[csu/coj 1079]树上路径查询 LCA

题意：询问树上从u到v的路径是否经过k

思路：把树dfs转化为有根树后，对于u,v的路径而言，设p为u，v的最近公共祖先，u到v的路径必定是可以看成两条路径的组合，u->p，v->p，这样一来便可以将判断条件转化为(LCA(u,k)=k  || LCA(v,k)=k) && LCA(k,p)=p。由于这个LCA询问里面需要用到中间结果p，所以这种方法用tarjan离线不行，只能用dfs+RMQ。

  1 #pragma comment(linker, "/STACK:10240000,10240000")

  2 

  3 #include <iostream>

  4 #include <cstdio>

  5 #include <algorithm>

  6 #include <cstdlib>

  7 #include <cstring>

  8 #include <map>

  9 #include <queue>

 10 #include <deque>

 11 #include <cmath>

 12 #include <vector>

 13 #include <ctime>

 14 #include <cctype>

 15 #include <stack>

 16 #include <set>

 17 #include <bitset>

 18 #include <functional>

 19 #include <numeric>

 20 #include <stdexcept>

 21 #include <utility>

 22 

 23 using namespace std;

 24 

 25 #define mem0(a) memset(a, 0, sizeof(a))

 26 #define mem_1(a) memset(a, -1, sizeof(a))

 27 #define lson l, m, rt << 1

 28 #define rson m + 1, r, rt << 1 | 1

 29 #define define_m int m = (l + r) >> 1

 30 #define rep_up0(a, b) for (int a = 0; a < (b); a++)

 31 #define rep_up1(a, b) for (int a = 1; a <= (b); a++)

 32 #define rep_down0(a, b) for (int a = b - 1; a >= 0; a--)

 33 #define rep_down1(a, b) for (int a = b; a > 0; a--)

 34 #define all(a) (a).begin(), (a).end()

 35 #define lowbit(x) ((x) & (-(x)))

 36 #define constructInt4(name, a, b, c, d) name(int a = 0, int b = 0, int c = 0, int d = 0): a(a), b(b), c(c), d(d) {}

 37 #define constructInt3(name, a, b, c) name(int a = 0, int b = 0, int c = 0): a(a), b(b), c(c) {}

 38 #define constructInt2(name, a, b) name(int a = 0, int b = 0): a(a), b(b) {}

 39 #define pchr(a) putchar(a)

 40 #define pstr(a) printf("%s", a)

 41 #define sstr(a) scanf("%s", a)

 42 #define sint(a) scanf("%d", &a)

 43 #define sint2(a, b) scanf("%d%d", &a, &b)

 44 #define sint3(a, b, c) scanf("%d%d%d", &a, &b, &c)

 45 #define pint(a) printf("%d\n", a)

 46 #define test_print1(a) cout << "var1 = " << a << endl

 47 #define test_print2(a, b) cout << "var1 = " << a << ", var2 = " << b << endl

 48 #define test_print3(a, b, c) cout << "var1 = " << a << ", var2 = " << b << ", var3 = " << c << endl

 49 #define mp(a, b) make_pair(a, b)

 50 #define pb(a) push_back(a)

 51 

 52 typedef long long LL;

 53 typedef pair<int, int> pii;

 54 typedef vector<int> vi;

 55 

 56 const int dx[8] = {0, 0, -1, 1, 1, 1, -1, -1};

 57 const int dy[8] = {-1, 1, 0, 0, 1, -1, 1, -1 };

 58 const int maxn = 4e5 + 7;

 59 const int md = 1e9 + 7;

 60 const int inf = 1e9 + 7;

 61 const LL inf_L = 1e18 + 7;

 62 const double pi = acos(-1.0);

 63 const double eps = 1e-6;

 64 

 65 template<class T>T gcd(T a, T b){return b==0?a:gcd(b,a%b);}

 66 template<class T>bool max_update(T &a,const T &b){if(b>a){a = b; return true;}return false;}

