Problem A Play with Floor and Ceil http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=18&page=show_problem&problem=1614
扩展gcd求解2元不定式 ax+by=c d=gcd(a,b)=ax+by; x=x*c/d y=y*c/d
1 #include<cstdio>
2 typedef long long LL;
3 LL ext_gcd(LL a,LL b,LL &x,LL &y) { //扩展gcd d=gcd(a,b)=a*x+b*y; return d,x,y;
4 LL t,ret;
5 if(!b) {
6 x=1;
7 y=0;
8 return a;
9 }
10 ret=ext_gcd(b,a%b,x,y);
11 t=x;
12 x=y;
13 y=t-a/b*y;
14 return ret;
15 }
16 int main(){
17 int t,x,k;
18 while(~scanf("%d",&t)){
19 while(t--){
20 scanf("%d%d",&x,&k);
21 LL a=x/k;
22 LL b=a;
23 if(x%k) b++;
24 LL tx,ty;
25 LL d=ext_gcd(a,b,tx,ty);
26 printf("%lld %lld\n",tx*x/d,ty*x/d);
27 }
28 }
29 return 0;
30 }
Alternate Task http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=117&page=show_problem&problem=2828
求因子的和
1 #include<cstdio>
2 int ds_func(int n){//求n所有除数的和
3 int ret=1,m=n,t;
4 for(int i=2;i*i<=n;i+=(i==2)?1:2){
5 if(!(n%i)){
6 t=i*i;
7 n/=i;
8 while(!(n%i)){
9 t*=i;
10 n/=i;
11 }
12 ret*=(t-1)/(i-1);
13 }
14 }
15 return n>1?ret*(n+1):ret;
16 }
17 int main(){
18 int s,cas=1;
19 while(~scanf("%d",&s),s){
20 int ans=-1;
21 for(int i=s;i>=1;i--){
22 if(ds_func(i)==s){
23 ans=i;
24 break;
25 }
26 }
27 printf("Case %d: %d\n",cas++,ans);
28 }
29 return 0;
30 }
1434 - YAPTCHA http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&category=447&problem=4180&mosmsg=Submission+received+with+ID+14036675
找规律，发现3*k+7是素数值为1，否则为0，素数筛法。
1 #include<cstdio>
2 #include<cstring>
3 #define mt(a,b) memset(a,b,sizeof(a))
4 const int M=3000010;
5 int pri[M],mark[M],pricnt;//mark[i]存i的最小因子，素数时mark[i]==i
6 void sieve_primes() { //筛素数
7 pricnt=0;
8 mt(mark,0);
9 mark[0]=mark[1]=1;
10 for(int i=2; i<M; i++) {
11 if(!mark[i]) pri[pricnt++]=mark[i]=i;
12 for(int j=0; pri[j]*i<M; j++) {
13 mark[i*pri[j]]=pri[j];
14 if(!(i%pri[j])) break;
15 }
16 }
17 }
18 int ans[M];
19 int main(){
20 sieve_primes();
21 ans[0]=0;
22 for(int i=1;i<=1000000;i++){
23 int j=3*i+7;
24 ans[i]=ans[i-1];
25 if(mark[j]==j) ans[i]++;
26 }
27 int t,n;
28 while(~scanf("%d",&t)){
29 while(t--){
30 scanf("%d",&n);
31 printf("%d\n",ans[n]);
32 }
33 }
34 return 0;
35 }
1415 - Gauss Prime http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=447&page=show_problem&problem=4161
1 #include<cstdio>
2 typedef long long LL;
3 LL mulmod(LL a,LL b,LL c) { //ret=(a*b)%c
4 LL ret=0;
5 for(; b; a=(a<<1)%c,b>>=1) {
6 if(b&1) {
7 ret=(ret+a)%c;
8 }
9 }
10 return ret;
11 }
12 LL powmod(LL a,LL b,LL c) { //ret=(a^b)%mod
13 LL ret=1%c;
14 for(; b; a=mulmod(a,a,c),b>>=1) {
15 if(b&1) {
16 ret=mulmod(ret,a,c);
17 }
18 }
19 return ret;
20 }
21 bool suspect(LL a,int s,LL d,LL n) {
22 LL x=powmod(a,d,n);
23 if(x==1) return true;
24 while(s--) {
25 if(x==n-1) return true;
26 x=mulmod(x,x,n);
27 }
28 return false;
29 }
30 const int test[]= {2,3,5,7,11,13,17,19,23,29,-1}; // for n < 10^16
31 bool isprime(LL n) { //Miller-Rabin 大素数测试
32 if(n<=1||(n>2&&(!(n&1)))) return false;
33 LL d=n-1;
34 int s=0;
35 while(!(d&1)) {
36 s++;
37 d>>=1;
38 }
39 for(int i=0; test[i]<n&&~test[i]; i++) {
40 if(!suspect(test[i],s,d,n)) return false;
41 }
42 return true;
43 }
44 int main(){
45 int t,a,b;
46 while(~scanf("%d",&t)){
47 while(t--){
48 scanf("%d%d",&a,&b);
49 if(a){
50 LL t=a*a+2*b*b;
51 if(isprime(t)){
52 puts("Yes");
53 continue;
54 }
55 }
56 puts("No");
57 }
58 }
59 return 0;
60 }
end
数论比赛
时间： 2024-08-28 09:28:05