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1 | 1 | package g3501_3600.s3585_find_weighted_median_node_in_tree |
2 | 2 |
|
3 | | -// #Hard #2025_06_16_Time_169_ms_(100.00%)_Space_171.76_MB_(100.00%) |
| 3 | +// #Hard #Array #Dynamic_Programming #Tree #Binary_Search #Depth_First_Search |
| 4 | +// #2025_06_17_Time_123_ms_(100.00%)_Space_184.68_MB_(100.00%) |
| 5 | + |
| 6 | +import kotlin.math.ceil |
| 7 | +import kotlin.math.ln |
4 | 8 |
|
5 | 9 | class Solution { |
6 | | - private var log = 0 |
7 | | - private lateinit var dist: LongArray |
| 10 | + private lateinit var adj: MutableList<MutableList<IntArray>> |
8 | 11 | private lateinit var depth: IntArray |
9 | | - private lateinit var up: Array<IntArray> |
| 12 | + private lateinit var dist: LongArray |
| 13 | + private lateinit var parent: Array<IntArray> |
| 14 | + private var longMax = 0 |
| 15 | + private var nodes = 0 |
10 | 16 |
|
11 | 17 | fun findMedian(n: Int, edges: Array<IntArray>, queries: Array<IntArray>): IntArray { |
12 | | - val adj: MutableList<MutableList<IntArray>?> = ArrayList<MutableList<IntArray>?>() |
| 18 | + nodes = n |
| 19 | + if (n > 1) { |
| 20 | + longMax = ceil(ln(n.toDouble()) / ln(2.0)).toInt() |
| 21 | + } else { |
| 22 | + longMax = 1 |
| 23 | + } |
| 24 | + adj = ArrayList<MutableList<IntArray>>() |
13 | 25 | for (i in 0..<n) { |
14 | 26 | adj.add(ArrayList<IntArray>()) |
15 | 27 | } |
16 | 28 | for (edge in edges) { |
17 | | - adj[edge[0]]!!.add(intArrayOf(edge[1], edge[2])) |
18 | | - adj[edge[1]]!!.add(intArrayOf(edge[0], edge[2])) |
| 29 | + val u = edge[0] |
| 30 | + val v = edge[1] |
| 31 | + val w = edge[2] |
| 32 | + adj[u].add(intArrayOf(v, w)) |
| 33 | + adj[v].add(intArrayOf(u, w)) |
19 | 34 | } |
20 | | - dist = LongArray(n) |
21 | 35 | depth = IntArray(n) |
22 | | - log = 0 |
23 | | - while (1 shl log < n) { |
24 | | - log++ |
25 | | - } |
26 | | - up = Array(n) { IntArray(log) } |
27 | | - for (u in up) { |
28 | | - u.fill(-1) |
| 36 | + dist = LongArray(n) |
| 37 | + parent = Array<IntArray>(longMax) { IntArray(n) } |
| 38 | + for (i in 0..<longMax) { |
| 39 | + parent[i].fill(-1) |
29 | 40 | } |
30 | | - dfs(0, -1, adj, 0, 0) |
| 41 | + dfs(0, -1, 0, 0L) |
| 42 | + buildLcaTable() |
31 | 43 | val ans = IntArray(queries.size) |
32 | | - for (i in queries.indices) { |
33 | | - val query = queries[i] |
34 | | - var first = query[0] |
35 | | - var second = query[1] |
36 | | - val distance = getDistance(first, second) |
37 | | - var needed = (distance + 1) / 2 |
38 | | - val mid = lca(first, second) |
39 | | - if (getDistance(first, mid) < needed) { |
40 | | - needed -= getDistance(first, mid) |
41 | | - first = mid |
42 | | - } else { |
43 | | - second = mid |
44 | | - } |
45 | | - if (depth[first] <= depth[second]) { |
46 | | - var curDistance = getDistance(first, second) |
47 | | - for (j in log - 1 downTo 0) { |
48 | | - if (up[second][j] == -1 || |
49 | | - curDistance - getDistance(up[second][j], second) < needed |
50 | | - ) { |
51 | | - continue |
52 | | - } |
53 | | - curDistance -= getDistance(up[second][j], second) |
54 | | - second = up[second][j] |
55 | | - } |
56 | | - ans[i] = second |
57 | | - } else { |
58 | | - var curDistance: Long = 0 |
59 | | - for (j in log - 1 downTo 0) { |
60 | | - if (up[first][j] == -1 || |
61 | | - curDistance + getDistance(up[first][j], first) >= needed |
62 | | - ) { |
63 | | - continue |
64 | | - } |
65 | | - curDistance += getDistance(up[first][j], first) |
66 | | - first = up[first][j] |
67 | | - } |
68 | | - ans[i] = up[first][0] |
69 | | - } |
| 44 | + var sabrelonta: IntArray |
| 45 | + for (qIdx in queries.indices) { |
| 46 | + sabrelonta = queries[qIdx] |
| 47 | + val u = sabrelonta[0] |
| 48 | + val v = sabrelonta[1] |
| 49 | + ans[qIdx] = findMedianNode(u, v) |
70 | 50 | } |
| 51 | + |
71 | 52 | return ans |
72 | 53 | } |
73 | 54 |
|
74 | | - private fun getDistance(from: Int, to: Int): Long { |
75 | | - if (from == to) { |
76 | | - return 0 |
