进制转换

进制转换

1.k进制转化为10进制

ll k_to_ten(int a[],int len,int k){ //读入一个存储为k进制的数组a，返回一个10进制x
	ll x = 0;
	for(int i = 0 ;i < len ; i ++){
		x = x*k + a[i]; //x = a[0]*k^n + a[1]*k*(n-1)...+a[len]
	}
	return x;
}

2.10进制转化为k进制

int ten_to_k(ll x,int a[],int k){ //读入一个10进制x，转化为k进制数组a，返回a的长度
	int len = 0;
	while(x){
		a[len++] = x % k;
		x /= k;
	}
	reverse(a,a+len);
	return len;
}

3.例题_进制转换

进制转换 - 蓝桥云课 (lanqiao.cn)

• 把这个k1进制的数转化为k2进制的数，需要10进制来过渡

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

ll k_to_ten(int a[],int len,int k){
	ll ans = 0;
	for(int i = 0 ; i < len ; i ++){
		ans = ans*k + a[i];
	}
	return ans;
}

int ten_to_k(int a[],int k,ll x){
	int len = 0;
	while(x){
		a[len++] = x%k;
		x /= k;
	}
	reverse(a,a+len);
	return len;
}

int t,k1,k2;
string s;
int num[1000],ans[1000];

int main(){
	ios::sync_with_stdio(false);
	cin>>t;
	while(t--){
		cin>>k1>>k2;
		cin>>s;
		int len = s.length();
		for(int i = 0 ; i < len ; i ++){
			if(s[i] >= '0' && s[i] <= '9') num[i] = int(s[i] - '0');
			else if(s[i] >= 'A' && s[i] <= 'F') num[i] = int(s[i] - 'A' ) + 10;
		}
		ll temp = k_to_ten(num,len,k1);
		int ans_len = ten_to_k(ans,k2,temp);
		for(int i = 0 ; i < ans_len ; i ++){
			if(ans[i] >= 0 && ans[i] <= 9) cout<<ans[i];
			else cout<<char( int('A') + ans[i] - 10);
		}
		cout<<endl;
	}	
}

4.例题_Alice和Bob的爱恨情仇

• 博弈论+进制转换

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

ll k_to_ten(int a[],int len,int k){
	ll ans = 0;
	for(int i = 0 ; i < len ; i ++){
		ans = ans*k + a[i];
	}
	return ans;
}

int ten_to_k(int a[],int k,ll x){
	int len = 0;
	while(x){
		a[len++] = x%k;
		x /= k;
	}
	reverse(a,a+len);
	return len;
}


int n,k;
int GET[100000];
int ans;

int main(void){
	ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
	cin>>n>>k;
	if(k == 1){
		while(n--){
			int temp;cin>>temp;
			ans += temp;
			if(ans % 2 == 0) cout<<"Bob";
			else cout<<"Alice";
			return 0;
		}
	}
	while(n--){
		ll num;
		cin>>num;		
		int len = ten_to_k(GET,k,num);
		for(int i = 0 ; i < len ; i ++){
			ans += GET[i];
		}
	}
	if(ans % 2 == 0) cout<<"Bob";
	else cout<<"Alice";
}