NOIP2013D1T3货车运输（最大生成树+倍增lca）

传送门

这道题，先用kruskal求一遍图中的最大生成树。

然后，倍增求lca，求lca的同时求出边权的最小值。

#include <cstring>
#include <cstdio>
#include <algorithm>

int n, m, cnt, q, t, k;
int f[], head[], p[][], minn[][], deep[];
bool vis[];
struct node
{
    int x, y, z;
}tree[];
struct Node
{
    int next, to, val;
}edge[];

inline void add(int a, int b, int c)
{
    edge[cnt].val = c;
    edge[cnt].to = b;
    edge[cnt].next = head[a];
    head[a] = cnt++;
}

inline int father(int a)
{
    return a == f[a] ? a : f[a] = father(f[a]);
}

inline bool cmp(node a, node b)
{
    return a.z > b.z;
}

void kruskal()
{
    int i;
    for(i = ; i <= m; i++)    scanf("%d %d %d", &tree[i].x, &tree[i].y, &tree[i].z);
    for(i = ; i <= n; i++) f[i] = i;
    std::sort(tree + , tree + m + , cmp);
    for(i = ; i <= m; i++)
    {
        int fa = father(tree[i].x), fb = father(tree[i].y);
        if(fa != fb)
        {
            f[fa] = fb;
            add(tree[i].x, tree[i].y, tree[i].z);
            add(tree[i].y, tree[i].x, tree[i].z);
        }
        if(k == n - ) break;
    }
}

void dfs(int i)
{
    int j;
    vis[i] = ;
    for(j = head[i]; j != -; j = edge[j].next)
     if(!vis[edge[j].to])
     {
         deep[edge[j].to] = deep[i] + ;
         p[edge[j].to][] = i;
         minn[edge[j].to][] = edge[j].val;
         dfs(edge[j].to);
     }
}

void init()
{
    int i, j;
    for(j = ; ( << j) <= n; j++)
     for(i = ; i <= n; i++)
     {
         p[i][j] = p[p[i][j - ]][j - ];
         minn[i][j] = std::min(minn[i][j - ], minn[p[i][j - ]][j - ]);
     }
}

int lca(int a, int b)
{
    int i, j, ret = ;
    if(deep[a] < deep[b]) std::swap(a, b);
    for(i = ; ( << i) <= deep[a]; i++);
    i--;
    for(j = i; j >= ; j--)
     if(deep[a] - ( << j) >= deep[b])
     {
         ret = std::min(ret, minn[a][j]);
         a = p[a][j];
     }
    if(a == b) return ret;
    for(j = i; j >= ; j--)
     if(p[a][j] != p[b][j])
     {
         ret = std::min(ret, std::min(minn[a][j], minn[b][j]));
         a = p[a][j];
         b = p[b][j];
     }
    ret = std::min(ret, std::min(minn[a][], minn[b][]));
    return ret;
}

int main()
{
    int i, j, x1, y1;
    scanf("%d %d", &n, &m);
    memset(head, -, sizeof(head));
    //memset(minn, 127 / 3, sizeof(minn));
    kruskal();
    for(i = ; i <= n; i++)
     if(!vis[i])
     {
         deep[i] = ;
         dfs(i);
     }
    init();
    scanf("%d", &q);
    for(i = ; i <= q; i++)
    {
        scanf("%d %d", &x1, &y1);
        if(father(x1) != father(y1)) printf("-1\n");
        else printf("%d\n", lca(x1, y1));
     }
    return ;

}

换了写法

惨啊，

i >= 0 我居然nc的用 i 代替

应该是 i >= 1 用 i 代替

 #include <cstdio>
 #include <cstring>
 #include <algorithm>

 const int MAXN = , MAXM = , INF = ;
 int n, m, q, cnt, tot;
 int head[MAXM], to[MAXM << ], next[MAXM << ], val[MAXM << ];
 int f1[MAXN], f[MAXN][], min[MAXN][], deep[MAXN];

 struct node
 {
     int x, y, z;
 }p[MAXM];

 inline bool cmp(node a, node b)
 {
     return a.z > b.z;
 }

 inline void add(int x, int y, int z)
 {
     to[cnt] = y;
     val[cnt] = z;
     next[cnt] = head[x];
     head[x] = cnt++;
 }

 inline int find(int x)
 {
     return x == f1[x] ? x : f1[x] = find(f1[x]);
 }

 inline int Min(int x, int y)
 {
     return x < y ? x : y;
 }

 inline void swap(int &x, int &y)
 {
     x ^= y ^= x ^= y;
 }

 inline void dfs(int u)
 {
     int i, v;
     deep[u] = deep[f[u][]] + ;
     for(i = ; f[u][i]; i++)
         f[u][i + ] = f[f[u][i]][i],
         min[u][i + ] = Min(min[u][i], min[f[u][i]][i]);
     for(i = head[u]; i ^ -; i = next[i])
     {
         v = to[i];
         if(!deep[v])
         {
             f[v][] = u;
             min[v][] = val[i];
             dfs(v);
         }
     }
 }

 inline int lca(int x, int y)
 {
     int i, ans = INF;
     if(deep[x] < deep[y]) swap(x, y);
     for(i = ; i >= ; i--)
         if(deep[f[x][i]] >= deep[y])
             ans = Min(ans, min[x][i]), x = f[x][i];
     if(x == y) return ans == INF ? - : ans;
     for(i = ; i >= ; i--)
         if(f[x][i] ^ f[y][i])
             ans = Min(ans, min[x][i]),
             ans = Min(ans, min[y][i]),
             x = f[x][i], y = f[y][i];
     ans = Min(ans, min[x][]);
     ans = Min(ans, min[y][]);
     return ans == INF ? - : ans;
 }

 int main()
 {
     //freopen("truck.in", "r", stdin);
     //freopen("truck.out", "w", stdout);
     int i, x, y, fx, fy;
     scanf("%d %d", &n, &m);
     memset(head, -, sizeof(head));
     memset(min,  / , sizeof(min));
     for(i = ; i <= m; i++) scanf("%d %d %d", &p[i].x, &p[i].y, &p[i].z);
     std::sort(p + , p + m + , cmp);
     for(i = ; i <= n; i++) f1[i] = i;
     for(i = ; i <= m; i++)
     {
         fx = find(p[i].x);
         fy = find(p[i].y);
         if(fx ^ fy)
         {
             f1[fx] = fy;
             tot++;
             add(p[i].x, p[i].y, p[i].z);
             add(p[i].y, p[i].x, p[i].z);
         }
         if(tot == n - ) break;
     }
     for(i = ; i <= n; i++)
         if(!deep[i])
             dfs(i);
     scanf("%d", &q);
     for(i = ; i <= q; i++)
     {
         scanf("%d %d", &x, &y);
         if(find(x) ^ find(y)) puts("-1");
         else printf("%d\n", lca(x, y));
     }
     return ;
 }