Educational Codeforces Round 78 (Rated for Div. 2) 题解

Posted 2020-11-23 jiaaaaaaaqi

• Shuffle Hashing
• A and B
• Berry Jam
• Segment Tree
• Tests for problem D
• Cards

Shuffle Hashing

[ Time Limit: 2 squad Memory Limit: 256 MB ]
处理出 (s_1) 中各个字符出现的次数，然后双指针维护 (s_2) 中每一段长度为 (len(s_1)) 的串中字符出现的次数，如果存在某一段和 (s_1) 的字符次数相同，则是答案。

view

#include <map>
#include <set>
#include <list>
#include <tuple>
#include <ctime>
#include <cmath>
#include <stack>
#include <queue>
#include <cfloat>
#include <string>
#include <vector>
#include <cstdio>
#include <bitset>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <unordered_map>
#define  lowbit(x)  x & (-x)
#define  mes(a, b)  memset(a, b, sizeof a)
#define  fi         first
#define  se         second
#define  pb         push_back
#define  pii        pair<int, int>
#define  INOPEN     freopen("in.txt", "r", stdin)
#define  OUTOPEN    freopen("out.txt", "w", stdout)

typedef unsigned long long int ull;
typedef long long int ll;
const int    maxn = 1e2 + 10;
const int    maxm = 1e5 + 10;
const ll     mod  = 1e9 + 7;
const ll     INF  = 1e18 + 100;
const int    inf  = 0x3f3f3f3f;
const double pi   = acos(-1.0);
const double eps  = 1e-8;
using namespace std;

int n, m, k;
int cas, tol, T;

int cnt[26];
char s1[maxn], s2[maxn];

bool ok() {
    for(int i=0; i<26; i++) if(cnt[i])  return 0;
    return 1;
}

int main() {
    scanf("%d", &T);
    while(T--) {
        mes(cnt, 0);
        scanf("%s%s", s1+1, s2+1);
        n = strlen(s1+1), m = strlen(s2+1);
        if(n>m) {
            puts("NO");
            continue;
        }
        for(int i=1; i<=n; i++) cnt[s1[i]-'a']++;
        for(int i=1; i<=n; i++) cnt[s2[i]-'a']--;
        bool f = 0;
        for(int i=n; i<=m; i++) {
            if(ok())    f = 1;
            if(i==m)    break;
            cnt[s2[i+1]-'a']--;
            cnt[s2[i-n+1]-'a']++;
        }
        puts(f ? "YES" : "NO");
    }
    return 0;
}

A and B

[ Time Limit: 1 squad Memory Limit: 256 MB ]
说出来你可能不信，强行 (oeis) 过了。

view

#include <map>
#include <set>
#include <list>
#include <tuple>
#include <ctime>
#include <cmath>
#include <stack>
#include <queue>
#include <cfloat>
#include <string>
#include <vector>
#include <cstdio>
#include <bitset>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <unordered_map>
#define  lowbit(x)  x & (-x)
#define  mes(a, b)  memset(a, b, sizeof a)
#define  fi         first
#define  se         second
#define  pb         push_back
#define  pii        pair<int, int>
#define  INOPEN     freopen("in.txt", "r", stdin)
#define  OUTOPEN    freopen("out.txt", "w", stdout)

typedef unsigned long long int ull;
typedef long long int ll;
const int    maxn = 1e5 + 10;
const int    maxm = 1e5 + 10;
const ll     mod  = 1e9 + 7;
const ll     INF  = 1e18 + 100;
const int    inf  = 0x3f3f3f3f;
const double pi   = acos(-1.0);
const double eps  = 1e-8;
using namespace std;

ll n, m;
int cas, tol, T;

int main() {
    scanf("%d", &T);
    while(T--) {
        ll a, b;
        scanf("%lld%lld", &a, &b);
        n = abs(a-b);
        ll k=0;
        for(; ; k++) {
            if(k*(k+1)/2 <= n && n<(k+1)*(k+2)/2)   break;
        }
        ll tk = k*(k+1)/2;
        ll ans;
        if(n == tk) ans = k;
        else {
            if(k%2 == 1) {
                if((n-tk)%2==1) ans = k+2;
                else    ans = k+1;
            } else {
                if((n-tk)%2==1) ans = k+1;
                else    ans = k+3;
            }
        }
        printf("%lld
", ans);
    }
    return 0;
}

