函数专题

第一题

#include<bits/stdc++.h> 
using namespace std;


int main() {
	int s,t;
	cin>>s>>t;
	int ans = 0 ;
	for (int i = s ; i <= t ; i ++ ) {
		int x = i,cnt = 0;
		while (x) {
			cnt++;
			x=x&(x-1);
		}
		if (cnt<=4) ans++;
	}
	cout<<ans<<endl;
	return 0	;
}

第二题

#include<bits/stdc++.h>
using namespace std;


int gcd(int a,int b) {
	while (b>0) {
		int tmp = a;
		a = b;
		b = tmp%b;
	}
	return a;
}
int GCD(int a,int b) {
	if (b==0) return a;
	return GCD(b,a%b);
}
int main() {
	//cout<<gcd(12,8)<<endl;
	int n,ans;
	cin>>n>>ans;
	for (int i = 2; i <= n ; i ++) {
		int x;cin>>x;
		ans = gcd(ans,x);
	}
	cout<<ans<<endl;
	return 0;
}

第三题

#include<bits/stdc++.h>
using namespace std;
int a,b;
bool iswq(int n){
	int x = n;
	int sum = 0;
	//a是n的约数，n/a也是n的因子.
	//a<=n/a a*a<=n 
	for (int i = 1; i*i <= n ; i ++) {
		if (n%i==0) {
			sum+=i;
			if (i>1&&i*i!=n) sum+=n/i;
		}
	}
	return sum==x;
}
string to16(int n) {
	string s="";
	while (n) {
		if (n%16>9) s = char(n%16+'A'-10)+s;
		else s = char('0'+n%16)+s;
		n/=16;
	}	
	return s;
}
int main() {
	int s,t;
	cin>>s>>t;
	iswq(6);
	while (s<=t) {
		if (iswq(s)) {
			cout<<to16(s)<<' ';
		}
		s++;
	}
	return 0;
}

第四题

#include<bits/stdc++.h>
using namespace std;

bool isprime(int x) {
	if (x<2) return false;
	if (x==2) return true;
	if (x%2==0) return false;
	for (int i = 3 ; i * i <= x ; i +=2) {
		if (x%i==0) return false;
	}
	return true;
}
int suo(int x) {
	int p = 10;
	//123%1000=123
	//123%100=23
	//123%10=3
	while (x/p!=0) p*=10;
	p/=10;
	return x%p;
}

int main() {
	int n;
	cin>>n;
	for (int i = 2; i <= n ; i ++ ) {
		int x = i;
		bool flag = true;
		while (x) {
			if (!isprime(x)) {
				flag=false;
				break;
			}
			x=suo(x);
		}
		if (flag) cout<<i<<' ';
	}
	cout<<endl;
	return 0;
}

第五题

#include<bits/stdc++.h>
using namespace std;
int a[10][10];
bool lie(int j) {
	bool p[10];memset(p,0,sizeof(p));
	for (int i = 1; i <= 9 ; i ++) 
	  if (p[a[i][j]]||a[i][j]==0) return false;
	  else p[a[i][j]]=true;
	return true;
}
bool hang(int i) {
	bool p[10];memset(p,0,sizeof(p));
	for (int j = 1; j <= 9 ; j ++) 
	  if (p[a[i][j]]||a[i][j]==0) return false;
	  else p[a[i][j]]=true;
	return true;
}

bool jgg(int x,int y) {
	//(1,1)(1,4),(1,7)
	//(4,1)(4,4),(4,7);
	//(7,1)(7,4),(7,7)
	bool p[10];memset(p,0,sizeof(p));
	for (int i = x ; i <= x+2; i ++ )
	  for (int j = y ; j <= y + 2; j ++ )
	    p[a[i][j]]=true;
	for (int i =1 ; i <= 9 ; i ++ ) if (p[i]==0) return false;
	return true;
}

int main() {
	int t;
	cin>>t;
	while (t--) {
		for (int i = 1; i <= 9 ;  i ++ )
		   for (int j = 1; j <= 9 ; j ++ ) cin>>a[i][j];
		bool flag=true;
		for (int i = 1; i <= 9 ; i ++ )
		   if (!(hang(i)&&lie(i))) flag=false;
		for (int i = 1; i <= 7 ; i += 3)
		   for (int j = 1; j <= 7 ; j += 3)
		      if (!jgg(i,j)) flag=false;
		if (flag) cout<<"Right"<<endl;
		else cout<<"Wrong"<<endl;
	}
}

第六题

#include<bits/stdc++.h>
using namespace std;
struct image{
	char a[30][30];
};
image a;
int n;
image rotate90(image a) {
	image b;
	for (int i = 1; i <= n ; i ++) {
		for (int j = 1; j <= n ; j ++ ) {
			b.a[j][n-i+1]=a.a[i][j];
		}
	}
	return b;
}
image add(image a,image b) {
	image c;
	for (int i = 1; i <= n ; i ++) {
		for (int j = 1; j <= n ; j ++) {
			int A = a.a[i][j]-48;
			int B = b.a[i][j]-48;
			c.a[i][j]=48+(A|B);
		}
	}
	return c;
}
int calc(image a) {
	int cnt = 0;
	for (int i = 1; i <= n ; i ++ )
		for (int j = 1; j <= n ; j ++ ) 
		  if (a.a[i][j]=='1') cnt++;
	return cnt;
} 
int main(){
	cin>>n;
	for (int i = 1; i <= n ; i ++ )
	   for (int j = 1; j <= n ; j ++ ) cin>>a.a[i][j];
	
	image r90,r180,r270;
	r90=rotate90(a);
	r180=rotate90(r90);
	r270=rotate90(r180);
	cout<<calc(a)<<endl;
	image x=add(a,r90);
	cout<<calc(x)<<endl;
	x = add(x,r180);
	cout<<calc(x)<<endl;
	x = add(x,r270);
	cout<<calc(x)<<endl;
	return 0;
}