CodeTON Round 1解题报告 – 我的学业笔记

今天这场比前天的Educational Codeforces Round 125打得舒服?

A. Good Pairs

容易知道只需输出序列中最大和最小的数的位置即可

B. Subtract Operation

以前的某场round有过类似操作的题，消减后我们可以发现只需查找是否存在$a_i+k=a_j$，有输出YES即可，否则为NO

C. Make Equal With Mod

分类讨论，当序列中不存在1时，答案为YES，存在1时，我们需要判断序列中是否存在$a_i-a_j=1$，存在输出NO，否则输出YES

D. K-good

题意是对于$n$是否存在$k$使得$n=\frac{k\times(k+1)}{2}+a\times k,a\in N$

容易发现$n$为奇数的时候答案为2

下面考虑$n$为奇数的情况，不妨设有$n \bmod k =0$，则此时上式可化为

$$\frac{2n}{k}=k+1+2 \times a \times k$$

于是我们发现需要将$n$分成奇数乘于偶数的形式，其中奇数要大于2，所以我们可以将$n$一直除2分解成$n=2^c\times p$，其中p为奇数

所以有p等于1时答案为-1，否则答案为min(2^(c+1),p)

code:

//A
#include <algorithm>
#include <bitset>
#include <map>
#include <vector>
#include <string>
#include <iostream>
#include <cmath>
#include <stack>
#include <set>
/*
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/hash_policy.hpp>
*/
using namespace std;

const double eps = 1e-10;
const double pi = 3.1415926535897932384626433832795;
const double eln = 2.718281828459045235360287471352;

#define f(i, a, b) for (int i = a; i <= b; i++)
#define LL long long
#define IN freopen("in.txt", "r", stdin)
#define OUT freopen("out.txt", "w", stdout)
#define scan(x) scanf("%d", &x)
#define mp make_pair
#define pb push_back
#define sqr(x) (x) * (x)
#define pr1(x) printf("Case %d: ",x)
#define pn1(x) printf("Case %d:\n",x)
#define pr2(x) printf("Case #%d: ",x)
#define pn2(x) printf("Case #%d:\n",x)
#define lowbit(x) (x&(-x))

#define fi first
#define se second
#define sz(x) int((x).size())
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define summ(a) (accumulate(all(a), 0ll))

typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef vector<int> vi;

LL tt,n,x;
int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    cin>>tt;
    f(sb,1,tt){
        cin>>n;
        vi v(n);
        int mi=0x3f3f3f3f,mib,ma=-1,mab=-1;
        f(i,1,n){
            cin>>x;
            if(x>ma){
                ma=x;
                mab=i;
            }
            if(x<mi){
                mi=x;
                mib=i;
            }
        }
        cout<<mib<<" "<<mab<<"\n";
    }
    return 0;
}

//B
#include <algorithm>
#include <bitset>
#include <map>
#include <vector>
#include <string>
#include <iostream>
#include <cmath>
#include <stack>
#include <set>
#include<numeric>
/*
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/hash_policy.hpp>
*/
using namespace std;

const double eps = 1e-10;
const double pi = 3.1415926535897932384626433832795;
const double eln = 2.718281828459045235360287471352;

#define f(i, a, b) for (int i = a; i <= b; i++)
#define LL long long
#define IN freopen("in.txt", "r", stdin)
#define OUT freopen("out.txt", "w", stdout)
#define scan(x) scanf("%d", &x)
#define mp make_pair
#define pb push_back
#define sqr(x) (x) * (x)
#define pr1(x) printf("Case %d: ",x)
#define pn1(x) printf("Case %d:\n",x)
#define pr2(x) printf("Case #%d: ",x)
#define pn2(x) printf("Case #%d:\n",x)
#define lowbit(x) (x&(-x))

#define fi first
#define se second
#define sz(x) int((x).size())
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define summ(a) (accumulate(all(a), 0ll))

typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef vector<LL> vi;

LL tt,n,k;

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    cin>>tt;
    f(sb,1,tt){
        cin>>n>>k;
        vi v(n);
        map<LL,int> vis;
        for(auto &it:v)cin>>it,vis[it]=1;
        int ok=0;
        for(auto it:v){
            if(vis.count(it+k)){
                ok=1;
                break;
            }
        }
        cout<<(ok?"YES\n":"NO\n");
    }
    return 0;
}

//C
#include <algorithm>
#include <bitset>
#include <map>
#include <vector>
#include <string>
#include <iostream>
#include <cmath>
#include <stack>
#include <set>
#include <numeric>
/*
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/hash_policy.hpp>
*/
using namespace std;

const double eps = 1e-10;
const double pi = 3.1415926535897932384626433832795;
const double eln = 2.718281828459045235360287471352;

#define f(i, a, b) for (int i = a; i <= b; i++)
#define LL long long
#define IN freopen("in.txt", "r", stdin)
#define OUT freopen("out.txt", "w", stdout)
#define scan(x) scanf("%d", &x)
#define mp make_pair
#define pb push_back
#define sqr(x) (x) * (x)
#define pr1(x) printf("Case %d: ", x)
#define pn1(x) printf("Case %d:\n", x)
#define pr2(x) printf("Case #%d: ", x)
#define pn2(x) printf("Case #%d:\n", x)
#define lowbit(x) (x & (-x))

#define fi first
#define se second
#define sz(x) int((x).size())
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define summ(a) (accumulate(all(a), 0ll))

typedef unsigned long long ull;
typedef pair<int, int> pii;
typedef vector<LL> vi;

LL tt, n;

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    cin >> tt;
    f(sb, 1, tt)
    {
        cin >> n;

        int ok = 1, ck1 = 0, cnt1 = 0,cnt2=0;
        vi v(n);
        for (auto &it : v)
        {
            cin >> it;
            if (it == 1)
                cnt1 += 1;
        }
        
        if(cnt1){
            sort(all(v));
            int len=v.size();
            for(int i=1;i<len;++i){
                if(v[i]-v[i-1]==1){
                    ok=0;
                    break;
                }
            }
        }else ok=1;

        cout<<(ok?"YES\n":"NO\n");
    }
    return 0;
}

//D
#include <algorithm>
#include <bitset>
#include <map>
#include <vector>
#include <string>
#include <iostream>
#include <cmath>
#include <stack>
#include <set>
/*
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/hash_policy.hpp>
*/
using namespace std;

const double eps = 1e-10;
const double pi = 3.1415926535897932384626433832795;
const double eln = 2.718281828459045235360287471352;

#define f(i, a, b) for (int i = a; i <= b; i++)
#define LL long long
#define IN freopen("in.txt", "r", stdin)
#define OUT freopen("out.txt", "w", stdout)
#define scan(x) scanf("%d", &x)
#define mp make_pair
#define pb push_back
#define sqr(x) (x) * (x)
#define pr1(x) printf("Case %d: ",x)
#define pn1(x) printf("Case %d:\n",x)
#define pr2(x) printf("Case #%d: ",x)
#define pn2(x) printf("Case #%d:\n",x)
#define lowbit(x) (x&(-x))

#define fi first
#define se second
#define sz(x) int((x).size())
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define summ(a) (accumulate(all(a), 0ll))

typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef vector<int> vi;

LL tt,n;

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    cin>>tt;
    f(sb,1,tt){
        cin>>n;
        if(n&1){
            cout<<"2\n";
        }else {
            LL cn=1;
            while((n&1)==0){
                n>>=1;
                cn+=1;
            }
            if(n==1)cout<<"-1\n";
            else cout<<min(1ll<<cn,n)<<"\n";
        }
    }
    return 0;
}

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