Dfs and Similar

Masha and a Beautiful Tree 经典的分治问题，记录区间的左右端点和区间范围即可。找到一个分支无解之后，及时退出。 // Date: Fri Dec 22 22:12:35 2023 #include <climits> #include <cmath> #include <cstdio> #include <cstdlib> #include <cstring> #include <algorithm> #include <functional> #include <iomanip> #include <iostream> #include <map> #include <queue> #include <set> #include <sstream> #include <stack> #include <string> #include <utility> #include <vector> using namespace std; const int INF = 0x3f3f3f3f, MOD = 1e9 + 7; const double eps = 1e-8; const int dir[8][2] = { {0, 1}, {0, -1}, {1, 0}, {-1, 0}, {1, 1}, {1, -1}, {-1, 1}, {-1, -1}, }; typedef long long ll; typedef unsigned long long ull; typedef vector<int> VI; typedef pair<int, int> PII; const ull Pr = 131; #define For(i, a, b) for (int i = int(a); i < int(b); ++i) #define Rof(i, a, b) for (int i = int(b) - 1; i >= int(a); --i) #define For1(i, a, b) for (int i = int(a); i <= int(b); ++i) #define Rof1(i, a, b) for (int i = int(b); i >= int(a); --i) #define ForE(i, j) for (int i = h[j]; i != -1; i = ne[i]) #define f1 first #define f2 second #define pb push_back #define has(a, x) (a.find(x) != a.end()) #define nonempty(a) (!a.empty()) #define all(a) (a).begin(), (a).end() #define SZ(a) int((a).size()) template <typename t> istream &operator>>(istream &in, vector<t> &vec) { for (t &x : vec) in >> x; return in; } template <typename t> ostream &operator<<(ostream &out, vector<t> &vec) { int n = SZ(vec); For(i, 0, n) { out << vec[i]; if (i < n - 1) out << ' '; } return out; } #ifdef _DEBUG #define debug1(x) cout << #x " = " << x << endl; #define debug2(x, y) cout << #x " = " << x << " " #y " = " << y << endl; #define debug3(x, y, z) \ cout << #x " = " << x << " " #y " = " << y << " " #z " = " << z << endl; #else #define debug1 #define debug2 #define debug3 #endif const int N = 300010; int t, n, a[N]; ll res; void dfs(int l, int r, int vl, int vr) { if (l >= r) return; if (res == -1) return; if (l + 1 == r) { if (a[l] > a[r]) { res++; swap(a[l], a[r]); } if (PII{vl, vr} != PII{a[l], a[r]}) { res = -1; } return; } int mid = (l + r) / 2, vmid = (vl + vr) / 2; if (a[l] >= vl && a[l] <= vmid) { dfs(l, mid, vl, vmid); dfs(mid + 1, r, vmid + 1, vr); } else { res++; dfs(l, mid, vmid + 1, vr); dfs(mid + 1, r, vl, vmid); } } int main(void) { #ifdef _DEBUG freopen("1741d.in", "r", stdin); #endif std::ios::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); cin >> t; while (t--) { cin >> n; For1(i, 1, n) cin >> a[i]; res = 0; dfs(1, n, 1, n); cout << res << '\n'; } return 0; }

