CCPC-Wannafly Winter Camp Day4 (Div2, onsite)

Replay

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Dup4：

• 两轮怎么退火啊？
• 简单树形dp都不会了，送了那么多罚时
• 简单题都不想清楚就乱写了，喵喵喵？

X：

• 欧拉怎么回路啊， 不会啊。
• 还是有没有手误？未思考清楚或者未检查就提交， 导致自己白送罚时。

A：夺宝奇兵

Solved.

考虑$所有i >= 2 需要跟i - 1 连两条边 只有两种可能 取最小的一种$

$注意n的两个点要连一条边$

 #include<bits/stdc++.h>

 using namespace std;

 typedef long long ll;

 const int maxn = 1e5 + ;

 struct node{
     int x1, x2, y1, y2;
 }arr[maxn];

 ll calc(int i,int j)
 {
     ll ans1 = abs(arr[i].x1 - arr[j].x1) + abs(arr[i].y1 - arr[j].y1) + abs(arr[i].x2 - arr[j].x2) + abs(arr[i].y2 - arr[j].y2);
     ll ans2 = abs(arr[i].x1 - arr[j].x2) + abs(arr[i].y1 - arr[j].y2) + abs(arr[i].x2 - arr[j].x1) + abs(arr[i].y2 - arr[j].y1);
     return min(ans1, ans2);
 }

 int n , m;

 int main()
 {
     while(~scanf("%d %d", &n, &m))
     {
         for(int i = ; i <= n; ++i) scanf("%d %d %d %d", &arr[i].x1, &arr[i].y1, &arr[i].x2, &arr[i].y2);
         ll ans = ;
         for(int i = ; i <= n; ++i) ans += calc(i, i - );
         ans += abs(arr[n].x1 - arr[n].x2) + abs(arr[n].y1 - arr[n].y2);
         printf("%lld\n", ans);
     }
     return ;
 }

C：最小边覆盖

Solved.

考虑$No的情况$

• 存在一个点的度数为0(没有被覆盖)
• 存在一条边所连接的两个点其度数 >= 2 即这条边去掉还是个最小边覆盖

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

 #define N 300010
 #define pii pair <int, int>
 int n, m;
 pii G[N];
 int d[N];

 bool f()
 {
     for (int i = ; i <= n; ++i) if (!d[i]) return false;
     for (int i = ; i <= m; ++i)
     {
         int u = G[i].first, v = G[i].second;
         if (d[u] >=  && d[v] >= )
             return false;
     }
     return true;
 }

 int main()
 {
     while (scanf("%d%d", &n, &m) != EOF)
     {
         memset(d, , sizeof d);
         for (int i = , u, v; i <= m; ++i)
         {
             scanf("%d%d", &u, &v);
             ++d[u], ++d[v];
             G[i] = pii(u, v);
         }
         puts(f() ? "Yes" : "No");
     }
     return ;
 }

F：小小马

Solved.

因为不同颜色出现次数相同， 所以步数一定是奇数。

暴力跑出大数据的状态， 发现颜色相同就输出No， 否则输出Yes。

小数据暴力跑即可

 #include<bits/stdc++.h>

 using namespace std;

 const int maxn = 1e6 + ;

 struct node{
     int x, y;
     int step;
     node(){}
     node(int x, int y, int step): x(x), y(y), step(step){}
 };

 int n, m;
 int sx, sy, ex, ey;
 int vis[][maxn][];
 int dir[][] = {-, -, -, , -, -, -, , , -, , , , -, , };

 int judge(int x, int y,int step)
 {
     if(x <  || x > n || y <  || y > m || vis[x][y][step % ]) return false;
     else return true;
 }

 void BFS()
 {
     memset(vis, , sizeof vis);
     queue<node>q;
     q.push(node(sx, sy, ));
     while(!q.empty())
     {
         node st = q.front();
         q.pop();
         node now = st;
         now.step++;
         for(int i = ; i < ; ++i)
         {
             now.x = st.x + dir[i][];
             now.y = st.y + dir[i][];
             if(judge(now.x, now.y, now.step))
             {
                 vis[now.x][now.y][now.step % ] = ;
                 q.push(now);
             }
         }
     }
 }

 int main()
 {
     while(~scanf("%d %d", &n, &m))
     {
         scanf("%d %d", &sx, &sy);
         scanf("%d %d", &ex, &ey);
         if(n <  || m < )
         {
             if(n > m)
             {
                 swap(n, m);
                 swap(sx, sy);
                 swap(ex, ey);
             }
             BFS();
             if(vis[ex][ey][]) puts("Yes");
             else puts("No");
         }
         else
         {
             int ans1 = (sx + sy) % ;
             int ans2 = (ex + ey) % ;
             if(ans1 != ans2) puts("Yes");
             else puts("No");
         }
     }
     return ;
 }

G：置置置换

Solved.

