*POW((q-1+MOD)%MOD,MOD-2,MOD))%MOD;tmp=(tmp*((qk-1+MOD)%MOD))%MOD;ans=((n*qk)%MOD+(p*tmp)%MOD)%MOD;cout<<ans<<endl;//}#ifdef DEBUGprintf("Time cost : %lf s\n",(double)clock()/CLOCKS_PER_SEC); #endif//cout << "Hello world!" << endl;return 0; }

Problem D?華華陪奕奕打怪獸

https://ac.nowcoder.com/acm/contest/894/D

題意：

題解：

C++版本一

?

Problem E?華華和奕奕學物理

https://ac.nowcoder.com/acm/contest/894/E

題意：
若op==1,輸入v,t,m,表示在t時刻從無窮高處以初速度v垂直向下拋出一個質量為m的小球。
若op==2,輸入v,t。表示詢問t時刻所有速度小于等于v的小球的動能之和是多少。

題解：樹狀數組+數學+物理

C++版本一題解：

若某一時刻a球比b球速度快，則a球始終比b球速度快。取T=300000。對于1操作 v1,t1,m1?？梢运愠鯲1=v1+g*(T-t1)。對于2操作，可以算出V2=v2+g*(T-t2)。則需要查詢的小球即是滿足V1<=V2的小球。然后根據公式m1*(v1+g*(t2-t1))^2,拆開，維護6個樹狀數組即可。

/* *@Author: STZG *@Language: C++ */ #include <bits/stdc++.h> #include<iostream> #include<algorithm> #include<cstdlib> #include<cstring> #include<cstdio> #include<string> #include<vector> #include<bitset> #include<queue> #include<deque> #include<stack> #include<cmath> #include<list> #include<map> #include<set> //#define DEBUG #define RI register int #define endl "\n" using namespace std; typedef long long ll; //typedef __int128 lll; const int N=4000000+10; const int M=100000+10; const int T=300000; const int MOD=1e9+7; const double PI = acos(-1.0); const double EXP = 1E-8; const int INF = 0x3f3f3f3f; int t,n,m,k,p,l,r,u,v,g=10; ll ans,cnt,flag,temp; ll bit[8][N]; void add(ll b[],int i,ll C){while(i<N){b[i]=(b[i]+C)%MOD;i+=i&-i;} } ll sum(ll b[],int i){ll ans=0;while(i>0){ans+=b[i];i-=i&-i;}return ans%MOD; } int main() { #ifdef DEBUGfreopen("input.in", "r", stdin);//freopen("output.out", "w", stdout); #endif//ios::sync_with_stdio(false);//cin.tie(0);//cout.tie(0);//scanf("%d",&t);//while(t--){scanf("%d",&n);while(n--){scanf("%d",&p);if(p==1){scanf("%d%d%d",&v,&t,&m);int V=v+g*(T-t);add(bit[1],V,1LL*m*v%MOD*v%MOD);add(bit[2],V,1LL*m*g*g%MOD);add(bit[3],V,1LL*m*g*g%MOD*t%MOD*t%MOD);add(bit[4],V,1LL*2*m*g*g%MOD*t%MOD);add(bit[5],V,1LL*2*m*v%MOD*g%MOD);add(bit[6],V,1LL*2*m*v%MOD*g*t%MOD);}else{scanf("%d%d",&v,&t);int V=min(v+g*(T-t),N-1);ans=0;ans+=sum(bit[1],V);ans+=sum(bit[2],V)*t%MOD*t%MOD;ans+=sum(bit[3],V);ans-=sum(bit[4],V)*t%MOD;ans+=sum(bit[5],V)*t%MOD;ans-=sum(bit[6],V);ans=(ans%MOD+MOD)%MOD;printf("%lld\n",ans);}}//}#ifdef DEBUGprintf("Time cost : %lf s\n",(double)clock()/CLOCKS_PER_SEC); #endif//cout << "Hello world!" << endl;return 0; }

Problem F?華華和奕奕的旅行

https://ac.nowcoder.com/acm/contest/894/F

題意：

題解：

C++版本一

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