White-Black Balanced Subtrees 一次 DFS 之后统计出各个节点子树的黑色节点和白色节点的个数。 // Date: Sat Dec 16 10:34:02 2023 #include <climits> #include <cmath> #include <cstdio> #include <cstdlib> #include <cstring> #include <algorithm> #include <functional> #include <iomanip> #include <iostream> #include <map> #include <queue> #include <set> #include <sstream> #include <stack> #include <string> #include <utility> #include <vector> using namespace std; const int INF = 0x3f3f3f3f, MOD = 1e9 + 7; const double eps = 1e-8; const int dir[8][2] = { {0, 1}, {0, -1}, {1, 0}, {-1, 0}, {1, 1}, {1, -1}, {-1, 1}, {-1, -1}, }; typedef long long ll; typedef unsigned long long ull; typedef vector<int> VI; typedef pair<int, int> PII; const ull Pr = 131; #define For(i, a, b) for (int i = int(a); i < int(b); ++i) #define Rof(i, a, b) for (int i = int(b) - 1; i >= int(a); --i) #define For1(i, a, b) for (int i = int(a); i <= int(b); ++i) #define Rof1(i, a, b) for (int i = int(b); i >= int(a); --i) #define ForE(i, j) for (int i = h[j]; i != -1; i = ne[i]) #define f1 first #define f2 second #define pb push_back #define has(a, x) (a.find(x) != a.end()) #define nonempty(a) (!a.empty()) #define all(a) (a).begin(), (a).end() #define SZ(a) int((a).size()) #ifdef _DEBUG #define debug1(x) cout << #x " = " << x << endl; #define debug2(x, y) cout << #x " = " << x << " " #y " = " << y << endl; #define debug3(x, y, z) \ cout << #x " = " << x << " " #y " = " << y << " " #z " = " << z << endl; #else #define debug1 #define debug2 #define debug3 #endif const int N = 4010, M = 10010; int h[N], w[N], b[N], t, n; int e[M], ne[M], idx; char color[N]; void Init() { idx = 0; memset(h, -1, sizeof h); memset(w, 0, sizeof w); memset(b, 0, sizeof b); } void Add(int a, int b) { e[idx] = b, ne[idx] = h[a], h[a] = idx++; } void dfs(int x) { int w1 = 0, b1 = 0; for (int i = h[x]; i != -1; i = ne[i]) { int j = e[i]; dfs(j); w1 += w[j]; b1 += b[j]; } if (color[x] == 'B') b1++; else w1++; w[x] = w1; b[x] = b1; } int main(void) { #ifdef _DEBUG freopen("1676g.in", "r", stdin); #endif std::ios::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); cin >> t; while (t--) { cin >> n; Init(); For1(i, 2, n) { int j; cin >> j; Add(j, i); } memset(color, 0, sizeof color); string s; cin >> s; For(i, 0, SZ(s)) { color[i + 1] = s[i]; } dfs(1); int res{}; For1(i, 1, n) { if (w[i] == b[i]) res++; } cout << res << '\n'; } return 0; }

Hamiltonian Wall 可以发现从一个 B 开始，只能向右、上、下走，并且应该优先走上、下的情况，这样才不会出现重复走到 B 的情况。由于起点不确定，但是只有两个。两次 DFS 就可以了，搜索完之后检查是不是所有的 B 都访问到了。 // Date: Sat Dec 16 09:14:16 2023 #include <climits> #include <cmath> #include <cstdio> #include <cstdlib> #include <cstring> #include <algorithm> #include <functional> #include <iomanip> #include <iostream> #include <map> #include <queue> #include <set> #include <sstream> #include <stack> #include <string> #include <utility> #include <vector> using namespace std; const int INF = 0x3f3f3f3f, MOD = 1e9 + 7; const double eps = 1e-8; const int dir[8][2] = { {1, 0}, {-1, 0}, {0, 1}, }; typedef long long ll; typedef unsigned long long ull; typedef vector<int> VI; typedef pair<int, int> PII; const ull Pr = 131; #define For(i, a, b) for (int i = int(a); i < int(b); ++i) #define Rof(i, a, b) for (int i = int(b) - 1; i >= int(a); --i) #define For1(i, a, b) for (int i = int(a); i <= int(b); ++i) #define Rof1(i, a, b) for (int i = int(b); i >= int(a); --i) #define ForE(i, j) for (int i = h[j]; i != -1; i = ne[i]) #define f1 first #define f2 second #define pb push_back #define has(a, x) (a.find(x) != a.end()) #define nonempty(a) (!a.empty()) #define all(a) (a).begin(), (a).end() #define SZ(a) int((a).size()) #ifdef _DEBUG #define debug1(x) cout << #x " = " << x << endl; #define debug2(x, y) cout << #x " = " << x << " " #y " = " << y << endl; #define debug3(x, y, z) \ cout << #x " = " << x << " " #y " = " << y << " " #z " = " << z << endl; #else #define debug1 #define debug2 #define debug3 #endif const int N = 200010; int t, n; bool vis[2][N]; char a[2][N]; bool check(int x, int y) { return x >= 0 && x < 2 && y >= 0 && y < n && a[x][y] == 'B' && !vis[x][y]; } void dfs(int x, int y) { vis[x][y] = true; int x1, y1; For(i, 0, 3) { x1 = x + dir[i][0]; y1 = y + dir[i][1]; if (check(x1, y1)) { dfs(x1, y1); return; } } } int main(void) { #ifdef _DEBUG freopen("1766c.in", "r", stdin); #endif std::ios::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); cin >> t; while (t--) { cin >> n >> a[0] >> a[1]; memset(vis, false, sizeof vis); bool flag = true; dfs(0, 0); For(i, 0, 2) { For(j, 0, n) { if (a[i][j] == 'B' && !vis[i][j]) { flag = false; break; } } if (!flag) break; } if (flag) { cout << "YES\n"; continue; } memset(vis, false, sizeof vis); flag = true; dfs(1, 0); For(i, 0, 2) { For(j, 0, n) { if (a[i][j] == 'B' && !vis[i][j]) { flag = false; break; } } if (!flag) break; } cout << (flag ? "YES" : "NO") << '\n'; } return 0; }