Voudy

Centroid Decomposition (min edge on path)

Apr 6th, 2017
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  1. import std.stdio;
  2. import std.algorithm;
  3. import std.typecons;
  4. import std.math;
  5.  
  6. alias pair = Tuple!(int, "num", int, "cost");
  7.  
  8. pair[][] g;
  9. int[] level, parent;
  10. int[][] dp;
  11. int n, m;
  12.  
  13. int dfs(int u, int size, ref int center, int prev = -1){
  14.     int sum = 1;
  15.     foreach(v; g[u])
  16.         if (v.num != prev && level[v.num] == -1)
  17.             sum += dfs(v.num, size, center, u);
  18.     if (center == -1 && (2 * sum >= size || prev == -1)) center = u;
  19.     return sum;
  20. }
  21.  
  22. void calc(int u, int depth, int dist = int.max, int prev = -1){
  23.     dp[depth][u] = dist;
  24.     foreach(v; g[u])
  25.         if (v.num != prev && level[v.num] == -1)
  26.             calc(v.num, depth, min(dist, v.cost), u);
  27. }
  28.  
  29. void build(int u, int size, int depth, int prev = -1){
  30.     int center = -1;
  31.     dfs(u, size, center);
  32.     level[center] = depth;
  33.     parent[center] = prev;
  34.     calc(center, depth);
  35.     foreach(v; g[center])
  36.         if (level[v.num] == -1)
  37.             build(v.num, size / 2, depth + 1, center);
  38. }
  39.  
  40. int get_center(int u, int v){
  41.     while (level[u] > level[v]) u = parent[u];
  42.     while (level[v] > level[u]) v = parent[v];
  43.     while (u != v) u = parent[u], v = parent[v];
  44.     return u;
  45. }
  46.  
  47. int ans(int u, int v){
  48.     int ls = get_center(u, v);
  49.     return min(dp[level[ls]][u], dp[level[ls]][v]);
  50. }
  51.  
  52. void main(){
  53.     readf("%s\n", &n);
  54.     g = new pair[][n];
  55.     dp = new int[][](2 + cast(int)log2(n), n);
  56.     level = new int[n + 1];
  57.     parent = new int[n];
  58.     level[] -= 1;
  59.     foreach(i; 1..n){
  60.         int u, w;
  61.         readf("%s %s\n", &u, &w);
  62.         --u;
  63.         g[u] ~= pair(i, w);
  64.         g[i] ~= pair(u, w);
  65.     }
  66.     build(0, n, 0);
  67.     readf("%s\n", &m);
  68.     foreach(i; 0..m){
  69.         int u, v;
  70.         readf("%s %s\n", &u, &v);
  71.         writeln(ans(u - 1, v - 1));
  72.     }
  73. }
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