2017 Chinese Multi-University Training, BeihangU Contest
思路：log10(2^m) = m*log10(2)
代码：
#pragma GCC optimize(2) #pragma GCC optimize(3) #pragma GCC optimize(4) #include<bits/stdc++.h> using namespace std; #define y1 y11 #define fi first #define se second #define pi acos(-1.0) #define LL long long //#define mp make_pair #define pb emplace_back #define ls rt<<1, l, m #define rs rt<<1|1, m+1, r #define ULL unsigned LL #define pll pair<LL, LL> #define pli pair<LL, int> #define pii pair<int, int> #define piii pair<int, pii> #define puu pair<ULL, ULL> #define pdd pair<long double, long double> #define mem(a, b) memset(a, b, sizeof(a)) #define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0); #define fopen freopen("in.txt", "r", stdin);freopen("out.txt", "w", stout); //head int n, cs = 0; int main() { while(~scanf("%d", &n)) { printf("Case #%d: %d\n", ++cs, (int)(n*log10(2.0))); } return 0; }
思路：大数比较大小
代码：
#include <cstdio> #include <vector> #include <cstring> #include <algorithm> #include <iostream> #include <queue> using namespace std; #define pb push_back #define fi first #define se second #define debug(x) cerr<<#x << " := " << x << endl; #define bug cerr<<"-----------------------"<<endl; #define FOR(a, b, c) for(int a = b; a <= c; ++ a) typedef long long ll; typedef long double ld; typedef pair<int, int> pii; typedef pair<ll, ll> pll; const int inf = 0x3f3f3f3f; const int mod = 1e9+7; /**********showtime************/ const int maxn = 1e5+9; char str[maxn]; string ss[maxn]; vector<pii>vec[30]; int a[30][maxn], mx[30]; int id[30], vis[30]; bool cmp(int &x, int &y) { if(mx[x] < mx[y]) return true; else if(mx[x] > mx[y]) return false; else { for (int i = mx[x]-1; i >= 0; --i) { if(a[x][i] > a[y][i]) return false; else if(a[x][i] < a[y][i]) return true; } } return false; } int main(){ int n, cas = 0; while(~scanf("%d", &n)) { for(int i=0; i<26; i++) vec[i].clear(), vis[i] = 0, mx[i] = 0; for(int i=0; i<26; i++) for(int j=0; j<maxn; j++) a[i][j] = 0; for(int i=1; i<=n; i++) { scanf("%s", str); ss[i] = string(str); vis[str[0] - 'a'] = 1; } for(int i=1; i<=n; i++) { int len = ss[i].length(); for(int j=0; j<len; j++) { a[ss[i][j] - 'a'][len - j - 1] ++; } } for(int i=0; i<26; i++) { int jin = 0; for(int j=0; j<maxn-1; j++) { a[i][j] += jin; jin = a[i][j] / 26; a[i][j] = a[i][j] % 26; if(a[i][j] > 0) { mx[i] = j+1; } } } for(int i=0; i<26; i++) id[i] = i; sort(id, id+26, cmp); int pos = 0; while(vis[id[pos]]) pos++; int pt = id[pos]; for(int i=pos; i>=0; i--) id[i] = id[i-1]; id[0] = pt; ll ans = 0; for(int i=0; i<26; i++) { ll base = 1; for(int j=0; j<maxn; j++) { ans = (ans + 1ll*i * base *a[id[i]][j] % mod)%mod; base = 1ll * base * 26 % mod; } } ++cas; printf("Case #%d: %lld\n",cas, ans); } return 0; }
思路：容斥，考虑对于每种颜色删去后，分成的块中的点两两之间对于这种颜色没有贡献
代码：
#pragma GCC optimize(2) #pragma GCC optimize(3) #pragma GCC optimize(4) #include<bits/stdc++.h> using namespace std; #define y1 y11 #define fi first #define se second #define pi acos(-1.0) #define LL long long //#define mp make_pair #define pb push_back #define ls rt<<1, l, m #define rs rt<<1|1, m+1, r #define ULL unsigned LL #define pll pair<LL, LL> #define pli pair<LL, int> #define pii pair<int, int> #define piii pair<pii, int> #define pdd pair<double, double> #define mem(a, b) memset(a, b, sizeof(a)) #define debug(x) cerr << #x << " = " << x << "\n"; #define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0); //head const int N = 2e5 + 5; vector<int> g[N], stk[N]; int n, u, v, c[N], sz[N], blo[N], top[N]; bool vis[N]; void dfs(int u, int o) { sz[u] = 1; for (int v : g[u]) { if(v != o) { dfs(v, u); sz[u] += sz[v]; } } blo[u] = sz[u]; } void DFS(int u, int o) { if(stk[c[u]].empty()) top[c[u]] -= sz[u]; else blo[stk[c[u]].back()] -= sz[u]; for (int v : g[u]){ if(v != o) { stk[c[u]].pb(v); DFS(v, u); stk[c[u]].pop_back(); } } } int cs = 0; int main() { while(~scanf("%d", &n)) { for (int i = 1; i <= n; ++i) scanf("%d", &c[i]), vis[c[i]] = true; for (int i = 1; i < n; ++i) scanf("%d %d", &u, &v), g[u].pb(v), g[v].pb(u); dfs(1, 0); int cc = 0; for (int i = 1; i <= n; ++i) if(vis[i]) top[i] = n, ++cc; else top[i] = 0; DFS(1, 0); LL ans = n*1LL*(n-1)/2*cc; for (int i = 2; i <= n; ++i) ans -= blo[i]*1LL*(blo[i]-1)/2; for (int i = 1; i <= n; ++i) ans -= top[i]*1LL*(top[i]-1)/2; printf("Case #%d: %lld\n", ++cs, ans); for (int i = 1; i <= n; ++i) g[i].clear(), vis[i] = false; } return 0; }
