2020-2021:teams:wangzai_milk:codeforce_1392部分题解
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2020-2021:teams:wangzai_milk:codeforce_1392部分题解 [2020/09/03 19:10] infinity37 [1392F] |
2020-2021:teams:wangzai_milk:codeforce_1392部分题解 [2020/09/03 19:34] (当前版本) infinity37 [1392H] |
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| ==== 1392G ==== | ==== 1392G ==== | ||
| ===题意=== | ===题意=== | ||
| + | 有$k$个位置，每个位置可以放0或1，有$n$个人，第$i$个人可以把$a_i$位置和$b_i$位置交换一次。给出初始位置的01和最终位置的01，要选一段人使得操作后位置相同个数最大。 | ||
| ===题解=== | ===题解=== | ||
| + | 考虑这个序列，其实交换$(l,r)$相对于对初始序列的$(1,l-1)$和最终序列的$(1,r)$做反向交换然后互相比较。预处理好然后计算更新答案就行。 | ||
| ===代码=== | ===代码=== | ||
| + | <hidden><code c++> | ||
| + | #include <bits/stdc++.h> | ||
| + | using namespace std; | ||
| + | typedef long long ll; | ||
| + | const int N = 2e6+5; | ||
| + | const int inf = 1e9; | ||
| + | int a[N],b[N],p[30],L[N],R[N]; | ||
| + | string ss,tt,s[N],t[N]; | ||
| + | int calc(string str) { | ||
| + | int ans = 0; | ||
| + | for (int i = 0;i <= str.size()-1;i++) | ||
| + | if (str[i]=='1')ans |= (1 << i); | ||
| + | return ans; | ||
| + | } | ||
| + | int getone(int x) { | ||
| + | int cnt = 0; | ||
| + | while (x) { | ||
| + | if (x&1)cnt++; | ||
| + | x>>=1; | ||
| + | } | ||
| + | return cnt; | ||
| + | } | ||
| + | int main() { | ||
| + | int n,m,k; | ||
| + | scanf("%d%d%d",&n,&m,&k); | ||
| + | cin >> ss >> tt; | ||
| + | s[0] = ss; | ||
| + | t[0] = tt; | ||
| + | for (int i = 1;i<= n;i++) | ||
| + | scanf("%d%d",&a[i],&b[i]),a[i]--,b[i]--; | ||
| + | for (int i = 0;i<= k;i++)p[i] = i; | ||
| + | for (int i = 0;i < (1<< k);i++) | ||
| + | L[i] = inf,R[i] = -inf; | ||
| + | for (int i = 1;i<= n;i++) { | ||
| + | s[i] = t[i] = string(k,'0'); | ||
| + | swap(p[a[i]],p[b[i]]); | ||
| + | for (int j = 0;j < k;j++) { | ||
| + | s[i][p[j]] = ss[j]; | ||
| + | t[i][p[j]] = tt[j]; | ||
| + | } | ||
| + | } | ||
| + | for (int i = 0;i<= n;i++) { | ||
| + | L[calc(s[i])] = min(L[calc(s[i])],i); | ||
| + | R[calc(t[i])] = max(R[calc(t[i])],i); | ||
| + | } | ||
| + | for (int i = (1<<k)-1;i >= 0;i--) | ||
| + | for (int j = 0;j < k;j++) | ||
| + | if ((1<<j)&i) { | ||
| + | L[i^(1<<j)] = min(L[i^(1<<j)],L[i]); | ||
| + | R[i^(1<<j)] = max(R[i^(1<<j)],R[i]); | ||
| + | } | ||
| + | int ans = 0,l = 1,r = 1; | ||
| + | for (int i = 0;i < (1<<k);i++) | ||
| + | if (R[i]-L[i]>=m && getone(i)>ans) { | ||
| + | ans = getone(i); | ||
| + | l = L[i]+1,r = R[i]; | ||
| + | } | ||
| + | printf("%d \n%d %d",k+2*ans-count(ss.begin(),ss.end(),'1')-count(tt.begin(),tt.end(),'1'),l,r); | ||
| + | return 0; | ||
| + | } | ||
| + | </code></hidden> | ||
| \\ | \\ | ||
| ==== 1392H ==== | ==== 1392H ==== | ||
| ===题意=== | ===题意=== | ||
| + | 给你$n$张数字牌和$m-n$张特殊牌河一个数字集合。进行如下操作： | ||
| + | |||
| + | 拿出最上面的那张卡片，如果卡片是数字牌，那么把这个数字放进集合。 | ||
| + | |||
| + | 其他情况下把所有卡片重新打乱。检验集合是否包含了所有数字，如果包含了结束游戏。 | ||
| + | |||
| + | 问期望操作次数。 | ||
| ===题解=== | ===题解=== | ||
| + | 期望操作次数是期望游戏轮数乘以期望每一轮次数。 | ||
| - | ===代码=== | + | 可以发现如果在游戏中摸到特殊牌那么一轮就会结束，那么我们算出所有排列中第一张特殊牌之前的牌数，然后+1除以排列数目就是每轮游戏操作次数的期望。这个的答案是$\frac{n}{m+1}+1$。 |
| + | 然后另一个部分则是$m\sum_{i=1}^n\frac{1}{i}+1$，最终答案就是这两者相乘。 | ||
| + | |||
| + | ===代码=== | ||
| + | <hidden><code c++> | ||
| + | #include <bits/stdc++.h> | ||
| + | using namespace std; | ||
| + | typedef long long ll; | ||
| + | const int mod = 998244353; | ||
| + | ll quick_pow(ll x,ll y) { | ||
| + | ll ans = 1; | ||
| + | while (y) { | ||
| + | if (y&1) ans = ans*x%mod; | ||
| + | x = x*x%mod; | ||
| + | y >>= 1; | ||
| + | } | ||
| + | return ans; | ||
| + | } | ||
| + | int main() { | ||
| + | int n,m; | ||
| + | scanf("%d%d",&n,&m); | ||
| + | ll ans1 = (1ll*n*quick_pow(m+1,mod-2)%mod+1)%mod; | ||
| + | ll ans2 = 0; | ||
| + | for (int i = 1;i<= n;i++) | ||
| + | ans2 = (ans2+quick_pow(i,mod-2))%mod; | ||
| + | ans2 = (ans2*m+1)%mod; | ||
| + | printf("%lld\n",ans1*ans2%mod); | ||
| + | return 0; | ||
| + | } | ||
| + | </code></hidden> | ||
| \\ | \\ | ||
2020-2021/teams/wangzai_milk/codeforce_1392部分题解.1599131441.txt.gz · 最后更改: 2020/09/03 19:10 由 infinity37
