Educational Codeforces Round 35

Educational Codeforces Round 35 

A. Nearest Minimums

找出最小的位置，相邻相减取最小

view code

#pragma GCC optimize("O3")
#pragma GCC optimize("Ofast,no-stack-protector")
#include<bits/stdc++.h>
using namespace std;
#define INF 0x3f3f3f3f
#define endl "
"
#define LL long long int
#define vi vector<int>
#define vl vector<LL>
#define all(V) V.begin(),V.end()
#define sci(x) scanf("%d",&x)
#define scl(x) scanf("%I64d",&x)
#define scs(s) scanf("%s",s)
#define pii pair<int,int>
#define pll pair<LL,LL>
#ifndef ONLINE_JUDGE
#define cout cerr
#endif
#define cmax(a,b) ((a) = (a) > (b) ? (a) : (b))
#define cmin(a,b) ((a) = (a) < (b) ? (a) : (b))
#define debug(x)  cerr << #x << " = " << x << endl
function<void(void)> ____ = [](){ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);};
template <typename T> vector<T>& operator << (vector<T> &__container, T x){ __container.push_back(x); return __container; }
template <typename T> ostream& operator << (ostream &out, vector<T> &__container){ for(T _ : __container) out << _ << ' '; return out; }
const int MAXN = 2e5+7;

void solve(){
    int n; sci(n);
    vi A(n); for(int &x : A) sci(x);
    int x = *min_element(all(A));
    vi pos; for(int i = 0; i < n; i++) if(A[i]==x) pos << i;
    int ret = INF;
    for(int i = 1; i < pos.size(); i++) cmin(ret,pos[i]-pos[i-1]);
    cout << ret << endl;
}
int main(){
    #ifndef ONLINE_JUDGE
    freopen("Local.in","r",stdin);
    freopen("ans.out","w",stdout);
    #endif
    solve();
    return 0;
}

B. Two Cakes

二分答案判断一下是否满足

view code

#pragma GCC optimize("O3")
#pragma GCC optimize("Ofast,no-stack-protector")
#include<bits/stdc++.h>
using namespace std;
#define INF 0x3f3f3f3f
#define endl "
"
#define LL long long int
#define vi vector<int>
#define vl vector<LL>
#define all(V) V.begin(),V.end()
#define sci(x) scanf("%d",&x)
#define scl(x) scanf("%I64d",&x)
#define scs(s) scanf("%s",s)
#define pii pair<int,int>
#define pll pair<LL,LL>
#ifndef ONLINE_JUDGE
#define cout cerr
#endif
#define cmax(a,b) ((a) = (a) > (b) ? (a) : (b))
#define cmin(a,b) ((a) = (a) < (b) ? (a) : (b))
#define debug(x)  cerr << #x << " = " << x << endl
function<void(void)> ____ = [](){ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);};
template <typename T> vector<T>& operator << (vector<T> &__container, T x){ __container.push_back(x); return __container; }
template <typename T> ostream& operator << (ostream &out, vector<T> &__container){ for(T _ : __container) out << _ << ' '; return out; }
const int MAXN = 2e5+7;

void solve(){
    int n, a, b;
    sci(n); sci(a); sci(b);
    int l = 1, r = min(a,b);
    while(l<=r){
        int mid = (l + r) >> 1;
        if(a / mid + b / mid >= n) l = mid + 1;
        else r = mid - 1;
    }
    cout << r << endl;
}
int main(){
    #ifndef ONLINE_JUDGE
    freopen("Local.in","r",stdin);
    freopen("ans.out","w",stdout);
    #endif
    solve();
    return 0;
}

C. Three Garlands

可以发现满足条件的只有四种：

1. 1 x x
2. 2 2 x
3. 3 3 3
4. 2 4 4

x为任意数

view code

#pragma GCC optimize("O3")
#pragma GCC optimize("Ofast,no-stack-protector")
#include<bits/stdc++.h>
using namespace std;
#define INF 0x3f3f3f3f
#define endl "
"
#define LL long long int
#define vi vector<int>
#define vl vector<LL>
#define all(V) V.begin(),V.end()
#define sci(x) scanf("%d",&x)
#define scl(x) scanf("%I64d",&x)
#define scs(s) scanf("%s",s)
#define pii pair<int,int>
#define pll pair<LL,LL>
#ifndef ONLINE_JUDGE
#define cout cerr
#endif
#define cmax(a,b) ((a) = (a) > (b) ? (a) : (b))
#define cmin(a,b) ((a) = (a) < (b) ? (a) : (b))
#define debug(x)  cerr << #x << " = " << x << endl
function<void(void)> ____ = [](){ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);};
template <typename T> vector<T>& operator << (vector<T> &__container, T x){ __container.push_back(x); return __container; }
template <typename T> ostream& operator << (ostream &out, vector<T> &__container){ for(T _ : __container) out << _ << ' '; return out; }
const int MAXN = 2e5+7;

