Codeforces Round 860 (Div. 2) 题解

文章包含多个C++代码实现,分别解决不同类型的数学和算法问题,如数组操作、最大值查找、整数分解、序列排列等。这些代码片段常用于编程竞赛或算法练习中。

A Showstopper

#include<bits/stdc++.h> 
using namespace std;
#define For(i,n) for(int i=1;i<=n;i++)
#define Fork(i,k,n) for(int i=k;i<=n;i++)
#define ForkD(i,k,n) for(int i=n;i>=k;i--)
#define Rep(i,n) for(int i=0;i<n;i++)
#define ForD(i,n) for(int i=n;i;i--)
#define RepD(i,n) for(int i=n;i>=0;i--)
#define Forp(x) for(int p=pre[x];p;p=next[p])
#define Forpiter(x) for(int &p=iter[x];p;p=next[p])  
#define Lson (o<<1)
#define Rson ((o<<1)+1)
#define MEM(a) memset(a,0,sizeof(a));
#define MEMI(a) memset(a,0x3f,sizeof(a));
#define MEMi(a) memset(a,128,sizeof(a));
#define MEMx(a,b) memset(a,b,sizeof(a));
#define INF (0x3f3f3f3f)
#define F (1000000007)
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define vi vector<int> 
#define pi pair<int,int>
#define SI(a) ((a).size())
#define Pr(kcase,ans) printf("Case #%d: %lld\n",kcase,ans);
#define PRi(a,n) For(i,n-1) cout<<a[i]<<' '; cout<<a[n]<<endl;
#define PRi2D(a,n,m) For(i,n) { \
						For(j,m-1) cout<<a[i][j]<<' ';\
						cout<<a[i][m]<<endl; \
						} 
#pragma comment(linker, "/STACK:102400000,102400000")
#define ALL(x) (x).begin(),(x).end()
#define gmax(a,b) a=max(a,b);
#define gmin(a,b) a=min(a,b);
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
ll mul(ll a,ll b){return (a*b)%F;}
ll add(ll a,ll b){return (a+b)%F;}
ll sub(ll a,ll b){return ((a-b)%F+F)%F;}
void upd(ll &a,ll b){a=(a%F+b%F)%F;}
inline int read()
{
	int x=0,f=1; char ch=getchar();
	while(!isdigit(ch)) {if (ch=='-') f=-1; ch=getchar();}
	while(isdigit(ch)) { x=x*10+ch-'0'; ch=getchar();}
	return x*f;
} 
int a[111],b[111];
int main()
{
//	freopen("A.in","r",stdin);
//	freopen(".out","w",stdout);
	
	int t=read();
	while(t--) {
		int n=read();
		For(i,n) a[i]=read();
		For(i,n) b[i]=read();
		For(i,n) if(a[i]>b[i]) swap(a[i],b[i]);
		int p=*max_element(a+1,a+1+n);
		int q=*max_element(b+1,b+1+n);
		if(p==a[n]&&q==b[n]) puts("Yes");else puts("No");
	}
	
