【每日一题|2025】2.24~3.2

个人主页：Guiat 归属专栏：每日一题

文章目录 1. 【2.24】P10424 [蓝桥杯 2024 省 B] 好数2. 【2.25】P8665 [蓝桥杯 2018 省 A] 航班时间3. 【2.26】P10905 [蓝桥杯 2024 省 C] 回文字符串4. 【2.27】P10425 [蓝桥杯 2024 省 B] R 格式5. 【2.28】P10426 [蓝桥杯 2024 省 B] 宝石组合6. 【3.1】P10912 [蓝桥杯 2024 国 B] 数星星7. 【3.2】P10914 [蓝桥杯 2024 国 B] 跳石头

正文

1. 【2.24】P10424 [蓝桥杯 2024 省 B] 好数

题目链接： .luogu /problem/P10424

【AC_Code】

#include <iostream> #define IOS ios :: sync_with_stdio(0); cin.tie(0); cout.tie(0); using namespace std; int N, cnt; bool check(int n) { int number = 1; while (n > 0) { if (number % 2 == 1) { if ((n % 10) % 2 == 0) return false; } else if ((n % 10) % 2 != 0) return false; n /= 10; number ++; } return true; } int main() { IOS; cin >> N; for (int i = 1; i <= N; i ++) if (check(i)) cnt ++; cout << cnt << '\n'; return 0; } 2. 【2.25】P8665 [蓝桥杯 2018 省 A] 航班时间

题目链接： .luogu /problem/P8665

【AC_Code】

#include <iostream> #include <iomanip> #define IOS ios :: sync_with_stdio(0); cin.tie(0); cout.tie(0); using namespace std; int solve() { int h1, m1, s1, h2, m2, s2, d = 0; char c1, c2, c3, c4, c5, c6; cin >> h1 >> c1 >> m1 >> c2 >> s1 >> h2 >> c3 >> m2 >> c4 >> s2; if (cin.peek() == ' ') cin >> c5 >> d >> c6; return (86400 * d + 3600 * h2 + 60 * m2 + s2) - (3600 * h1 + 60 * m1 + s1); } int main() { IOS; int T; cin >> T; while (T --) { int ans = (solve() + solve()) >> 1; cout << setw(2) << setfill('0') << ans / 3600 << ':' << setw(2) << setfill('0') << (ans % 3600) / 60 << ':' << setw(2) << setfill('0') << ans % 60 << '\n'; } return 0; } 3. 【2.26】P10905 [蓝桥杯 2024 省 C] 回文字符串

题目链接： .luogu /problem/P10905

【AC_Code】

#include <iostream> #include <string> #define IOS ios :: sync_with_stdio(0); cin.tie(0); cout.tie(0); using namespace std; void solve() { string s; cin >> s; int l = 0, r = s.length() - 1; while (s[l] == 'l' || s[l] == 'q' || s[l] == 'b') l ++; while (s[r] == 'l' || s[r] == 'q' || s[r] == 'b') r --; bool flag = true; for (int i = l, j = 0; i <= (l + r) / 2; i ++, j ++) if (s[i] != s[r - j]) flag = false; if ( ! flag ) cout << "No\n"; else if (l == 0) cout << "Yes\n"; else if (r == s.length() - 1) cout << "No\n"; else if (s.length() - r < l) cout << "No\n"; else { l --; r ++; while (s[l] == s[r] && l >= 0 && r <= s.length()) l --, r ++; if (r == s.length() || l == -1) cout << "Yes\n"; else cout << "No\n"; } } int main() { IOS; int T; cin >> T; while (T--) solve(); return 0; } 4. 【2.27】P10425 [蓝桥杯 2024 省 B] R 格式

