[NOIP2013 提高组] 货车运输

Posted 2022-02-13 xiyuping

[NOIP2013 提高组] 货车运输

先考虑建最大生成树，但单次查询复杂度O(n)，于是用LCA的O(nlogn)预处理一下

#include <bits/stdc++.h>
using namespace std;
#define INF 0x3f3f3f
const int maxn = 10000 + 10;
const int maxm = 50000 + 10;
int n, m, q, head[maxn], f[maxn], tot;
int fa[maxn][16], w[maxn][16], dep[maxn], rt, t;
struct Edge 
    int x, y, w;
 e[maxm];
struct node 
    int to, next, val;
 tree[maxm << 1];

inline bool cmp(Edge a, Edge b)  return a.w > b.w; 
inline void add(int x, int y, int w) 
    tree[++tot].to = y;
    tree[tot].val = w;
    tree[tot].next = head[x];
    head[x] = tot;


int find(int x) 
    if (x != f[x])
        f[x] = find(f[x]);
    return f[x];


inline void Kruskal() 
    for (int i = 1; i <= n; i++) f[i] = i;
    sort(e + 1, e + m + 1, cmp);
    int ans = 0;
    for (int i = 1; i <= m; i++) 
        int a = find(e[i].x), b = find(e[i].y);
        if (a != b) 
            f[a] = b;
            ans++;
            add(e[i].x, e[i].y, e[i].w);
            add(e[i].y, e[i].x, e[i].w);
        
    


void dfs(int x, int pre, int val) 
    dep[x] = dep[pre] + 1;
    w[x][0] = val;
    fa[x][0] = pre;
    for (int i = 1; i <= t; i++) 
        fa[x][i] = fa[fa[x][i - 1]][i - 1];
        w[x][i] = min(w[x][i - 1], w[fa[x][i - 1]][i - 1]);
    
    for (int i = head[x]; i; i = tree[i].next) 
        if (tree[i].to != pre) 
            dfs(tree[i].to, x, tree[i].val);
        
    


inline int LCA(int x, int y) 
    if (dep[x] < dep[y])
        swap(x, y);
    int ans = INF;
    for (int i = t; i >= 0; i--)
        if (dep[fa[x][i]] >= dep[y]) 
            ans = min(ans, w[x][i]);
            x = fa[x][i];
        
    if (x == y)
        return ans;
    for (int i = t; i >= 0; i--)
        if (fa[x][i] != fa[y][i]) 
            ans = min(ans, min(w[x][i], w[y][i]));
            x = fa[x][i], y = fa[y][i];
        
    int val = w[x][0];
    if (fa[x][0] != y)
        val = min(val, w[y][0]);
    return min(ans, val);


int main() 
    memset(fa, INF, sizeof(fa));
    memset(w, INF, sizeof(w));
    scanf("%d%d", &n, &m);
    t = log2(n) + 1;
    for (int i = 1; i <= m; i++) 
        scanf("%d%d%d", &e[i].x, &e[i].y, &e[i].w);
    
    Kruskal();
    for (int i = 1; i <= n; i++)
        if (i == f[i])
            dfs(i, i, INF);
    scanf("%d", &q);
    while (q--) 
        int x, y;
        scanf("%d%d", &x, &y);
        if (find(x) != find(y))
            printf("-1\\n");
        else
            printf("%d\\n", LCA(x, y));
    
    return 0;