Berry Jam

[ Time Limit: 2 squad Memory Limit: 256 MB ]
预处理后半段中 (1) 比 (2) 多吃 (x) 瓶所需要的最少步数，然后枚举前半段中吃到第 (i) 瓶处，(1) 还需要比 (2) 多吃 (y) 瓶，然后在后半段预处理中找答案。

view

#include <map>
#include <set>
#include <list>
#include <tuple>
#include <ctime>
#include <cmath>
#include <stack>
#include <queue>
#include <cfloat>
#include <string>
#include <vector>
#include <cstdio>
#include <bitset>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <unordered_map>
#define  lowbit(x)  x & (-x)
#define  mes(a, b)  memset(a, b, sizeof a)
#define  fi         first
#define  se         second
#define  pb         push_back
#define  pii        pair<int, int>
#define  INOPEN     freopen("in.txt", "r", stdin)
#define  OUTOPEN    freopen("out.txt", "w", stdout)

typedef unsigned long long int ull;
typedef long long int ll;
const int    maxn = 2e5 + 10;
const int    maxm = 1e5 + 10;
const ll     mod  = 1e9 + 7;
const ll     INF  = 1e18 + 100;
const int    inf  = 0x3f3f3f3f;
const double pi   = acos(-1.0);
const double eps  = 1e-8;
using namespace std;

int n, m;
int cas, tol, T;

int a[maxn];
unordered_map<int, int> mp;

int main() {
    scanf("%d", &T);
    while(T--) {
        mp.clear();
        scanf("%d", &n);
        int y = 0;
        for(int i=1; i<=n+n; i++) {
            scanf("%d", &a[i]);
            y += a[i]==1 ? 1:-1;
        }
        if(y == 0) {
            printf("0
");
            continue;
        }
        mp[0] = 0;
        for(int i=n+1, x=0; i<=n+n; i++) {
            x += a[i]==1 ? 1:-1;
            if(!mp.count(x))    mp[x] = i-n;
        }
//      for(auto t : mp)    printf("%d %d
", t.fi, t.se);
        int ans = inf;
        for(int i=n; i>=0; i--) {
            if(mp.count(y)) 
                ans = min(ans, n-i+mp[y]);
            if(!i)  break;
            y -= a[i]==1 ? 1:-1;
        }
        printf("%d
", ans);
    }
    return 0;
}

Segment Tree

[ Time Limit: 2 squad Memory Limit: 256 MB ]
把线段先按 (l) 在按 (r) 排序，然后枚举第 (i) 条线段，判断它可以和哪些线段连边。

可以发现，在枚举第 (i) 条线段时，前 (i-1) 条线段的 (l) 一定都是比我的 (l) 小的，所以我其实是需要找到前 (i-1) 条线段中，找到所有满足 (p[i].l leq p[j].r leq p[i].r) 的所有 (j)。

这一段区间是连续的，所以我们可以维护一个 (set) 的 (pair)，用来存放前 (i-1) 条边的 (r) 位置和编号。然后用 (set) 的二分来快速找到所有的 (j)。

又因为想要形成一棵树，这也就意味着最多只会添加 (n-1) 条边，那么整体复杂度就不会太大。

view

#include <map>
#include <set>
#include <list>
#include <tuple>
#include <ctime>
#include <cmath>
#include <stack>
#include <queue>
#include <cfloat>
#include <string>
#include <vector>
#include <cstdio>
#include <bitset>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <unordered_map>
#define  lowbit(x)  x & (-x)
#define  mes(a, b)  memset(a, b, sizeof a)
#define  l          first
#define  r          second
#define  pb         push_back
#define  pii        pair<int, int>
#define  INOPEN     freopen("in.txt", "r", stdin)
#define  OUTOPEN    freopen("out.txt", "w", stdout)
 
typedef unsigned long long int ull;
typedef long long int ll;
const int    maxn = 5e5 + 10;
const int    maxm = 1e5 + 10;
const ll     mod  = 1e9 + 7;
const ll     INF  = 1e18 + 100;
const int    inf  = 0x3f3f3f3f;
const double pi   = acos(-1.0);
const double eps  = 1e-8;
using namespace std;

