最小排列
在每个给定的数字输出前按从小到大的顺序输出所有比它小的数字
#pragma comment(linker, "/STACK:102400000,102400000") #include<stdio.h> #include<string.h> #include<stdlib.h> #include<vector> #include<algorithm> #include<iostream> #include<map> #include<queue> #include<stack> #include<string> #include<functional> #include<math.h> //#include<bits/stdc++.h> using namespace std; typedef long long lint; typedef vector<int> VI; typedef pair<int, int> PII; typedef queue<int> QI; void makedata() { freopen("input.txt", "w", stdout); fclose(stdout); } int a[110000]; bool f[110000]; int main() { #ifndef ONLINE_JUDGE freopen("input.txt", "r", stdin); #endif //makedata(); std::ios::sync_with_stdio(0), cin.tie(0); int n, m, x; memset(f, false, sizeof(f)); cin >> n >> m; for (int i = 0; i < m; i++) { cin >> a[i]; f[a[i]] = true; } int p = 1; for (int i = 0; i < m; i++) { for (int j = p; j < a[i]; j++) { if (!f[j]) { cout << j << endl; } } cout << a[i] << endl; p = max(p, a[i]); while (f[p]) p++; } for (int i = p; i <= n; i++) cout << i << endl; return 0; }
最大前缀和
枚举每个前缀，选出左侧最小的k个数字和右侧最大的k个数字，枚举0~k次交换
#pragma comment(linker, "/STACK:102400000,102400000") #include<stdio.h> #include<string.h> #include<stdlib.h> #include<vector> #include<algorithm> #include<iostream> #include<map> #include<queue> #include<stack> #include<string> #include<functional> #include<math.h> //#include<bits/stdc++.h> using namespace std; typedef long long lint; typedef vector<int> VI; typedef pair<int, int> PII; typedef queue<int> QI; void makedata() { freopen("input.txt", "w", stdout); fclose(stdout); } class Virtul_List { public: int data[100000], pre[100000], nex[100000], head, end, sz; bool exist[100000]; Virtul_List() {}; void build(PII * a, int n) { for (int i = 0; i < n; i++) data[i] = a[i].first; head = 0, end = -1, sz = n; for (int i = 1; i < n; i++) pre[i] = i - 1; for (int i = 0; i < n; i++) nex[i] = i + 1; nex[n - 1] = end; memset(exist, true, sizeof(exist)); } void insert(int x, int w) { int l = x, r = nex[x]; data[sz] = w; nex[l] = sz, pre[sz] = l, nex[sz] = r, pre[r] = sz; sz++; } void erase(int x) { if (x == end) return; if (x >= sz || !exist[x]) return; if (x == head) { head = nex[x]; } else { int l = pre[x], r = nex[x]; nex[l] = r, pre[r] = l; } exist[x] = false; } int next(int x) { return nex[x]; } }; Virtul_List vl; map<PII, int> mp; int a[100000]; PII b[100000]; int main() { #ifndef ONLINE_JUDGE freopen("input.txt", "r", stdin); #endif //makedata(); std::ios::sync_with_stdio(0), cin.tie(0); int n, k, m[4], M[4]; cin >> n >> k; for (int i = 0; i < n; i++) { cin >> a[i]; b[i] = make_pair(-a[i], i); } sort(b, b + n); for (int i = 0; i < n; i++) b[i].first *= -1; mp.clear(); for (int i = 0; i < n; i++) mp[b[i]] = i; vl.build(b, n); lint ans = 0, sum = 0; m[0] = m[1] = m[2] = 1000000001; for (int i = 0; i < n; i++) { sum += a[i]; vl.erase(mp[make_pair(a[i], i)]); ans = max(ans, sum); m[3] = a[i]; sort(m, m + 4); lint tmp = sum; int head = vl.head; for (int i = 0; i < k; i++) { if (head == vl.end) continue; tmp = tmp - m[i] + vl.data[head]; ans = max(ans, tmp); head = vl.next(head); } } cout << ans << endl; return 0; }
质数
打出2~10^6的质数表，枚举每个质数，在l~r内枚举其倍数
#pragma comment(linker, "/STACK:102400000,102400000") #include<stdio.h> #include<string.h> #include<stdlib.h> #include<vector> #include<algorithm> #include<iostream> #include<map> #include<queue> #include<stack> #include<string> #include<functional> #include<math.h> //#include<bits/stdc++.h> using namespace std; typedef long long lint; typedef vector<int> VI; typedef pair<int, int> PII; typedef queue<int> QI; void makedata() { freopen("input.txt", "w", stdout); fclose(stdout); } bool f[1100000]; int p[1100000], a[1100000], c[1100000]; int main() { #ifndef ONLINE_JUDGE freopen("input.txt", "r", stdin); #endif //makedata(); std::ios::sync_with_stdio(0), cin.tie(0); int n = 0, l, r; cin >> l >> r; memset(f, true, sizeof(f)); f[0] = f[1] = false; for (int i = 2; i < 1000000; i++) { if (f[i]) { p[n++] = i; for (int j = i + i; j < 1000000; j += i) f[j] = false; } } for (int i = l; i <= r; i++) a[i - l] = i; memset(c, 0, sizeof(c)); for (int i = 0; i < n; i++) { int j = l / p[i]; if (l % p[i] != 0) j++; j *= p[i]; for (; j <= r; j += p[i]) { while (a[j - l] % p[i] == 0) a[j - l] /= p[i], c[j - l]++; } } int ans = 0; for (int i = l; i <= r; i++) { if (a[i - l] != 1) c[i - l]++; if (f[c[i - l]]) ans++; } cout << ans << endl; return 0; }
随机排列2
每次x值在位置i出发生改变时表示此时p[i]是p[1~i]中最大的值，这件事发生的次数为n!/i
#pragma comment(linker, "/STACK:102400000,102400000") #include<stdio.h> #include<string.h> #include<stdlib.h> #include<vector> #include<algorithm> #include<iostream> #include<map> #include<queue> #include<stack> #include<string> #include<functional> #include<math.h> //#include<bits/stdc++.h> using namespace std; typedef long long lint; typedef vector<int> VI; typedef pair<int, int> PII; typedef queue<int> QI; void makedata() { freopen("input.txt", "w", stdout); fclose(stdout); } inline lint pow(lint a, lint b, lint p) { lint rtn = 1; while (b) { if (b & 1) rtn = rtn * a % p; a = a * a % p; b >>= 1; } return rtn; } int main() { #ifndef ONLINE_JUDGE freopen("input.txt", "r", stdin); #endif //makedata(); std::ios::sync_with_stdio(0), cin.tie(0); int n; cin >> n; lint frac = 1; for (int i = 1; i <= n; i++) frac = frac * i % 1000000007; lint ans = 0; for (int i = 1; i <= n; i++) { ans += (frac * pow(i, 1000000005, 1000000007)) % 1000000007; ans %= 1000000007; } cout << ans << endl; return 0; }