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301

Advanced mathematics

linear algebra

probability theory

408

data structure

operating system

Chapter I overview of computer system

Chapter 2 processes and threads

Chapter 3 memory management

Chapter IV document management

Chapter V input / Output （I/O) management

#include<bits/stdc++.h>
using namespace std;
#define fir first
#define sec second
#define ll long long
#define debug(x) {
      cout<<#x<<" = "<<x<<" ";}
#define debug1(a) {
      debug(a);cout<<endl;}
#define debug2(a,b) {
      debug(a);debug1(b);}
#define debug3(a,b,c) {
      debug(a);debug2(b,c);}
#define debug4(a,b,c,d) {
      debug(a);debug3(b,c,d);}
#define debugvector(x) {
      cout<<#x<<": ";for(int asd=0;asd<x.size();asd++)cout<<x[asd]<<" ";cout<<endl;}
#define debugvec(x,n) {
      cout<<#x<<": ";for(int asd=0;asd<n;asd++)cout<<x[asd]<<" ";cout<<endl;}
#define debugvp(x){
      cout << #x << ": "; for (int asd = 0; asd < x.size(); asd++) printf("{%d,%d} ",x[asd].fir,x[asd].sec) ; cout << endl; }
#define debugmap(q) {
      cout<<#q<<": ";for(auto x:q) printf("{%d,%d} ",x.first,x.second) ;cout<<endl; }

    int lb(int i) {
     return i & -i; }
    void update(int i, int x) {
     while (i <= n)vt[i] += x,i+=lb(i); }
    int get(int i) {
    
        int ans = 0;
        while (i)ans += vt[i], i -= lb(i);
        return ans;
    }
ll qpow(ll x,ll n){
    
	ll ans=1;
	while(n){
    
		if(n%2==1)ans=ans*x;
		x=x*x;
		n/=2;
	}
	return ans;
}
ll jc(int x,ll mol){
    
	ll ans=1;
	while(x>0)ans*=x--,ans%=mol;
	return ans;
}
ll eular(ll n){
    // Euler function , Pray with n The number of Coprime 
    ll ans = n;
    for(int i=2; i*i <= n; ++i)
    {
    
        if(n%i == 0)
        {
    
            ans = ans/i*(i-1);
            while(n%i == 0)
                n/=i;
        }
    }
    if(n > 1) ans = ans/n*(n-1);
    return ans;
}
upper_bound() Function returns an iterator , Point to the key value in the container >key The first element of .
lower_bound() Function returns an iterator , Point to the key value in the container >=key The first element of .
num[upper_bound(num,num+size,a-1)-num-1]
ll gcd(ll a,ll b){
    
	if(a<b)return gcd(b,a);
	if(b==0)return a;
	return gcd(b,a%b);
}

                fraction inter = new fraction(numstring[0]);
for(int i=0;i<ans.size();i++){
    
	cout<<ans[i];
	if(i==ans.size()-1)cout<<endl;
	else cout<<" ";
}
int gcd(int a,int b){
    
	if(a<b)return gcd(b,a);
	if(b==0)return a;
	return gcd(b,a%b);
} 
const int MANX=1010;
ll C[MAXN][MAXN];
void zuheshu(int MAXN,ll mol){
    
	int i,j;
	for(i=0;i<MAXN;i++){
    
		C[i][i]=C[i][0]=1;
		for(j=1;j<i;j++){
    
			C[i][j]=(C[i-1][j-1]+C[i-1][j])%mol;
		}
	}
}


vector<int> zhishu(int n) {
    
	int i,flag;
	vector<int>v;
	for(i=2; i<=n; i++) {
    
		flag=1;
		for(int j=0; j<v.size()&&v[j]*v[j]<=i; j++)
			if(i%v[j]==0) {
    
				flag=0;
				break;
			}
		if(flag)v.push_back(i);
	}
	return v;
}
int getMax(int l, int r)
{
    
    int mid=log2(r-l+1);
    return max(num[mid][l],num[mid][r+1-(1<<mid)]);
}
    int to = log2(n);
    for (int j = 1; j <= to; j++)
    {
    
        for (i = 1;i+(1<<j)-1<=n; i++)
        {
    
            num[j][i] = max(num[j - 1][i], num[j - 1][i + (1 << (j - 1))]);
        }
    }
string a_to_b(string s, int a, int b) {
    
	int ans = 0, i;
	int k = 1;
	int t;
	for (i = s.size() - 1; i >= 0; i--) {
    
		if (s[i] >= '0' && s[i] <= '9')t = s[i] - '0';
		else t = s[i] - 'A'+10;
		ans +=t* k;
		k *= a;
	}
	k = 1;
	string s2="";
	while (ans) {
    
		t = ans % b;
		if (t <= 9)s2 += '0' + t;
		else s2 += +'A' - 10+t;
		ans /= b;
	}
	if (s2.size() == 0)s2 = "0";
	return s2;
}
struct matrix {
    
	ll num[10][10];
	int n,m;
	struct matrix operator *(struct matrix b) {
    
		struct matrix c;
		c.n=n;
		c.m=b.m;
		for(int i=0; i<c.n; i++) 
			for(int j=0; j<c.m; j++) 
				c.num[i][j]=0;
		for(int i=0; i<n; i++) {
    
			for(int j=0; j<b.m; j++) {
    
				for(int k=0; k<m; k++) {
    
					c.num[i][j]+=num[i][k]*b.num[k][j];
					c.num[i][j]%=mod;
				}
			}
		}
		return c;
	}
};