• LCA


    LCA(Lowest Common Ancesor)

    链式前向星模板

     1 #include<iostream>
     2 #include<cstring>
     3 #include<cmath>
     4 #define mem(a,x) memset(a,x,sizeof(a))
     5 using namespace std;
     6 const int N = 1e4 + 5;
     7 int fa[N][15];
     8 int head[N];
     9 int vis[N];
    10 int cur;
    11 int depth[N];
    12 bool Du[N];
    13 int ans[N];
    14 int n;
    15 struct Edge {
    16     int to;
    17     int nex;
    18 }edge[N];
    19 void AddEdge(int u, int v) {
    20     edge[cur].to = v;
    21     edge[cur].nex = head[u];
    22     head[u] = cur++;
    23 }
    24 void init() {
    25     mem(head, -1);
    26     mem(fa, 0);
    27     mem(Du, 0);
    28     mem(depth, 0);
    29     cur = 0;
    30 }
    31 void dfs(int v, int p, int d) {
    32     fa[v][0] = p;
    33     depth[v] = d;
    34     for (int i = head[v]; i != -1; i = edge[i].nex) {
    35         dfs(edge[i].to, v, d + 1);
    36     }
    37 }
    38 int LCA(int s, int t) {
    39     if (depth[s] < depth[t])
    40         swap(s, t);
    41     int temp = depth[s] - depth[t];
    42     for (int i = 0; (1 << i) <= temp; i++)
    43     {
    44         if ((1<<i)&temp)
    45             s = fa[s][i];
    46     }
    47     if (s == t)return s;
    48     for (int i = (int)log2(n*1.0); i >= 0; i--) {
    49         if (fa[s][i] != fa[t][i]) {
    50             s = fa[s][i];
    51             t = fa[t][i];
    52         }
    53     }
    54     return fa[s][0];
    55 }
    56 int main()
    57 {
    58     int T, s, t, root;
    59     cin >> T;
    60     while (T--)
    61     {
    62         init();
    63         cin >> n;
    64         for (int i = 0; i < n - 1; i++) {
    65             cin >> s >> t;
    66             AddEdge(s, t);
    67             Du[t] = 1;
    68         }
    69         for (int i = 1; i <= n; i++){
    70             if (Du[i] == 0){
    71                 root = i;
    72                 break;
    73             }
    74         }
    75         dfs(root, -1, 0);
    76         for (int j = 0; (1 << (j + 1)) < n; j++) {
    77             for (int i = 1; i <= n; i++) {
    78                 if (fa[i][j] < 0)
    79                     fa[i][j + 1] = -1;
    80                 else fa[i][j + 1] = fa[fa[i][j]][j];
    81             }
    82         }
    83         cin >> s >> t;
    84         cout << LCA(s, t) << endl;
    85     }
    86 }
    View Code

     连接表模板

     1 /*
     2 邻接表存较慢
     3 考虑链式前向星*/
     4 #include<iostream>
     5 #include<cstring>
     6 #include<cmath>
     7 #include<vector>
     8 #define mem(a,x) memset(a,x,sizeof(a))
     9 using namespace std;
    10 const int N = 1e4 + 5;
    11 int father[N][15];
    12 int depth[N];
    13 int Du[N];
    14 int max_log;
    15 struct  Node{
    16     vector<int>G;
    17 };
    18 Node tree[N];
    19  void dfs(int v, int p, int d) {
    20      father[v][0] = p;
    21      depth[v] = d;
    22      for (int i = 0; i < tree[v].G.size(); i++) {
    23          if (tree[v].G[i] != p)dfs(tree[v].G[i], v, d + 1);
    24      }
    25 }
    26 void init() {
    27     memset(Du, 0, sizeof(Du));
    28     //for (int i = 0; i < 15; i++)G[i].clear();
    29     memset(tree, 0, sizeof(tree));
    30     memset(depth, 0, sizeof(depth));
    31     memset(father, 0, sizeof(father));
    32 }
    33 int LCA(int u, int v) {
    34     if (depth[u]>depth[v])swap(u, v);
    35     int temp = depth[v] - depth[u];
    36     for (int i = 0; (1 << i) <= temp; i++) {
    37         if ((1 << i)&temp) {//如果temp是1011,1分别左移1,2,3,4位,与temp&,如果当前temp在i为1,说明可以提高i位
    38             v= father[v][i];//depth[v]大,先将v提高与u水平
    39         }
    40     }
    41     if (u == v)return u;
    42     for (int i = max_log; i >= 0; i--) {
    43         if (father[u][i] != father[v][i]) {
    44             u = father[u][i];
    45             v = father[v][i];
    46         }
    47     }
    48     return father[u][0];
    49 }
    50 int main() {
    51     int T, s, t, root;
    52     cin >> T;
    53     while (T--)
    54     {
    55     
    56         int n;
    57         cin >> n;
    58         init();
    59         max_log = int(log2(1.0*n));
    60         for (int i = 0; i < n - 1; i++) {
    61             cin >> s >> t;
    62             tree[s].G.push_back(t);
    63             Du[t] = 1;
    64         }
    65         for (int i = 1; i <= n; i++) {
    66             if (Du[i] == 0) {
    67                 root = i;
    68                 break;
    69             }
    70         }
    71         dfs(root, -1, 0);
    72         for (int j = 0; (1 << (j + 1)) < n; j++) {
    73             for (int i = 1; i <= n; i++) {
    74                 if (father[i][j] < 0)
    75                     father[i][j + 1] = -1;
    76                 else father[i][j + 1] = father[father[i][j]][j];
    77             }
    78         }
    79         cin >> s >> t;
    80         cout << LCA(s, t) << endl;
    81     }
    82     return 0;
    83 }
    View Code