 67 template<class T>bool min_update(T &a,const T &b){if(b<a){a = b; return true;}return false;}

 68 template<class T>T condition(bool f, T a, T b){return f?a:b;}

 69 template<class T>void copy_arr(T a[], T b[], int n){rep_up0(i,n)a[i]=b[i];}

 70 int make_id(int x, int y, int n) { return x * n + y; }

 71 

 72 struct SparseTable {

 73     int d[maxn][22];

 74     int t[maxn];

 75     void Init_min(int a[], int n) {

 76         rep_up0(i, n) d[i][0] = a[i];

 77         for (int j = 1; (1 << j) <= n; j++) {

 78             for (int i = 0; i + (1 << j) - 1 < n; i++) {

 79                 d[i][j] = min(d[i][j - 1], d[i + (1 << (j - 1))][j - 1]);

 80             }

 81         }

 82         int p = -1;

 83         rep_up1(i, n) {

 84             if ((i & (i - 1)) == 0) p++;

 85             t[i] = p;

 86         }

 87     }

 88     void Init_max(int a[], int n) {

 89         rep_up0(i, n) d[i][0] = a[i];

 90         for (int j = 1; (1 << j) <= n; j++) {

 91             for (int i = 0; i + (1 << j) - 1 < n; i++) {

 92                 d[i][j] = max(d[i][j - 1], d[i + (1 << (j - 1))][j - 1]);

 93             }

 94         }

 95         int p = -1;

 96         rep_up1(i, n) {

 97             if ((i & (i - 1) == 0)) p++;

 98             t[i] = p;

 99         }

100     }

101     int RMQ_min(int L, int R) {

102         int p = t[R - L + 1];

103         return min(d[L][p], d[R - (1 << p) + 1][p]);

104     }

105     int RMQ_max(int L, int R) {

106         int p = t[R - L + 1];

107         return max(d[L][p], d[R - (1 << p) + 1][p]);

108     }

109 };

110 

111 SparseTable st;

112 

113 struct Graph {

114     vector<vector<int> > G;

115     void clear() { G.clear(); }

116     void resize(int n) { G.resize(n + 2); }

117     void add(int u, int v) { G[u].push_back(v); }

118     vector<int> & operator [] (int u) { return G[u]; }

119 };

120 Graph G;

121 

122 int dfs_clock;

123 int a[maxn], b[maxn], r[maxn];

124 

125 void dfs(int u, int fa) {

126     r[u] = dfs_clock;

127     a[dfs_clock ++] = u;

128     int sz = G[u].size();

129     rep_up0(i, sz) {

130         int v = G[u][i];

131         if (fa != v) {

132             dfs(v, u);

133             a[dfs_clock ++] = u;

134         }

135     }

136 }

137 

138 int LCA(int u, int v) {

139     if (r[u] > r[v]) swap(u, v);

140     return a[st.RMQ_min(r[u], r[v])];

141 }

142 

143 bool chk(int u, int v, int w) {

144     int pos = LCA(u, v);

145     return (LCA(u, w) == w || LCA(v, w) == w) && LCA(pos, w) == pos;

146 }

147 

148 int main() {

149     //freopen("in.txt", "r", stdin);

150     int n, q;

151     while (cin >> n >> q) {

152         G.clear();

153         G.resize(n);

154         rep_up0(i, n - 1) {

155             int u, v;

156             sint2(u, v);

157             G.add(u, v);

158             G.add(v, u);

159         }

160         dfs_clock = 0;

161         dfs(1, 0);

162         rep_up0(i, dfs_clock) b[i] = r[a[i]];

163         st.Init_min(b, dfs_clock);

164         rep_up0(i, q) {

165             int u, v, w;

166             sint3(u, v, w);

167             puts(chk(u, v, w)? "YES" : "NO");

168         }

169         cout << endl;

170     }

171     return 0;

172 }

View Code