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| 1 | +using ll = long long; |
| 2 | +const int MAXN = 100000; |
| 3 | +const int LOGN = 17; |
| 4 | + |
| 5 | +class Solution { |
| 6 | +public: |
| 7 | + vector<pair<int,int>> adj[MAXN]; |
| 8 | + int up[MAXN][LOGN+1]; |
| 9 | + int depth[MAXN]; |
| 10 | + ll distRoot[MAXN]; |
| 11 | + |
| 12 | + void dfs(int cur, int parent) |
| 13 | + { |
| 14 | + up[cur][0] = parent; |
| 15 | + for(auto &[v,w]: adj[cur]) |
| 16 | + { |
| 17 | + if(v == parent) continue; |
| 18 | + depth[v] = depth[cur] + 1; |
| 19 | + distRoot[v] = distRoot[cur] + w; |
| 20 | + dfs(v, cur); |
| 21 | + } |
| 22 | + } |
| 23 | + |
| 24 | + int lca(int a, int b) |
| 25 | + { |
| 26 | + if(depth[a] < depth[b]) swap(a,b); |
| 27 | + int diff = depth[a] - depth[b]; |
| 28 | + for(int k = 0; k <= LOGN; k++){ |
| 29 | + if(diff & (1<<k)) a = up[a][k]; |
| 30 | + } |
| 31 | + if(a == b) return a; |
| 32 | + for(int k = LOGN; k >= 0; k--){ |
| 33 | + if(up[a][k] != up[b][k]){ |
| 34 | + a = up[a][k]; |
| 35 | + b = up[b][k]; |
| 36 | + } |
| 37 | + } |
| 38 | + return up[a][0]; |
| 39 | + } |
| 40 | + |
| 41 | + int stepUp(int u, int k) { |
| 42 | + for (int i=16; i>=0; i--) { |
| 43 | + if ((k>>i)&1) { |
| 44 | + u = up[u][i]; |
| 45 | + } |
| 46 | + } |
| 47 | + return u; |
| 48 | + } |
| 49 | + |
| 50 | + ll dist(int a, int b) |
| 51 | + { |
| 52 | + int c = lca(a,b); |
| 53 | + return distRoot[a] + distRoot[b] - 2*distRoot[c]; |
| 54 | + } |
| 55 | + |
| 56 | + vector<int> findMedian(int n, vector<vector<int>>& edges, vector<vector<int>>& queries) { |
| 57 | + for (int i = 0; i < n-1; i++) |
| 58 | + { |
| 59 | + int u = edges[i][0], v = edges[i][1], w = edges[i][2]; |
| 60 | + adj[u].push_back({v,w}); |
| 61 | + adj[v].push_back({u,w}); |
| 62 | + } |
| 63 | + |
| 64 | + depth[0] = 0; |
| 65 | + distRoot[0] = 0; |
| 66 | + dfs(0, 0); |
| 67 | + |
| 68 | + for(int k = 1; k <= LOGN; k++) { |
| 69 | + for(int v = 0; v < n; v++) { |
| 70 | + up[v][k] = up[up[v][k-1]][k-1]; |
| 71 | + } |
| 72 | + } |
| 73 | + |
| 74 | + vector<int>rets; |
| 75 | + for (auto& q: queries) |
| 76 | + { |
| 77 | + int u = q[0], v = q[1]; |
| 78 | + int c = lca(u,v); |
| 79 | + ll total = dist(u,c)+dist(c,v); |
| 80 | + |
| 81 | + int step1 = depth[u]-depth[c]; |
| 82 | + int step2 = depth[v]-depth[c]; |
| 83 | + |
| 84 | + int low = 0, high = step1+step2; |
| 85 | + int k; |
| 86 | + while (low < high) { |
| 87 | + int mid = low + (high-low)/2; |
| 88 | + ll d; |
| 89 | + if (mid <= step1) { |
| 90 | + k = stepUp(u, mid); |
| 91 | + d = distRoot[u] - distRoot[k]; |
| 92 | + } else { |
| 93 | + k = stepUp(v, step2 - (mid-step1)); |
| 94 | + d = total - (distRoot[v] - distRoot[k]); |
| 95 | + } |
| 96 | + if (d >= total*0.5) |
| 97 | + high = mid; |
| 98 | + else |
| 99 | + low = mid+1; |
| 100 | + } |
| 101 | + int step = low; |
| 102 | + if (step<=step1) |
| 103 | + rets.push_back(stepUp(u, step)); |
| 104 | + else |
| 105 | + rets.push_back(stepUp(v, step2-(step-step1))); |
| 106 | + } |
| 107 | + |
| 108 | + return rets; |
| 109 | + } |
| 110 | +}; |
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