# Grodno 2015 (Urozero May 2015 Day 5)

A. Palindromes

B. Modules

#include<cstdio>
#include<algorithm>
#include<bitset>
#include<cmath>
using namespace std;
const int N=505,M=1000;
int n,i,j,k,a[N],ans;
bitset<M>f[N][N];
int main(){
scanf("%d",&n);
if(n<1||n>300)while(1);
for(i=1;i<=n;i++){
scanf("%d",&a[i]);
if(a[i]<1||a[i]>300)while(1);
}
sort(a+1,a+n+1);
if(n==1)return printf("%d",a[1]),0;
if(n==2)return printf("%d",abs(a[1]-a[2])),0;
n--;
f[1][n+1][a[1]]=1;
f[0][n][a[n]]=1;
for(i=0;i<=n+1;i++)for(j=n+1;j>i;j--){
if(i+1<j)for(k=0;k<M;k++){
if(f[i][j][k]){
if(abs(k-a[i+1])>=M)while(1);
if(abs(k-a[j-1])>=M)while(1);
f[i+1][j][abs(k-a[i+1])]=1;
f[i][j-1][abs(k-a[j-1])]=1;
}
}
if(i+1==j)for(k=0;k<M;k++)if(f[i][j][k])ans=max(ans,abs(k-a[n+1]));
}
/*ans=abs(a[n-1]-a[n-2]);
for(i=n-3;i;i--)ans=abs(ans-a[i]);
ans=abs(ans-a[n]);*/
printf("%d",ans);
}
/*
8
4 7 3 1 4 6 10 5
*/


C. Rooks

#include<stdio.h>
#include<iostream>
#include<string.h>
#include<string>
#include<ctype.h>
#include<math.h>
#include<set>
#include<map>
#include<vector>
#include<queue>
#include<bitset>
#include<algorithm>
#include<time.h>
using namespace std;
void fre() {  }
#define MS(x, y) memset(x, y, sizeof(x))
#define ls o<<1
#define rs o<<1|1
typedef long long LL;
typedef unsigned long long UL;
typedef unsigned int UI;
template <class T1, class T2>inline void gmax(T1 &a, T2 b) { if (b > a)a = b; }
template <class T1, class T2>inline void gmin(T1 &a, T2 b) { if (b < a)a = b; }
const int N = 1e5 + 10, M = 0, Z = 1e9 + 7, inf = 0x3f3f3f3f;
template <class T1, class T2>inline void gadd(T1 &a, T2 b) { a = (a + b) % Z; }
int casenum, casei;
int n;

int main()
{
while(~scanf("%d", &n)){
printf("%d\n", (1 + n * n) * n * n / 2 - (1 + n * n) * n / 2);
}

return 0;
}
/*
【trick&&吐槽】

【题意】

【分析】

【时间复杂度&&优化】

*/


D. Triangles

#include<stdio.h>
#include<iostream>
#include<string.h>
#include<string>
#include<ctype.h>
#include<math.h>
#include<set>
#include<map>
#include<vector>
#include<queue>
#include<bitset>
#include<algorithm>
#include<time.h>
using namespace std;
void fre() {  }
#define MS(x, y) memset(x, y, sizeof(x))
#define ls o<<1
#define rs o<<1|1
typedef long long LL;
typedef unsigned long long UL;
typedef unsigned int UI;
template <class T1, class T2>inline void gmax(T1 &a, T2 b) { if (b > a)a = b; }
template <class T1, class T2>inline void gmin(T1 &a, T2 b) { if (b < a)a = b; }
const int N = 1e5 + 10, M = 0, Z = 1e9 + 7, inf = 0x3f3f3f3f;
template <class T1, class T2>inline void gadd(T1 &a, T2 b) { a = (a + b) % Z; }
int casenum, casei;
int P;
bool ok(LL a, LL c)
{
LL b = (a * a - c * c) / c;
return a + b + c <= P;
}
int v[N],p[N],tot,mu[N];
vector<int>mud[N];
inline int askcoprime(int x,int l,int r){
if(l>r)return 0;
//x>=1,l>=1
int ret=0;
for(int i=0;i<mud[x].size();i++){
int d=mud[x][i];
ret+=mu[d]*(r/d-(l-1)/d);
}
return ret;
}
void sieve(){
int i,j;
for(mu[1]=1,i=2;i<N;i++){
if(!v[i])mu[i]=-1,p[tot++]=i;
for(j=0;j<tot&&1LL*i*p[j]<N;j++){
v[i*p[j]]=1;
if(i%p[j])mu[i*p[j]]=-mu[i];else break;
}
}
for(i=1;i<N;i++)if(mu[i])for(j=i;j<N;j+=i)mud[j].push_back(i);
}
//
int main()
{
sieve();
while(~scanf("%d", &P))
{
LL ans = 0;
//x = sqrt(c)
for(LL x = 1; x * x <= P; ++x)
{
LL c = x * x;

