struct Scanner { private var elements = [String]() private var index = 0 mutating func peek() -> String { while elements.count == index { elements = readLine()!.split(separator: " ").map(String.init) index = 0 } return elements[index] } mutating func next() -> String { defer { index += 1 } return peek() } mutating func nextInt() -> Int { return Int(next())! } mutating func nextInts(_ n: Int) -> [Int] { return (0 ..< n).map { _ in nextInt() } } mutating func nextDouble() -> Double { return Double(next())! } } struct Array2D { let n1: Int let n2: Int private var elements: [Element] init(repeating: Element, _ n1: Int, _ n2: Int) { self.n1 = n1 self.n2 = n2 self.elements = [Element](repeating: repeating, count: n1 * n2) } subscript(i: Int, j: Int) -> Element { get { elements[i * n2 + j] } set { elements[i * n2 + j] = newValue } } } var scanner = Scanner() let N = scanner.nextInt() let Q = scanner.nextInt() let C = scanner.nextInt() var tree = [[(Int, Int)]](repeating: [], count: N) for _ in 0 ..< N - 1 { let u = scanner.nextInt() - 1 let v = scanner.nextInt() - 1 let l = scanner.nextInt() tree[u].append((v, l)) tree[v].append((u, l)) } var distance = Array2D(repeating: 0, N, N) func dfs(u: Int, parent: Int?, root: Int) { for (v, w) in tree[u] where v != parent { distance[root, v] = distance[root, u] + w dfs(u: v, parent: u, root: root) } } for i in 0 ..< N { dfs(u: i, parent: nil, root: i) } let X = scanner.nextInts(Q).map { $0 - 1 } let inf = Int.max / 2 var dp = Array2D(repeating: inf, Q, N) dp[0, X[0]] = 0 extension Array where Element == Int { func prefixMinimum(initialValue: Int) -> [Element] { var result = [initialValue] for element in self { result.append(Swift.min(result.last!, element)) } return result } func suffixMinimum(initialValue: Int) -> [Element] { reversed().prefixMinimum(initialValue: initialValue).reversed() } } for i in 0 ..< Q - 1 { var dp2 = [Int](repeating: inf, count: N) func dfs(_ u: Int, _ parent: Int?) { dp2[u] = dp[i, u] for (v, w) in tree[u] where v != parent { dfs(v, u) dp2[u] = min(dp2[u], dp2[v] + w) } } func dfs2(_ u: Int, _ parent: Int?) { let prefix = tree[u].map { (v, w) in dp2[v] + w }.prefixMinimum(initialValue: dp[i, u]) let suffix = tree[u].map { (v, w) in dp2[v] + w }.suffixMinimum(initialValue: dp[i, u]) dp[i + 1, u] = min(dp[i + 1, u], prefix.last! + C + distance[u, X[i + 1]]) for (i, (v, _)) in tree[u].enumerated() where v != parent { dp2[u] = min(prefix[i], suffix[i + 1]) dfs2(v, u) } } dfs(0, nil) dfs2(0, nil) for j in 0 ..< N where dp[i, j] != inf { dp[i + 1, j] = min(dp[i + 1, j], dp[i, j] + distance[X[i], X[i + 1]]) // for k in 0 ..< N { // dp[i + 1, k] = min(dp[i + 1, k], dp[i, j] + C + distance[j, k] + distance[k, X[i + 1]]) // dp[i + 1, k] = min(dp[i + 1, k], dp[i, j] + distance[X[i], k] + distance[k, X[i + 1]]) // } } let m = (0 ..< N).map { dp[i, $0] }.min()! for j in 0 ..< N { dp[i + 1, j] = min(dp[i + 1, j], m + distance[X[i], j] + distance[j, X[i + 1]]) } } print((0 ..< N).map { dp[Q - 1, $0] }.min()!)