题目链接： .luogu /problem/P10425

【AC_Code】

#include <iostream> #include <algorithm> #define IOS ios :: sync_with_stdio(0); cin.tie(0); cout.tie(0); using namespace std; const int N = 1e6; int n, a[N], pos, len; string q; void solve() { reverse(q.begin(), q.end()); pos = q.find('.'); q.erase(pos, 1); len = q.size(); for (int i = 0; i < len; i ++) a[i + 1] = q[i] - '0'; for (int i = 1; i <= n; i ++) { for (int i = 1; i <= len; i ++) a[i] *= 2; for (int i = 1; i <= len; i ++) a[i + 1] += a[i] / 10, a[i] %= 10; if (a[len + 1]) len ++; } if (a[pos] >= 5) a[pos + 1] ++; for (int i = pos + 1; i <= len; i ++) a[i + 1] += a[i] / 10, a[i] %= 10; if (a[len + 1]) len ++; for (int i = len; i > pos; i --) cout << a[i]; cout << '\n'; } int main() { IOS; cin >> n >> q; solve(); return 0; } 5. 【2.28】P10426 [蓝桥杯 2024 省 B] 宝石组合

题目链接： .luogu /problem/P10426

【AC_Code】

#include <iostream> #include <vector> #include <algorithm> #define IOS ios :: sync_with_stdio(0); cin.tie(0); cout.tie(0); using namespace std; const int MAXN = 1e5 + 10; int n, h[MAXN]; vector<int> fac[MAXN]; int gcd(int a, int b) { return __gcd(a, b); } void solve() { cin >> n; for (int i = 1; i <= n; ++ i) cin >> h[i]; sort(h + 1, h + 1 + n); for (int i = 1; i <= n; ++ i) for (int j = 1; j * j <= h[i]; ++j) { if (h[i] % j == 0) { fac[j].push_back(h[i]); if (h[i] / j != j) fac[h[i] / j].push_back(h[i]); } } for (int i = MAXN; i >= 1; -- i) { if (fac[i].size() >= 3) { int a = fac[i][0], b = fac[i][1], c = fac[i][2]; if (gcd(gcd(a, b), c) == i) { cout << a << " " << b << " " << c << "\n"; return; } } } } int main() { IOS; solve(); return 0; } 6. 【3.1】P10912 [蓝桥杯 2024 国 B] 数星星

题目链接： .luogu /problem/P10912

【AC_Code】

#include <iostream> #include <vector> #include <algorithm> #define IOS ios :: sync_with_stdio(0); cin.tie(0); cout.tie(0); using namespace std; const int N = 1e5 + 10, mod = 1e9 + 7; int n, a[N], b[N], c[N], f[N], l, r, ans; vector<int> vec[N]; int fun(int x, int y) { return 1ll * b[x] * f[y] % mod * f[x - y] % mod; } void DFS(int x, int y) { for (auto n : vec[x]) if (n != y) DFS(n, x); if (static_cast<int> (vec[x].size()) + 1 >= 1) { int p = min(r - 1, static_cast<int> (vec[x].size())); for (int i = l - 1; i <= p; i ++) ans = (ans + fun(vec[x].size(), i)) % mod; } } void solve() { cin >> n; b[0] = c[0] = 1; b[1] = 1; c[1] = 1; f[0] = 1; f[1] = 1; for (int i = 2; i <= n; i ++) { b[i] = 1ll * b[i - 1] * i % mod; c[i] = 1ll * c[mod % i] * (mod - mod / i) % mod; f[i] = 1ll * f[i - 1] * c[i] % mod; } for (int i = 1; i < n; i ++) { int x, y; cin >> x >> y; vec[x].push_back(y); vec[y].push_back(x); } cin >> l >> r; DFS(1, 0); cout << ans << '\n'; } int main() { IOS; solve(); return 0; } 7. 【3.2】P10914 [蓝桥杯 2024 国 B] 跳石头

题目链接： .luogu /problem/P10914

【AC_Code】

#include <iostream> #include <bitset> #define IOS ios :: sync_with_stdio(0); cin.tie(0); cout.tie(0); using namespace std; const int N = 4e4 + 10; int c[N], n, ans; bitset<N> f[N]; void solve() { cin >> n; for (int i = 1; i <= n; i ++) { cin >> c[i]; f[i][c[i]] = 1; } for (int i = n; i >= 1; i --) { if (i + c[i] <= n) f[i] |= f[i + c[i]]; if (2 * i <= n) f[i] |= f[2 * i]; ans = max(ans, (int)f[i].count()); } cout << ans << '\n'; } int main() { IOS; solve(); return 0; }

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