LL L = x + 1;
LL R = x;

LL l = x + 1;
LL r = x + x - 1;
while(l <= r)
{
LL mid = (l + r >> 1);
if(ok(mid * x, c))
{
R = mid;
l = mid + 1;
}
else
{
r = mid - 1;
}
}
//a is [L, R]

if(L <= R)
{
}
}
printf("%lld\n", ans % Z);
}
return 0;
}
/*
【trick&&吐槽】

【题意】

【分析】

【时间复杂度&&优化】

*/


E. Supercomputer

F. Simple problem

#include<cstdio>
#include<iostream>
#include<queue>
#include<set>
#include<cstdlib>
using namespace std;
typedef long long ll;
ll K,A,B,P;set<ll>T;
void OK(){
puts("YES");
for(set<ll>::iterator it=T.begin();it!=T.end();it++)printf("%lld ",*it);
exit(0);
}
inline void gao(ll x){
ll l=A/x*x;
while(1){
if(l>=B)return;
if(l>A&&l<B){
puts("YES");
for(ll i=1;i<=K;i++)printf("%lld ",l);
exit(0);
T.insert(l);
//if(T.size()==K)OK();
}
l+=x;
}
}
int main(){
cin>>A>>B>>K>>P;
if(P==1)return puts("NO"),0;
for(ll i=2;i*i<=P;i++)if(P%i==0){
gao(i);
while(P%i==0)P/=i;
}
if(P>1)gao(P);
puts("NO");
}


G. Ancient problem

#include<cstdio>
typedef long long LL;
const int N=1010, Z = 1e9 + 7;
int n;
LL p[N], a[N], ans;

LL extend_gcd(LL a, LL b, LL &x, LL &y)
{
if(b == 0){
x = 1; y = 0;
return a;
}
else{
LL r = extend_gcd(b, a % b, y, x);
y -= x * (a / b);
return r;
}
}

LL line_mod_equation(LL a, LL b, LL n){
LL x, y;
LL d = extend_gcd(a, n, x, y);
LL ans;
if(b % d == 0){
x %= n; x += n; x %= n;
ans = x * (b / d) % (n / d);
}
return ans;
}

LL quickmul(LL x, LL y)
{
LL ans = 1;
while(y){
if(y & 1) ans = ans * x % Z;
y >>= 1;
x = x * x % Z;
}
return ans;
}

int main(){
while(~ scanf("%d", &n)){
for(int i = 1; i <= n; i ++){
scanf("%lld", &p[i]);
}
ans = 1;
for(int i = 1; i <= n; i ++){
a[i] = 1;
for(int j = 1; j <= n; j ++){
if(i != j) a[i] = a[i] * p[j] % p[i];
}
LL y = line_mod_equation(a[i], 1, p[i]);
a[i] = 1;
for(int j = 1; j <= n; j ++){
if(i != j) a[i] = a[i] * p[j] % (Z - 1);
}
ans = ans * quickmul(p[i], a[i] * y % (Z - 1)) % Z;
}
printf("%lld\n", ans);
}
return 0;
}