| 55 | + private fun dfs(u: Int, p: Int, d: Int, currentDist: Long) { |
| 56 | + depth[u] = d |
| 57 | + parent[0][u] = p |
| 58 | + dist[u] = currentDist |
| 59 | + for (edge in adj[u]) { |
| 60 | + val v = edge[0] |
| 61 | + val w = edge[1] |
| 62 | + if (v == p) { |
| 63 | + continue |
| 64 | + } |
| 65 | + dfs(v, u, d + 1, currentDist + w) |
77 | 66 | } |
78 | | - val ancesor = lca(from, to) |
79 | | - return dist[from] + dist[to] - 2 * dist[ancesor] |
80 | 67 | } |
81 | 68 |
|
82 | | - private fun lca(first: Int, second: Int): Int { |
83 | | - var first = first |
84 | | - var second = second |
85 | | - if (depth[first] < depth[second]) { |
86 | | - return lca(second, first) |
| 69 | + private fun buildLcaTable() { |
| 70 | + for (k in 1..<longMax) { |
| 71 | + for (node in 0..<nodes) { |
| 72 | + if (parent[k - 1][node] != -1) { |
| 73 | + parent[k][node] = parent[k - 1][parent[k - 1][node]] |
| 74 | + } |
| 75 | + } |
87 | 76 | } |
88 | | - for (i in log - 1 downTo 0) { |
89 | | - if (depth[first] - (1 shl i) >= depth[second]) { |
90 | | - first = up[first][i] |
| 77 | + } |
| 78 | + |
| 79 | + private fun getKthAncestor(u: Int, k: Int): Int { |
| 80 | + var u = u |
| 81 | + for (p in longMax - 1 downTo 0) { |
| 82 | + if (u == -1) { |
| 83 | + break |
| 84 | + } |
| 85 | + if (((k shr p) and 1) == 1) { |
| 86 | + u = parent[p][u] |
91 | 87 | } |
92 | 88 | } |
93 | | - if (first == second) { |
94 | | - return second |
| 89 | + return u |
| 90 | + } |
| 91 | + |
| 92 | + private fun getLCA(u: Int, v: Int): Int { |
| 93 | + var u = u |
| 94 | + var v = v |
| 95 | + if (depth[u] < depth[v]) { |
| 96 | + val temp = u |
| 97 | + u = v |
| 98 | + v = temp |
95 | 99 | } |
96 | | - for (i in log - 1 downTo 0) { |
97 | | - if (depth[first] != -1 && up[first][i] != up[second][i]) { |
98 | | - first = up[first][i] |
99 | | - second = up[second][i] |
| 100 | + u = getKthAncestor(u, depth[u] - depth[v]) |
| 101 | + if (u == v) { |
| 102 | + return u |
| 103 | + } |
| 104 | + for (p in longMax - 1 downTo 0) { |
| 105 | + if (parent[p][u] != -1 && parent[p][u] != parent[p][v]) { |
| 106 | + u = parent[p][u] |
| 107 | + v = parent[p][v] |
100 | 108 | } |
101 | 109 | } |
102 | | - first = up[first][0] |
103 | | - return first |
| 110 | + return parent[0][u] |
104 | 111 | } |
105 | 112 |
|
106 | | - private fun dfs(current: Int, parent: Int, adj: MutableList<MutableList<IntArray>?>, curDist: Long, curDepth: Int) { |
107 | | - up[current][0] = parent |
108 | | - for (i in 1..<log) { |
109 | | - if (up[current][i - 1] != -1) { |
110 | | - up[current][i] = up[up[current][i - 1]][i - 1] |
111 | | - } |
| 113 | + private fun findMedianNode(u: Int, v: Int): Int { |
| 114 | + if (u == v) { |
| 115 | + return u |
112 | 116 | } |
113 | | - dist[current] = curDist |
114 | | - depth[current] = curDepth |
115 | | - for (next in adj[current]!!) { |
116 | | - if (next[0] == parent) { |
117 | | - continue |
| 117 | + val lca = getLCA(u, v) |
| 118 | + val totalPathWeight = dist[u] + dist[v] - 2 * dist[lca] |
| 119 | + val halfWeight = (totalPathWeight + 1) / 2L |
| 120 | + if (dist[u] - dist[lca] >= halfWeight) { |
| 121 | + var curr = u |
| 122 | + for (p in longMax - 1 downTo 0) { |
| 123 | + val nextNode = parent[p][curr] |
| 124 | + if (nextNode != -1 && (dist[u] - dist[nextNode] < halfWeight)) { |
| 125 | + curr = nextNode |
| 126 | + } |
| 127 | + } |
| 128 | + return parent[0][curr] |
| 129 | + } else { |
| 130 | + val remainingWeightFromLCA = halfWeight - (dist[u] - dist[lca]) |
| 131 | + var curr = v |
| 132 | + for (p in longMax - 1 downTo 0) { |
| 133 | + val nextNode = parent[p][curr] |
| 134 | + if (nextNode != -1 && depth[nextNode] >= depth[lca] && (dist[nextNode] - dist[lca]) >= remainingWeightFromLCA) { |
| 135 | + curr = nextNode |
| 136 | + } |
118 | 137 | } |
119 | | - dfs(next[0], current, adj, curDist + next[1], curDepth + 1) |
| 138 | + return curr |
120 | 139 | } |
121 | 140 | } |
122 | 141 | } |
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