void solve(){
    vi A(3);
    for(int &x : A) sci(x);
    sort(all(A));
    if(A[0]==1 or (A[0]==A[1] and A[0]==2) or (A[0]==A[1] and A[1]==A[2] and A[0]==3) or (A[0]==2 and A[1]==A[2] and A[1]==4)) cout << "YES" << endl;
    else cout << "NO" << endl;
}
int main(){
    #ifndef ONLINE_JUDGE
    freopen("Local.in","r",stdin);
    freopen("ans.out","w",stdout);
    #endif
    solve();
    return 0;
}

D. Inversion Counting

假设原来([l,r])区间内的逆序对数量为(x)，假设区间长度为(L)，那么翻转之后变成了(frac{Lcdot (L+1)}{2}-x)

那么如果(frac{Lcdot (L+1)}{2})是偶数，奇偶性不变，否则奇偶性改变

view code

#pragma GCC optimize("O3")
#pragma GCC optimize("Ofast,no-stack-protector")
#include<bits/stdc++.h>
using namespace std;
#define INF 0x3f3f3f3f
#define endl "
"
#define LL long long int
#define vi vector<int>
#define vl vector<LL>
#define all(V) V.begin(),V.end()
#define sci(x) scanf("%d",&x)
#define scl(x) scanf("%I64d",&x)
#define scs(s) scanf("%s",s)
#define pii pair<int,int>
#define pll pair<LL,LL>
#ifndef ONLINE_JUDGE
#define cout cerr
#endif
#define cmax(a,b) ((a) = (a) > (b) ? (a) : (b))
#define cmin(a,b) ((a) = (a) < (b) ? (a) : (b))
#define debug(x)  cerr << #x << " = " << x << endl
function<void(void)> ____ = [](){ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);};
template <typename T> vector<T>& operator << (vector<T> &__container, T x){ __container.push_back(x); return __container; }
template <typename T> ostream& operator << (ostream &out, vector<T> &__container){ for(T _ : __container) out << _ << ' '; return out; }
const int MAXN = 2e5+7;

void solve(){
    int n; sci(n);
    vi A(n); for(int &x : A) sci(x);
    int even = true;
    for(int i = 1; i < n; i++) for(int j = 0; j < i; j++) if(A[j]>A[i]) even ^= 1;
    int m; sci(m);
    while(m--){
        int l, r; sci(l); sci(r);
        int x = r - l + 1;
        if((x*(x-1)/2)&1) even ^= 1;
        cout << (even ? "even" : "odd") << endl;
    }
}
int main(){
    #ifndef ONLINE_JUDGE
    freopen("Local.in","r",stdin);
    freopen("ans.out","w",stdout);
    #endif
    solve();
    return 0;
}

E. Stack Sorting

先跑给定了的，显然如果遇到最小值就把最小值从栈里拿出来

如果栈内存在一个元素比栈顶小，输出(-1)

现在考虑剩下的值，显然每次把小于等于栈顶的全部取出是最优的，由于要最大字典序，那就逆序输出即可

view code

#pragma GCC optimize("O3")
#pragma GCC optimize("Ofast,no-stack-protector")
#include<bits/stdc++.h>
using namespace std;
#define INF 0x3f3f3f3f
#define endl "
"
#define LL long long int
#define vi vector<int>
#define vl vector<LL>
#define all(V) V.begin(),V.end()
#define sci(x) scanf("%d",&x)
#define scl(x) scanf("%I64d",&x)
#define scs(s) scanf("%s",s)
#define pii pair<int,int>
#define pll pair<LL,LL>
#ifndef ONLINE_JUDGE
#define cout cerr
#endif
#define cmax(a,b) ((a) = (a) > (b) ? (a) : (b))
#define cmin(a,b) ((a) = (a) < (b) ? (a) : (b))
#define debug(x)  cerr << #x << " = " << x << endl
function<void(void)> ____ = [](){ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);};
template <typename T> vector<T>& operator << (vector<T> &__container, T x){ __container.push_back(x); return __container; }
template <typename T> ostream& operator << (ostream &out, vector<T> &__container){ for(T _ : __container) out << _ << ' '; return out; }
const int MAXN = 2e5+7;