H. Combinatorics

#include<cstdio>
typedef long long ll;
const int M=300000,P=1000000007;
int n,i,all,sub;ll a[55],s[55];
int 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86433112,818254617,198532616,870605651,646184883,327890704,438569183,364380585,624902060,63375050,381703446,897560127,903288230,542351792,143745971,907002124,502614804,260466949,729521334,827102807,34223419,880521254,281744795,469449264,52363853,52097767,585145563,237120480,905415848,680015907,969123061,964404181,563045796,333219547,789556231,638406068,918664302,213092254,740938590,381785483,966640179,387628955,662565976,866444111,699722694,508943810,792638611,793307102,970104063,826766689,506416432,3624695,443183564,312329365,907388810,901161015,948724148,362928234,380480024,289805123,767370785,62659548,801639277,609048943,26804576,989024750,274007936,778983779,814306574,315177422,811826264,991853918,323582350,973313674,759005373,82441236,892050437,698308420,678383330,492881183,221350454,808369065,801413581,500512522,976705957,412675227,349322665,713258160,776502975,803331189,772391340,445933418,131731042,660234457,486620721,3991476,878640901,804861409,322961008,364058973,506421625,354103106,260831555,359056292,12618703,344608141,50477806,217298111,524150252,395850518,235142930,19270208,366761197,187697925,120685561,258450659,446634274,954913,154622141,186631946,33495801,181835443,338471174,808138529,285892973,437310030,371007759,10430738,652336595,96008232,34847604,826784106,864696066,304794421,918564215,282183879,10393336,567473423,326708726,832860641,817925464,816547758,426786760,636346220,217118148,790758484,89856602,946149627,420034479,792270972,600743238,514349511,71050762,104677203,860090592,205004338,630391823,462880311,793657339,4283891,598513367,458983926,411673788,354893353,712921767,716425891,842530849,965785236,311669452,108224705,560260153,633400565,545638190,790523771,318580210,668677123,910026008,881482632,42587322,437155518,792299597,36670825,84428155,929269243,944491355,528255018,629894526,512634493,445396258,186968777,320428001,924265341,860842034,296589615,520374634,171989322,457294725,967284733,679659893,63126637,603739686,812501999,671517513,916660987,858814345,246311854,164992964,165393390,8195350,483975089,509406823,114644779,685723887,53102426,617666448,207172258,623151847,532702135,768941501,429707160,198803488,779734593,642939667,53635336,960584207,116164597,197001309,536841269,368324673,630057303,792914276,386541987,994065976,627500870,573443769,599685896,966533706,301196854,759137421,371930700,775556523,767790141,20211256,379943099,792894374,824619763,946198358,373451745,596952378,752243809,114955307,925139828,268761837,860551136,818476649,578471809,348246100,576368335,52979524,120815665,592296500,119895268,98016105,291993453,23895805,206526983,441442575,847549272,724553294,374116154,782816485,550507082,420567331,976517503,555103342,946033733,886354425,216046746,283129306,85104325,312720425,877002932,383521365,765080455,599755664,894658473,474857680,780882948,311490118,74434897,433350723,35784547,128900492,973737505,168759145,139066955,353658242,869544707,778368564,590393084,926316480};
inline int pow(int a,int b){
int t=1;
for(;b;b>>=1,a=1LL*a*a%P)if(b&1)t=1LL*t*a%P;
return t;
}
inline int F(int n){
int ret=f[n/M];
for(int i=n/M*M+1;i<=n;i++)ret=1LL*ret*i%P;
return ret;
}
inline ll C(ll n,ll m){
if(n<m)return 0;
if(n==m)return 1;
if(!m)return 1;
return 1LL*F(n)*pow(F(m),P-2)%P*pow(F(n-m),P-2)%P;
}
int lucas(ll n,ll m){
if(n<m)return 0;
if(n==m)return 1;
if(!m)return 1;
return 1LL*C(n%P,m%P)*lucas(n/P,m/P)%P;
}
int main(){
scanf("%d",&n);
for(i=1;i<=n;i++)scanf("%lld",&a[i]);
for(i=n;i;i--)s[i]=s[i+1]+a[i];
all=sub=1;
for(i=n-1;i;i--){
all=1LL*all*lucas(s[i],a[i])%P;
sub=1LL*sub*lucas(s[i]-1,s[i+1])%P;
}
all=all-sub;
all%=P;
all+=P;
all%=P;
printf("%d",all);
}


I. Boring problem

#include<cstdio>
typedef __int128 lll;
long long P=1000000008LL;
lll cal(lll n){
lll A=n*(n+1)*(n+1)/2%P;
lll B=n*(n+1)*(n*2+1)/6%P;
A-=B;
A=A+P;
return A%P;
}
int main(){
int n,m;
scanf("%d%d",&n,&m);
lll A=cal(n),B=cal(m);
A=A*B%P;
A=(A+P)%P;
long long ans=A;
printf("%lld",ans);
}


J. Equation

K. Game

#include<cstdio>
#include<bitset>
using namespace std;
const int N=305,M=N*N/2;
int n,m,i,j;bitset<M>f[N];
int main(){
scanf("%d%d",&n,&m);
if(m==0)return puts("YES"),0;
if(m>=M)return puts("NO"),0;
for(i=1;i<n;i++){
f[i][i*(n-i)]=1;
for(j=i+1;j<n;j++)f[j]|=f[i]<<((j-i)*(n-j));
}
for(i=1;i<=n;i++)if(f[i][m])return puts("YES"),0;
puts("NO");
}


posted @ 2018-04-13 01:51 Claris 阅读(...) 评论(...) 编辑 收藏