	return 0;
}

B Three Sevens

#include<bits/stdc++.h> 
using namespace std;
#define For(i,n) for(int i=1;i<=n;i++)
#define Fork(i,k,n) for(int i=k;i<=n;i++)
#define ForkD(i,k,n) for(int i=n;i>=k;i--)
#define Rep(i,n) for(int i=0;i<n;i++)
#define ForD(i,n) for(int i=n;i;i--)
#define RepD(i,n) for(int i=n;i>=0;i--)
#define Forp(x) for(int p=pre[x];p;p=next[p])
#define Forpiter(x) for(int &p=iter[x];p;p=next[p])  
#define Lson (o<<1)
#define Rson ((o<<1)+1)
#define MEM(a) memset(a,0,sizeof(a));
#define MEMI(a) memset(a,0x3f,sizeof(a));
#define MEMi(a) memset(a,128,sizeof(a));
#define MEMx(a,b) memset(a,b,sizeof(a));
#define INF (0x3f3f3f3f)
#define F (1000000007)
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define vi vector<int> 
#define pi pair<int,int>
#define SI(a) ((a).size())
#define Pr(kcase,ans) printf("Case #%d: %lld\n",kcase,ans);
#define PRi(a,n) For(i,n-1) cout<<a[i]<<' '; cout<<a[n]<<endl;
#define PRi2D(a,n,m) For(i,n) { \
						For(j,m-1) cout<<a[i][j]<<' ';\
						cout<<a[i][m]<<endl; \
						} 
#pragma comment(linker, "/STACK:102400000,102400000")
#define ALL(x) (x).begin(),(x).end()
#define gmax(a,b) a=max(a,b);
#define gmin(a,b) a=min(a,b);
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
ll mul(ll a,ll b){return (a*b)%F;}
ll add(ll a,ll b){return (a+b)%F;}
ll sub(ll a,ll b){return ((a-b)%F+F)%F;}
void upd(ll &a,ll b){a=(a%F+b%F)%F;}
inline int read()
{
	int x=0,f=1; char ch=getchar();
	while(!isdigit(ch)) {if (ch=='-') f=-1; ch=getchar();}
	while(isdigit(ch)) { x=x*10+ch-'0'; ch=getchar();}
	return x*f;
} 
#define MAXN (50100)
vi a[MAXN];
bool b[MAXN];
int m;
bool ck() {
	vi ans;
	ForD(i,m) {
		bool fl=0;
		for(int p:a[i]) {
			if(!b[p]) {
				b[p]=1;
				if(!fl) ans.pb(p);
				fl=1;
			}				
		}
		if(!fl) return 0;
	}
	reverse(ALL(ans));
	for(int i:ans) cout<<i<<' ';
	cout<<endl;return 1;
}
int main()
{
//	freopen("B.in","r",stdin);
//	freopen(".out","w",stdout);
	int T=read();
	while(T--) {
		m=read();
		For(i,m) {
			int p=read();
			while(p--) {
				int c=read();
				a[i].pb(c);
				b[c]=0;
			}
		}
		if(!ck()) puts("-1");
		For(i,m) a[i].resize(0);
	}
	
	
	return 0;
}

C

#include<bits/stdc++.h> 
using namespace std;
#define For(i,n) for(int i=1;i<=n;i++)
#define Fork(i,k,n) for(int i=k;i<=n;i++)
#define ForkD(i,k,n) for(int i=n;i>=k;i--)
#define Rep(i,n) for(int i=0;i<n;i++)
#define ForD(i,n) for(int i=n;i;i--)
#define RepD(i,n) for(int i=n;i>=0;i--)
#define Forp(x) for(int p=pre[x];p;p=next[p])
#define Forpiter(x) for(int &p=iter[x];p;p=next[p])  
#define Lson (o<<1)
#define Rson ((o<<1)+1)
#define MEM(a) memset(a,0,sizeof(a));
#define MEMI(a) memset(a,0x3f,sizeof(a));
#define MEMi(a) memset(a,128,sizeof(a));
#define MEMx(a,b) memset(a,b,sizeof(a));
#define INF (0x3f3f3f3f)
#define F (1000000007)
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define vi vector<int> 
#define pi pair<int,int>
#define SI(a) ((a).size())
#define Pr(kcase,ans) printf("Case #%d: %lld\n",kcase,ans);
#define PRi(a,n) For(i,n-1) cout<<a[i]<<' '; cout<<a[n]<<endl;
#define PRi2D(a,n,m) For(i,n) { \
						For(j,m-1) cout<<a[i][j]<<' ';\
						cout<<a[i][m]<<endl; \
						} 
#pragma comment(linker, "/STACK:102400000,102400000")
#define ALL(x) (x).begin(),(x).end()
#define gmax(a,b) a=max(a,b);
#define gmin(a,b) a=min(a,b);
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
ll mul(ll a,ll b){return (a*b)%F;}
ll add(ll a,ll b){return (a+b)%F;}
ll sub(ll a,ll b){return ((a-b)%F+F)%F;}
void upd(ll &a,ll b){a=(a%F+b%F)%F;}
inline int read()
{
	int x=0,f=1; char ch=getchar();
	while(!isdigit(ch)) {if (ch=='-') f=-1; ch=getchar();}
	while(isdigit(ch)) { x=x*10+ch-'0'; ch=getchar();}
	return x*f;
} 
#define MAXN (202020)
int n;
ll a[MAXN],b[MAXN];
ll __gcd(ll a,ll b){
	if(!b) return a;return __gcd(b,a%b);
}
ll __lcm(ll a,ll b){
	return a/__gcd(a,b)*b;
}
int main()
{
//	freopen("C.in","r",stdin);
//	freopen(".out","w",stdout);
	int T=read();
	while(T--) {
		n=read();
		For(i,n) a[i]=read(),b[i]=read();
		ll p=0,q=0,ans=0;
		For(i,n) {
			ll mi=b[i];
			ll ma=b[i]*a[i];
			if(!p && !q) {
				p=mi,q=ma;
			}
			else {
				p=__lcm(p,mi);
				q=__gcd(q,ma);
				if(q%p!=0) {
					++ans;
					p=mi,q=ma;
				}
			}
		}
		cout<<ans+1<<endl;
	}
	