void solve(){
    int n, k;
    sci(n); sci(k);
    vi A(k);
    for(int &x : A) sci(x);
    int cur = 1;
    stack<int> stk;
    for(int i = 0; i < k; i++){
        if(A[i]==cur){
            cur++;
            while(!stk.empty() and stk.top()==cur){
                cur++;
                stk.pop();
            }
        }else{
            if(!stk.empty() and stk.top()<A[i]){
                cout << -1 << endl;
                return;
            }else stk.push(A[i]);
        }
    }
    while(cur<=n){
        if(stk.empty()){
            for(int i = n; i >= cur; i--) A << i;
            break;
        }
        for(int i = stk.top() - 1; i >= cur; i--) A << i;
        cur = stk.top() + 1;
        stk.pop();
    }
    for(int x : A) cout << x << ' '; cout << endl;
}
int main(){
    #ifndef ONLINE_JUDGE
    freopen("Local.in","r",stdin);
    freopen("ans.out","w",stdout);
    #endif
    solve();
    return 0;
}

F. Tree Destruction

考虑倒着来做，相当于确定一个起始点，然后不断加点进去

那么显然先找出直径，然后把其他点补上，距离取各个点到直径两端点的最大值即可

view code

#pragma GCC optimize("O3")
#pragma GCC optimize("Ofast,no-stack-protector")
#include<bits/stdc++.h>
using namespace std;
#define INF 0x3f3f3f3f
#define endl "
"
#define LL long long int
#define vi vector<int>
#define vl vector<LL>
#define all(V) V.begin(),V.end()
#define sci(x) scanf("%d",&x)
#define scl(x) scanf("%I64d",&x)
#define scs(s) scanf("%s",s)
#define pii pair<int,int>
#define pll pair<LL,LL>
#ifndef ONLINE_JUDGE
#define cout cerr
#endif
#define cmax(a,b) ((a) = (a) > (b) ? (a) : (b))
#define cmin(a,b) ((a) = (a) < (b) ? (a) : (b))
#define debug(x)  cerr << #x << " = " << x << endl
function<void(void)> ____ = [](){ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);};
template <typename T> vector<T>& operator << (vector<T> &__container, T x){ __container.push_back(x); return __container; }
template <typename T> ostream& operator << (ostream &out, vector<T> &__container){ for(T _ : __container) out << _ << ' '; return out; }
const int MAXN = 2e5+7;
int n, dis[MAXN], par[MAXN];
LL ret;
vi G[MAXN];
vector<pair<pii,int> > vec;
void dfs(int u, int fa){
    dis[u] = dis[fa] + 1;
    par[u] = fa;
    for(int v : G[u]) if(v!=fa) dfs(v,u);
}

void dfs(int u, int rt, int rrt, int lca){
    int dis1 = dis[u];
    int dis2 = dis[u] + dis[rrt] - 2 * dis[lca];
    if(dis1>dis2) vec << make_pair(make_pair(u,rt),u);
    else vec << make_pair(make_pair(u,rrt),u);
    ret += max(dis1,dis2);
    for(int v : G[u]) if(v!=par[u]) dfs(v,rt,rrt,lca);
}

