#include #include #include #include using namespace std; const int LIM = 800002; const int MAXK = 10; int N, K; vector children[LIM]; // dp[i][j] = max # of guessable nodes only considering i's subtree, // such that i's subtree size is j (with j capping out at K + 1) int dp[LIM][MAXK + 2]; // dp2[s] = max # of guessable nodes only considering current node's subtree // such that its subtree size is s (with s capping out at K + 1) int dp2[MAXK + 2]; // dp3[a][b] = max # of guessable nodes only considering current node's subtree // such that it has a children (with a capping out at K) // one of which has subtree size 2 if and only if b = 1, // and the rest of which have subtree sizes either 1 or > K int dp3[MAXK + 1][2]; void rec(int i) { // Recursively compute children's DP values. for (int c : children[i]) { rec(c); } // Use children's DP values. memset(dp2, -1, sizeof dp2); memset(dp3, -1, sizeof dp3); dp2[1] = dp3[0][0] = 0; for (int c : children[i]) { // Assume no new guessable nodes. for (int s1 = K + 1; s1 >= 1; s1--) { int d1 = dp2[s1]; if (d1 >= 0) { for (int s2 = 1; s2 <= K + 1; s2++) { int d2 = dp[c][s2]; if (d2 >= 0) { int s = min(K + 1, s1 + s2); dp2[s] = max(dp2[s], d1 + d2); } } } } // New guessable node, situation 1: // - Node i has 1 child // - That child's subtree size is > K (that child is guessable) int d1 = dp[c][K + 1]; if (d1 >= 0) { dp[i][K + 1] = max(dp[i][K + 1], d1 + 1); } // New guessable node, situation 2: // - Node i has at least K children // - One child's subtree size is exactly 2 (that child's single child is // guessable) // - Each other child's subtree size is either exactly 1, or > K for (int a1 = K; a1 >= 0; a1--) { for (int b1 : {1, 0}) { d1 = dp3[a1][b1]; if (d1 >= 0) { int a2 = min(K, a1 + 1); int d2 = max(dp[c][1], dp[c][K + 1]); if (d2 >= 0) { dp3[a2][b1] = max(dp3[a2][b1], d1 + d2); } if (!b1 && (d2 = dp[c][2]) >= 0) { dp3[a2][1] = max(dp3[a2][1], d1 + d2); } } } } } // Merge sub-DP results into main DP. for (int s1 = 1; s1 <= K + 1; s1++) { // No new guessable nodes. dp[i][s1] = max(dp[i][s1], dp2[s1]); } int d1 = dp3[K][1]; if (d1 >= 0) { // New guessable node, situation 2. dp[i][K + 1] = max(dp[i][K + 1], d1 + 1); } } int solve() { for (int i = 0; i < N; i++) { children[i].clear(); } // Input. cin >> N >> K; for (int i = 1; i < N; i++) { int p; cin >> p; children[p - 1].push_back(i); } // Tree DP. memset(dp, -1, sizeof(dp[0]) * N); rec(0); // Compute answer. int ans = 0; for (int i = 1; i <= K + 1; i++) { ans = max(ans, dp[0][i]); } return ans; } int main() { int T; cin >> T; for (int t = 1; t <= T; t++) { cout << "Case #" << t << ": " << solve() << endl; } return 0; }