	
	return 0;
}

D Shocking Arrangement

#include<bits/stdc++.h> 
using namespace std;
#define For(i,n) for(int i=1;i<=n;i++)
#define Fork(i,k,n) for(int i=k;i<=n;i++)
#define ForkD(i,k,n) for(int i=n;i>=k;i--)
#define Rep(i,n) for(int i=0;i<n;i++)
#define ForD(i,n) for(int i=n;i;i--)
#define RepD(i,n) for(int i=n;i>=0;i--)
#define Forp(x) for(int p=pre[x];p;p=next[p])
#define Forpiter(x) for(int &p=iter[x];p;p=next[p])  
#define Lson (o<<1)
#define Rson ((o<<1)+1)
#define MEM(a) memset(a,0,sizeof(a));
#define MEMI(a) memset(a,0x3f,sizeof(a));
#define MEMi(a) memset(a,128,sizeof(a));
#define MEMx(a,b) memset(a,b,sizeof(a));
#define INF (0x3f3f3f3f)
#define F (1000000007)
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define vi vector<int> 
#define pi pair<int,int>
#define SI(a) ((a).size())
#define Pr(kcase,ans) printf("Case #%d: %lld\n",kcase,ans);
#define PRi(a,n) For(i,n-1) cout<<a[i]<<' '; cout<<a[n]<<endl;
#define PRi2D(a,n,m) For(i,n) { \
						For(j,m-1) cout<<a[i][j]<<' ';\
						cout<<a[i][m]<<endl; \
						} 
#pragma comment(linker, "/STACK:102400000,102400000")
#define ALL(x) (x).begin(),(x).end()
#define gmax(a,b) a=max(a,b);
#define gmin(a,b) a=min(a,b);
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
ll mul(ll a,ll b){return (a*b)%F;}
ll add(ll a,ll b){return (a+b)%F;}
ll sub(ll a,ll b){return ((a-b)%F+F)%F;}
void upd(ll &a,ll b){a=(a%F+b%F)%F;}
inline int read()
{
	int x=0,f=1; char ch=getchar();
	while(!isdigit(ch)) {if (ch=='-') f=-1; ch=getchar();}
	while(isdigit(ch)) { x=x*10+ch-'0'; ch=getchar();}
	return x*f;
} 
ll a[301000],ans[301000];
int main()
{
//	freopen("D.in","r",stdin);
//	freopen(".out","w",stdout);
	
	int T=read();
	while(T--) {
		int n=read();
		For(i,n) a[i]=read();
		int p=*max_element(a+1,a+1+n);
		int q=*min_element(a+1,a+1+n);
		if(p<=0||q>=0) puts("No");
		else {
			vi v[2];
			For(i,n) {
				if(a[i]>0) v[0].pb(a[i]);
				else v[1].pb(a[i]);
			}
			puts("Yes");
			ll s=0;
			int p0=0,p1=0;
			For(i,n) {
				int c;
				if(s<0 || (s==0 &&p0<SI(v[0])) ) {
					c=v[0][p0++];
				} else {
					c=v[1][p1++];
				}
				s+=c;
				ans[i]=c;
			}
			PRi(ans,n)
		}
	}
	