$在已知1-n的方案数， 枚举n+1出现的位置$

$当枚举到位置x的时候， 选出x-1个数放在前x个， 然后计算方案数 统计即可$

$2 \cdot ans_{n + 1} = \sum\limits_{i = 0}^{n} C_n^i \cdot ans_i \cdot ans_{n - i}$

 #include <bits/stdc++.h>

 using namespace std;

 typedef long long ll;

 const ll MOD = (ll)1e9 + ;
 const int maxn = 1e3 + ;

 int n;
 ll fac[maxn];
 ll inv[maxn];
 ll invfac[maxn];

 ll ans[maxn];

 void Init()
 {
     fac[] = , inv[] = , invfac[] = ;
     for(int i = ; i < maxn; ++i)
     {
         fac[i] = fac[i - ] * i % MOD;
         inv[i] = inv[MOD % i] * (MOD - MOD / i) % MOD;
         invfac[i] = invfac[i - ] * inv[i]  % MOD;
     }
 }

 ll calc(int n, int m)
 {
     if(n == m || m == ) return 1ll;
     return fac[n] * invfac[m] % MOD * invfac[n - m] % MOD;
 }

 int main()
 {
     Init();
     ans[] = ans[] = ;
     for(int i = ; i +  < maxn; ++i)
     {
         for(int j = ; j <= i; ++j)
         {
             ans[i + ] = (ans[i + ] + calc(i, j) * ans[j] % MOD * ans[i - j] % MOD) % MOD;
         }
         ans[i + ] = (ans[i + ] * inv[]) % MOD;
     }
     while (scanf("%d", &n) != EOF)
     {
         printf("%lld\n", ans[n]);
     }
     return ;
 }

I：咆咆咆哮

Solved.

考虑如果选择$a_i的个数固定为x，那么对于所有选取b_i的卡牌来说它的贡献是固定的$

枚举$x, 再贪心选取即可$

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

 #define ll long long
 #define N 1010
 int n, a[N], b[N];

 ll f(int x)
 {
     priority_queue <ll> pq;
     ll res = ;
     for (int i = ; i <= n; ++i)
     {
         res += a[i];
         pq.push(1ll * b[i] * x - a[i]);
     }
     for (int i = ; i <= n - x; ++i)
     {
         res += pq.top();
         pq.pop();
     }
     return res;
 }

 int main()
 {
     while (scanf("%d", &n) != EOF)
     {
         for (int i = ; i <= n; ++i) scanf("%d%d", a + i, b + i);
         ll res = ;
         for (int i = ; i <= n; ++i)
             res = max(res, f(i));
         printf("%lld\n", res);
     }
     return ;
 }

Div1：

三分

好像满足凸性？ 我不会证啊。..

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

 #define ll long long
 #define N 100010
 int n, a[N], b[N];

 ll check(int x)
 {
     ll res = ;
     priority_queue <ll> pq;
     for (int i = ; i <= n; ++i)
     {
         res = res + a[i];
         pq.push(1ll * b[i] * x - a[i]);
     }
     for (int i = n - x; !pq.empty() && i; --i)
     {
         res += pq.top(); pq.pop();
     }
     return res;
 }

 int main()
 {
     while (scanf("%d", &n) != EOF)
     {
         for (int i = ; i <= n; ++i) scanf("%d%d", a + i, b + i);
         int l = , r = n; ll res = ;
         while (r - l >= )
         {
             int midl = (l + r) >> ;
             int midr = (midl + r) >> ;
             ll tmpl = check(midl);
             ll tmpr = check(midr);
             if (tmpl <= tmpr)
             {
                 res = max(res, tmpr);
                 l = midl + ;
             }
             else
             {
                 res = max(res, tmpl);
                 r = midr - ;
             }
         }
         printf("%lld\n", res);
     }
     return ;
 }

K：两条路径

Solved.

考虑$x作为交它的权值要被算上$

在考虑两条路径可以选取端点，端点的选择在其儿子对应的子树中选取一个点且仅能选取一个

树形DP即可

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

 #define ll long long
 #define N 100010
 #define INFLL 0x3f3f3f3f3f3f3f3f
 int n, q;
 ll val[N];
 vector <int> G[N];
 ll Bit[], f[N];

 void DFS(int u, int fa)
 {
     f[u] = -INFLL;
     for (auto v : G[u]) if (v != fa)
     {
         DFS(v, u);
         f[u] = max(f[u], f[v]);
     }
     f[u] = max(f[u], 0ll);
     f[u] += val[u];
 }

 void out(ll x)
 {
     if (x < ) putchar('-'), x = -x;
     string res = "";
     while (x)
     {
         res += (x %  + '');
         x /= ;
     }
     reverse(res.begin(), res.end());
     cout << res << "\n";
 }

 int main()
 {
     Bit[] = ;
     for (int i = ; i <= ; ++i) Bit[i] = Bit[i - ] << ;
     while (scanf("%d", &n) != EOF)
     {
         for (int i = ; i <= n; ++i) G[i].clear();
         for (int i = , x; i <= n; ++i)
         {
             scanf("%d", &x);
             if (!x)
             {
                 val[i] = ;
                 continue;
             }
             int vis = ;
             if (x < )
             {
                 x = -x;
                 vis = -;
             }
             --x;
             val[i] = Bit[x] * vis;
         }
         for (int i = , u, v; i < n; ++i)
         {
             scanf("%d%d", &u, &v);
             G[u].push_back(v);
             G[v].push_back(u);
         }
         int x;
         scanf("%d", &q);
         while (q--)
         {
             scanf("%d", &x);
             priority_queue <ll> pq;
             for (auto v : G[x])
             {
                 DFS(v, x);
                 pq.push(f[v]);
             }
             ll res = val[x];
             for (int i = ; i <=  && !pq.empty() && pq.top() > ; ++i)
             {
                 res += pq.top(); pq.pop();
             }
             //cout << res << endl;
             out(res);
         }
     }
     return ;
 }