思路：a的某个长度为x环可以和b中长度为x因子的环构成函数
代码：
#pragma GCC optimize(2) #pragma GCC optimize(3) #pragma GCC optimize(4) #include<bits/stdc++.h> using namespace std; #define y1 y11 #define fi first #define se second #define pi acos(-1.0) #define LL long long //#define mp make_pair #define pb push_back #define ls rt<<1, l, m #define rs rt<<1|1, m+1, r #define ULL unsigned LL #define pll pair<LL, LL> #define pli pair<LL, int> #define pii pair<int, int> #define piii pair<pii, int> #define pdd pair<double, double> #define mem(a, b) memset(a, b, sizeof(a)) #define debug(x) cerr << #x << " = " << x << "\n"; #define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0); //head const int N = 1e5 + 5; const int MOD = 1e9 + 7; int n, m, a[N], b[N], ca[N], cb[N]; LL ans[N]; bool vis[N], vv[N]; LL q_pow(LL n, LL k) { LL res = 1; while(k) { if(k&1) res = (res * n) % MOD; n = (n * n) % MOD; k >>= 1; } return res; } int main() { int cs = 0; while(~scanf("%d %d", &n, &m)) { for (int i = 0; i < n; ++i) vis[i] = false, ca[i+1] = 0, ans[i+1] = 0; for (int i = 0; i < m; ++i) vv[i] = false, cb[i+1] = 0; for (int i = 0; i < n; ++i) scanf("%d", &a[i]); for (int i = 0; i < m; ++i) scanf("%d", &b[i]); for (int i = 0; i < n; ++i) { if(!vis[i]) { int now = i, cc = 0; while(!vis[now]) { vis[now] = true; now = a[now]; ++cc; } ca[cc]++; } } for (int i = 0; i < m; ++i) { if(!vv[i]) { int now = i, cc = 0; while(!vv[now]) { vv[now] = true; now = b[now]; ++cc; } cb[cc] ++; } } LL res = 1; for (int i = 1; i <= m; ++i) { cb[i] = (cb[i]*1LL*i)%MOD; for (int j = i; j <= n; j += i) { ans[j] = (ans[j] + cb[i]) % MOD; } } for (int j = 1; j <= n; ++j) { if(ca[j]) { res = (res * q_pow(ans[j], ca[j])) % MOD; } } printf("Case #%d: %lld\n", ++cs, res); } return 0; }
思路：nth_element
代码：
#pragma GCC optimize(2) #pragma GCC optimize(3) #pragma GCC optimize(4) #include<bits/stdc++.h> using namespace std; #define y1 y11 #define fi first #define se second #define pi acos(-1.0) #define LL long long //#define mp make_pair #define pb push_back #define ls rt<<1, l, m #define rs rt<<1|1, m+1, r #define ULL unsigned LL #define pll pair<LL, LL> #define pli pair<LL, int> #define pii pair<int, int> #define piii pair<pii, int> #define pdd pair<double, double> #define mem(a, b) memset(a, b, sizeof(a)) #define debug(x) cerr << #x << " = " << x << "\n"; #define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0); //head const int N = 1e7 + 5; unsigned x, A, y, B, z, C; int n, m, b[105], id[105]; unsigned a[N], ans[N]; inline unsigned rng61() { unsigned t; x = x ^ (x << 16); x = x ^ (x >> 5); x = x ^ (x << 1); t = x; x = y; y = z; z = (t ^ x) ^ y; return z; } int cs = 0; int main() { while(~scanf("%d %d %u %u %u", &n, &m, &A, &B, &C)) { for (int i = 1; i <= m; ++i) scanf("%d", &b[i]); x = A, y = B, z = C; for (int i = 1; i <= n; ++i) a[i] = rng61(); printf("Case #%d: ", ++cs); for (int i = 1; i <= m; ++i) id[i] = i; sort(id+1, id+1+m, [](int x, int y){ return b[x] < b[y]; }); nth_element(a+1, a+b[id[m]]+1, a+n+1); ans[id[m]] = a[b[id[m]]+1]; for (int i = m-1; i >= 1; --i) { nth_element(a+1, a+b[id[i]]+1, a+b[id[i+1]]+1); ans[id[i]] = a[b[id[i]]+1]; } for (int i = 1; i <= m; ++i) printf("%u%c", ans[i], " \n"[i==m]); } return 0; }
思路：打表找规律
代码：
#pragma GCC optimize(2) #pragma GCC optimize(3) #pragma GCC optimize(4) #include<bits/stdc++.h> using namespace std; #define y1 y11 #define fi first #define se second #define pi acos(-1.0) #define LL long long //#define mp make_pair #define pb emplace_back #define ls rt<<1, l, m #define rs rt<<1|1, m+1, r #define ULL unsigned LL #define pll pair<LL, LL> #define pli pair<LL, int> #define pii pair<int, int> #define piii pair<int, pii> #define puu pair<ULL, ULL> #define pdd pair<long double, long double> #define mem(a, b) memset(a, b, sizeof(a)) #define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0); #define fopen freopen("in.txt", "r", stdin);freopen("out.txt", "w", stout); //head LL n, k; int main() { int cs = 0; while(~scanf("%lld %lld", &n, &k)) { LL res; if(n == 2) res = k%2 == 0? 2 : 1; else if(k <= n-1) res = k; else { if(k%(n-1) == 1) { --k; if((k/(n-1))%2) res = n; else res = n-1; } else { res = k%(n-1); if(res == 0) res = n-1; --res; } } printf("Case #%d: %lld\n", ++cs, res); } return 0; }