	return 0;
}

E Multitest Generator

#include<bits/stdc++.h> 
using namespace std;
#define For(i,n) for(int i=1;i<=n;i++)
#define Fork(i,k,n) for(int i=k;i<=n;i++)
#define ForkD(i,k,n) for(int i=n;i>=k;i--)
#define Rep(i,n) for(int i=0;i<n;i++)
#define ForD(i,n) for(int i=n;i;i--)
#define RepD(i,n) for(int i=n;i>=0;i--)
#define Forp(x) for(int p=pre[x];p;p=next[p])
#define Forpiter(x) for(int &p=iter[x];p;p=next[p])  
#define Lson (o<<1)
#define Rson ((o<<1)+1)
#define MEM(a) memset(a,0,sizeof(a));
#define MEMI(a) memset(a,0x3f,sizeof(a));
#define MEMi(a) memset(a,128,sizeof(a));
#define MEMx(a,b) memset(a,b,sizeof(a));
#define INF (0x3f3f3f3f)
#define F (1000000007)
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define vi vector<int> 
#define pi pair<int,int>
#define SI(a) ((a).size())
#define Pr(kcase,ans) printf("Case #%d: %lld\n",kcase,ans);
#define PRi(a,n) For(i,n-1) cout<<a[i]<<' '; cout<<a[n]<<endl;
#define PRi2D(a,n,m) For(i,n) { \
						For(j,m-1) cout<<a[i][j]<<' ';\
						cout<<a[i][m]<<endl; \
						} 
#pragma comment(linker, "/STACK:102400000,102400000")
#define ALL(x) (x).begin(),(x).end()
#define gmax(a,b) a=max(a,b);
#define gmin(a,b) a=min(a,b);
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
ll mul(ll a,ll b){return (a*b)%F;}
ll add(ll a,ll b){return (a+b)%F;}
ll sub(ll a,ll b){return ((a-b)%F+F)%F;}
void upd(ll &a,ll b){a=(a%F+b%F)%F;}
inline int read()
{
	int x=0,f=1; char ch=getchar();
	while(!isdigit(ch)) {if (ch=='-') f=-1; ch=getchar();}
	while(isdigit(ch)) { x=x*10+ch-'0'; ch=getchar();}
	return x*f;
} 
#define MAXN (301000)
ll a[MAXN];
ll f[MAXN];
ll ans[MAXN];
ll ma[MAXN],sfa[MAXN];
ll la[MAXN];
int main()
{
	freopen("E.in","r",stdin);
//	freopen(".out","w",stdout);
	int T=read();
	while(T--) {
		int n=read();
		For(i,n) a[i]=read();
		For(i,n) f[i]=-1; f[n+1]=0;
		ForD(i,n) {
			if(i+a[i]+1<=n+1 && f[i+a[i]+1]!=-1)
			f[i]=f[i+a[i]+1]+1;
		}
		ma[n+1]=0;
		ForD(i,n) ma[i]=max(ma[i+1],f[i]);
//		PRi(f,n)
//		PRi(ma,n)
		int fma=1;
		ForD(i,n) if(f[i]==fma) la[fma]=i,++fma;
		ForD(i,n) {
			sfa[i]=ma[i+1]+1;
			if(i+a[i]+1<=n+1)
				gmax(sfa[i],1+sfa[i+a[i]+1])
		}
		
		For(i,n) ans[i]=2;
		ForD(i,n-1) {
			if(a[i]==f[i+1]) ans[i]=0;
		}
		ForD(i,n-1) if(ans[i]==2) {
			if(f[i+1]!=-1) ans[i]=1;
			else if(a[i]==1) ans[i]=1;
			else if(a[i]<=sfa[i+1] ) ans[i]=1;
		}
		PRi(ans,(n-1))
	}
	return 0;
}

F Gifts from Grandfather Ahmed

from any 2n−12n−12n1 integers, you can choose nnn with a sum divisible by nnn (Erdős–Ginzburg–Ziv theorem)
所以直接暴力对最小的班级暴力背包,最后最大的那个加一个元素