int n, m;
int cas, tol, T;

int fa[maxn];
pii p[maxn];
set<pii> st;

int find(int x) {
    return fa[x]==x ? x : fa[x]=find(fa[x]);
}

bool bind(int x, int y) {
    x = find(x), y = find(y);
    if(x == y)  return 0;
    fa[x] = y;
    return 1;
}

int main() {
    scanf("%d", &n);
    for(int i=1; i<=n; i++) {
        scanf("%d%d", &p[i].l, &p[i].r);
        fa[i] = i;
    }
    sort(p+1, p+1+n);
    st.clear();
    int sz = 0, f = 1;
    for(int i=1; i<=n; i++) {
        auto pos = st.lower_bound({p[i].l, -1});
        for(auto j = pos; j!=st.end(); j++) {
            if((*j).l > p[i].r) break;
            sz++;
            if(sz==n || !bind(i, (*j).r)) {
                f = 0;
                break;
            }
        }
        if(!f)  break;
        st.insert({p[i].r, i});
    }
    set<int> ans;
    for(int i=1; i<=n; i++) ans.insert(find(i));
    puts(ans.size()==1&&f ? "YES" : "NO");
    return 0;
}

Tests for problem D

[ Time Limit: 2 squad Memory Limit: 256 MB ]
考虑模拟一下第一个样例，它的放置规则是先把 (1) 看成整棵树的根，那么可以先确定 (p[1].r = 2*n)，然后它有两个直接儿子，所以我需要在 (r) 前面留两个空给这两个儿子放 (r) 用，现在已经没有直接儿子了，为了防止新的交叉出现，接下来我就放上自己的 (l)，对于下面的儿子也是同理，可以递归处理。

然后就是儿子的 (l) 问题了，由于 (1) 的各个儿子不能有交叉部分，也就意味着这些得是重合起来的，所以一开始放在最后的 (r)，其对应的 (l) 就应该尽量小，所以我越早放在后面的儿子，应该越晚去 (dfs) 确定其 (l)。

为了防止数字重复被用到，可以用一个 (set) 来维护还可以用的数字。

view

#include <map>
#include <set>
#include <list>
#include <tuple>
#include <ctime>
#include <cmath>
#include <stack>
#include <queue>
#include <cfloat>
#include <string>
#include <vector>
#include <cstdio>
#include <bitset>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <unordered_map>
#define  lowbit(x)  x & (-x)
#define  mes(a, b)  memset(a, b, sizeof a)
#define  l          first
#define  r          second
#define  pb         push_back
#define  pii        pair<int, int>
#define  INOPEN     freopen("in.txt", "r", stdin)
#define  OUTOPEN    freopen("out.txt", "w", stdout)
 
typedef unsigned long long int ull;
typedef long long int ll;
const int    maxn = 5e5 + 10;
const int    maxm = 1e5 + 10;
const ll     mod  = 1e9 + 7;
const ll     INF  = 1e18 + 100;
const int    inf  = 0x3f3f3f3f;
const double pi   = acos(-1.0);
const double eps  = 1e-8;
using namespace std;

int n, m;
int cas, tol, T;

set<int> st;
pii p[maxn];
vector<int> g[maxn];

void dfs(int u, int fa) {
    int len = g[u].size();
    for(int i=0; i<len; i++) if(g[u][i] != fa) {
        p[g[u][i]].r = *(--st.end());
        st.erase((--st.end()));
    }
    p[u].l = *(--st.end());
    st.erase((--st.end()));
//  printf("p%d .l = %d .r = %d
", u, p[u].l, p[u].r);
    for(int i=len-1; ~i; i--) if(g[u][i] != fa) {
        dfs(g[u][i], u);
    }
}

int main() {
    scanf("%d", &n);
    for(int i=2, u, v; i<=n; i++) {
        scanf("%d%d", &u, &v);
        g[u].pb(v), g[v].pb(u);
    }
    p[1].r = 2*n;
    for(int i=1; i<2*n; i++)    st.insert(i);
    dfs(1, 1);
    for(int i=1; i<=n; i++) printf("%d %d
", p[i].l, p[i].r);
    return 0;
}
/*
3
1 2
1 3
*/

Cards

[ Time Limit: 4 squad Memory Limit: 256 MB ]
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