void solve(){
    sci(n);
    for(int i = 1; i < n; i++){
        int u, v; sci(u); sci(v);
        G[u] << v; G[v] << u;
    }
    dis[0] = -1;
    dfs(1,0);
    int rt = 1;
    for(int i = 1; i <= n; i++) if(dis[i]>dis[rt]) rt = i;
    dfs(rt,0);
    int anotherrt = rt;
    for(int i = 1; i <= n; i++) if(dis[i]>dis[anotherrt]) anotherrt = i;
    vector<bool> vis(n+1,false);
    int u = anotherrt;
    while(par[u]){
        vis[u] = true;
        vec << make_pair(make_pair(anotherrt,par[u]),par[u]);
        ret += dis[anotherrt] - dis[par[u]];
        u = par[u];
    }
    vis[rt] = true;
    u = anotherrt;
    while(u){
        for(int v : G[u]) if(!vis[v]) dfs(v,rt,anotherrt,u);
        u = par[u];
    }
    cout << ret << endl;
    for(auto p = vec.rbegin(); p != vec.rend(); p++) cout << p->first.first << ' ' << p->first.second << ' ' << p->second << endl;
}
int main(){
    #ifndef ONLINE_JUDGE
    freopen("Local.in","r",stdin);
    freopen("ans.out","w",stdout);
    #endif
    solve();
    return 0;
}

G. Mass Change Queries

考虑线段树，每个节点存一下每个值的映射，每次修改考虑把原来映射为(x)的点，映射到(y)

(pushdown)操作就把左右儿子的映射全部更新一遍

view code

#pragma GCC optimize("O3")
#pragma GCC optimize("Ofast,no-stack-protector")
#include<bits/stdc++.h>
using namespace std;
#define INF 0x3f3f3f3f
#define endl "
"
#define LL long long int
#define vi vector<int>
#define vl vector<LL>
#define all(V) V.begin(),V.end()
#define sci(x) scanf("%d",&x)
#define scl(x) scanf("%I64d",&x)
#define scs(s) scanf("%s",s)
#define pii pair<int,int>
#define pll pair<LL,LL>
#ifndef ONLINE_JUDGE
#define cout cerr
#endif
#define cmax(a,b) ((a) = (a) > (b) ? (a) : (b))
#define cmin(a,b) ((a) = (a) < (b) ? (a) : (b))
#define debug(x)  cerr << #x << " = " << x << endl
function<void(void)> ____ = [](){ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);};
template <typename T> vector<T>& operator << (vector<T> &__container, T x){ __container.push_back(x); return __container; }
template <typename T> ostream& operator << (ostream &out, vector<T> &__container){ for(T _ : __container) out << _ << ' '; return out; }
const int MAXN = (1 << 18) + 7;
const int MAXV = 101;
struct SegmentTree{
    int l[MAXN<<1], r[MAXN<<1];
    int f[MAXN<<1][MAXV];
    #define ls(rt) rt << 1
    #define rs(rt) rt << 1 | 1
    void build(int L, int R, int rt = 1){
        l[rt] = L; r[rt] = R;
        for(int i = 1; i < MAXV; i++) f[rt][i] = i;
        if(L + 1 == R) return;
        int mid = (L + R) >> 1;
        build(L,mid,ls(rt)); build(mid,R,rs(rt));
    }
    void pushdown(int rt){
        for(int i = 1; i < MAXV; i++){
            f[ls(rt)][i] = f[rt][f[ls(rt)][i]];
            f[rs(rt)][i] = f[rt][f[rs(rt)][i]];
        }
        for(int i = 1; i < MAXV; i++) f[rt][i] = i;
    }
    void modify(int L, int R, int x, int y, int rt = 1){
        if(L>=r[rt] or l[rt]>=R) return;
        if(L<=l[rt] and r[rt]<=R){
            for(int i = 1; i < MAXV; i++) if(f[rt][i]==x) f[rt][i] = y;
            return;
        }
        pushdown(rt);
        modify(L,R,x,y,ls(rt)); modify(L,R,x,y,rs(rt));
    }
    void print(vi &A, int rt = 1){
        if(l[rt]+1==r[rt]){
            cout << f[rt][A[l[rt]]] << ' ';
            return;
        }
        pushdown(rt);
        print(A,ls(rt)); print(A,rs(rt));
    }
}ST;
void solve(){
    int n; sci(n);
    vi A(n); for(int &x : A) sci(x);
    ST.build(0,n);
    int m; sci(m);
    while(m--){
        int l, r, x, y;
        sci(l); sci(r); sci(x); sci(y);
        l--; r--;
        if(x==y) continue;
        ST.modify(l,r+1,x,y);
    }
    ST.print(A);
}
int main(){
    #ifndef ONLINE_JUDGE
    freopen("Local.in","r",stdin);
    freopen("ans.out","w",stdout);
    #endif
    solve();
    return 0;
}