#include<bits/stdc++.h> 
using namespace std;
#define For(i,n) for(int i=1;i<=n;i++)
#define Fork(i,k,n) for(int i=k;i<=n;i++)
#define ForkD(i,k,n) for(int i=n;i>=k;i--)
#define Rep(i,n) for(int i=0;i<n;i++)
#define ForD(i,n) for(int i=n;i;i--)
#define RepD(i,n) for(int i=n;i>=0;i--)
#define Forp(x) for(int p=pre[x];p;p=next[p])
#define Forpiter(x) for(int &p=iter[x];p;p=next[p])  
#define Lson (o<<1)
#define Rson ((o<<1)+1)
#define MEM(a) memset(a,0,sizeof(a));
#define MEMI(a) memset(a,0x3f,sizeof(a));
#define MEMi(a) memset(a,128,sizeof(a));
#define MEMx(a,b) memset(a,b,sizeof(a));
#define INF (0x3f3f3f3f)
#define F (1000000007)
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define vi vector<int> 
#define pi pair<int,int>
#define SI(a) ((a).size())
#define Pr(kcase,ans) printf("Case #%d: %lld\n",kcase,ans);
#define PRi(a,n) For(i,n-1) cout<<a[i]<<' '; cout<<a[n]<<endl;
#define PRi2D(a,n,m) For(i,n) { \
						For(j,m-1) cout<<a[i][j]<<' ';\
						cout<<a[i][m]<<endl; \
						} 
#pragma comment(linker, "/STACK:102400000,102400000")
#define ALL(x) (x).begin(),(x).end()
#define gmax(a,b) a=max(a,b);
#define gmin(a,b) a=min(a,b);
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
ll mul(ll a,ll b){return (a*b)%F;}
ll add(ll a,ll b){return (a+b)%F;}
ll sub(ll a,ll b){return ((a-b)%F+F)%F;}
void upd(ll &a,ll b){a=(a%F+b%F)%F;}
inline int read()
{
	int x=0,f=1; char ch=getchar();
	while(!isdigit(ch)) {if (ch=='-') f=-1; ch=getchar();}
	while(isdigit(ch)) { x=x*10+ch-'0'; ch=getchar();}
	return x*f;
} 
#define MAXN (301)
ll a[MAXN];
ll p[MAXN],s[MAXN];
vi v;
vi ans[1000];
int main()
{
//	freopen("F.in","r",stdin);
//	freopen(".out","w",stdout);
	int T=1;
	while(T--) {
		int n=read(),k=read();
		For(i,n) a[i]=read(),v.pb(a[i]);
		ll pans=0;
		For(i,k) s[i]=read();
		iota(p+1,p+1+k,1);
		sort(p+1,p+1+k,[&](int a,int b) {return s[a]<s[b]; } );
		For(tt,k) {
			int i=p[tt];
			if(tt<k) {
				vector<vector<vector<int> > > f(SI(v)+1, vector<vector<int> >(s[i]+1, vector<int>(s[i],0)));
				vector<vector<vector<int> > > pr(SI(v)+1, vector<vector<int> >(s[i]+1, vector<int>(s[i],0)));
				f[0][0][0]=1;
				int sz=s[i];
				Rep(i,SI(v)) Rep(j,min(i,sz)+1 ) Rep(k,sz) {
					if(f[i][j][k]) {
						f[i+1][j][k]=1;
						if(j<sz)f[i+1][j+1][(k+v[i])%sz]=1;
					}
				}
				int x=SI(v),j=sz,k=0;
				vi id;
				assert(f[x][j][k]);
				while(j>0) {
					if(x>j&f[x-1][j][k]) --x;
					else {
						x--,j--,k=((k-v[x])%sz+sz)%sz;
						ans[i].pb(v[x]);
						v.erase(v.begin()+x);
					}
				}
				
			}
			else {
				ll t=0;
				for(auto p:v) t+=p,ans[i].pb(p);
				pans=s[i]-t%s[i];
				ans[i].pb(pans);
			}
		}

		cout<<pans<<endl;
		For(i,k) {
			for(auto j:ans[i]) cout<<j<<' ';
			cout<<endl;
		}
		For(i,k) ans[i].resize(0);
		
	}
	return 0;
}

### 关于Codeforces Round 704 Div. 2 的信息 对于Codeforces Round 704 Div. 2的比赛,虽然未直接提及具体题目解析参赛体验的内容,但是可以根据平台的一贯风格推测该轮比赛同样包含了多种算法挑战。通常这类赛事会涉及数据结构、动态规划、图论等方面的知识。 考虑到提供的参考资料并未覆盖到此特定编号的比赛详情[^1],建议访问Codeforces官方网站查询官方题解是浏览社区论坛获取其他选手分享的经验总结。一般而言,在赛后不久就会有详细的解答发布出来供学习交流之用。 为了帮助理解同类型的竞赛内容,这里提供了一个基于过往相似赛事的例子——如何通过居中子数组特性来解决问题的方法: ```cpp // 假设有一个函数用于处理给定条件下的数组恢复问题 vector<int> restoreArray(vector<vector<int>>& adjacentPairs) { unordered_map<int, vector<int>> adj; for (auto& p : adjacentPairs){ adj[p[0]].push_back(p[1]); adj[p[1]].push_back(p[0]); } int start = 0; for(auto& [num, neighbors] : adj){ if(neighbors.size() == 1){ start = num; break; } } vector<int> res(adjacentPairs.size() + 1); unordered_set<int> seen; function<void(int,int)> dfs = [&](int node, int idx){ seen.insert(node); res[idx] = node; for(auto next : adj[node]){ if(!seen.count(next)){ dfs(next, idx + 1); } } }; dfs(start, 0); return res; } ``` 上述代码展示了利用深度优先搜索(DFS)重建原始序列的一种方式,这与某些情况下解决Codeforces比赛中遇到的问题思路相吻合[^4]。 #### 注意事项 由于缺乏针对Codeforces Round 704 Div. 2的具体材料支持,以上解释更多依赖于对同类活动的理解以及编程技巧的应用实例来进行说明。
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