    树上距离 HDU-6115

      1 #define _CRT_SECURE_NO_WARNINGS
      2 #include<iostream>
      3 #include<cstring>
      4 #include<cmath>
      5 #include<algorithm>
      6 #include<vector>
      7 #define mem(a,x) memset(a,x,sizeof(a))
      8 const int INF = 0x3f3f3f3f;
      9 using namespace std;
     10 const int N = 100010;
     11 int fa[N][25];
     12 int head[N];
     13 int cur;
     14 int depth[N];
     15 int dis[N];//到根节点的距离
     16 vector<int>vec[N];
     17 int n,m;
     18 struct Edge {
     19     int to;
     20     int cost;
     21     int nex;
     22 }edge[2*N];
     23 //edge[i].to表示第i条边的终点,edge[i].nex表示与第i条边同起点的下一条边的存储位置,edge[i].cost为边权值.
     24 //head[i]保存的是以i为起点的所有边中编号最大的那个, 而把这个当作顶点i的第一条起始边的位置
     25 void AddEdge(int u, int v, int w) {
     26     edge[cur].to = v;
     27     edge[cur].cost = w;
     28     edge[cur].nex = head[u];
     29     head[u] = cur++;
     30 }
     31 void init() {
     32     mem(head, -1);
     33     mem(fa, 0);
     34     mem(depth, 0);
     35     mem(dis, 0);
     36     cur = 0;
     37 }
     38 void dfs(int v, int p, int d,int cost) {
     39     fa[v][0] = p;
     40     depth[v] = d;
     41     dis[v] = cost;
     42     for (int i = head[v]; i != -1; i = edge[i].nex) {
     43         if(!depth[edge[i].to])//无向图
     44         dfs(edge[i].to, v, d + 1,dis[v]+edge[i].cost);
     45     }
     46 }
     47 /*
     48 void dfs(int v, int f, int cost)
     49 {
     50     dis[v] = cost;
     51     for (int i = head[v]; i != -1; i = edge[i].nex)
     52     {
     53         int u = edge[i].to;
     54         if (u == f) continue;
     55         if (!depth[u])
     56             depth[u] = depth[v] + 1, fa[u][0] = v, dfs(u, v, dis[v] + edge[i].cost);
     57     }
     58 }
     59 */
     60 int LCA(int s, int t) {
     61     if (depth[s] < depth[t])
     62         swap(s, t);
     63     int temp = depth[s] - depth[t];
     64     for (int i = 0; (1 << i) <= temp; i++)
     65     {
     66         if ((1 << i)&temp)
     67             s = fa[s][i];
     68     }
     69     if (s == t)return s;
     70     for (int i = (int)log2(n*1.0); i >= 0; i--) {
     71         if (fa[s][i] != fa[t][i]) {
     72             s = fa[s][i];
     73             t = fa[t][i];
     74         }
     75     }
     76     return fa[s][0];
     77 }
     78 int main()
     79 {
     80     int T, s, t,w, root;
     81     scanf("%d", &T);
     82     while (T--)
     83     {
     84         init();
     85         scanf("%d%d", &n, &m);
     86         for (int i = 0; i < n - 1; i++) {
     87             scanf("%d%d%d", &s, &t, &w);
     88             AddEdge(s, t,w);
     89             AddEdge(t, s, w);
     90             //Du[t] = 1;
     91         }
     92         //找到根节点
     93 
     94         for (int i = 1; i <= m; i++)
     95         {
     96             int num, v;
     97             scanf("%d", &num);
     98             for (int j = 1; j <= num; j++)
     99             {
    100                 scanf("%d", &v);
    101                 vec[i].push_back(v);
    102             }
    103         }
    104         //选择1为根
    105         dfs(1, -1,0,0);
    106         for (int j = 0; (1 << (j + 1)) < n; j++) {
    107             for (int i = 1; i <= n; i++) {
    108                 if (fa[i][j] < 0)
    109                     fa[i][j + 1] = -1;
    110                 else fa[i][j + 1] = fa[fa[i][j]][j];
    111             }
    112         }
    113         int q;
    114         scanf("%d",&q);
    115         for (int i = 1; i <= q; i++)
    116         {
    117             int v, u, ans = INF;
    118             scanf("%d%d", &v, &u);
    119             for (int j = 0; j < vec[v].size(); j++)
    120                 for (int  k = 0; k < vec[u].size(); k++)
    121                     ans = min(ans, dis[vec[v][j]] + dis[vec[u][k]] - dis[LCA(vec[v][j], vec[u][k])] * 2);
    122             printf("%d
    ", ans);
    123         }
    124         for (int i = 1; i <= m; i++) vec[i].clear();
    125     }
    126     return 0;
    127 }
    View Code
    不疯魔不成活
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  • 原文地址:https://www.cnblogs.com/gzr2018/p/10439716.html
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