大概题意:每个非叶子节点有一个标记(max or min)表示取子节点的最大值或最小值,假设有x个叶子,我们给叶子节点分配1-x的值,求根节点最大值为多少。
http://codeforces.com/contest/1153/problem/D
做法:
dp[i]表示节点i可以取到的最大值,我们用1表示可以取到最大值,2表示可以取到次大值
j是i的子节点
假设i是max,dp[i] = max(dp[j]
i是min, dp[i] = sigma dp[j], 比如两个节点都可以取到最大值,那么无论怎么分配再取最小值,应该就是次大值.一次类推,如果三个子节点,那么结果取到的第三大的值.
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;
/**
* Created by dezhonger on 2019/4/14
*/
public class D {
public static void main(String[] args) {
InputStream inputStream = System.in;
OutputStream outputStream = System.out;
InputReader in = new InputReader(inputStream);
PrintWriter out = new PrintWriter(outputStream);
Task solver = new Task();
solver.solve(1, in, out);
out.close();
}
static class Task {
private int n;
private int[] m;
private int[] pa;
private List<Integer>[] nodes;
//dp[i]表示该结点可以取到的最大值,1表示最大值,2次大值
private int[] dp;
public void solve(int testNumber, InputReader in, PrintWriter out) {
n = in.nextInt();
m = new int[n + 1];
pa = new int[n + 1];
dp = new int[n + 1];
for (int i = 1; i <= n; i++) m[i] = in.nextInt();
nodes = new List[n + 1];
for (int i = 1; i <= n; i++) nodes[i] = new ArrayList<>();
for (int i = 2; i <= n; i++) {
pa[i] = in.nextInt();
nodes[pa[i]].add(i);
}
int leafNumber = 0;
for (int i = 1; i <= n; i++) {
if (nodes[i].size() == 0) leafNumber++;
}
dfs(1);
System.out.println(leafNumber + 1 - dp[1]);
}
private void dfs(int nodeNumber) {
//叶子节点
if (nodes[nodeNumber].size() == 0) {
//1表示最大值
dp[nodeNumber] = 1;
return;
}
//1:max 0:min
for (int v : nodes[nodeNumber]) {
dfs(v);
}
if (m[nodeNumber] == 1) {
dp[nodeNumber] = Integer.MAX_VALUE;
for (int v : nodes[nodeNumber]) {
//小的表示最大值
dp[nodeNumber] = Math.min(dp[nodeNumber], dp[v]);
}
} else {
dp[nodeNumber] = 0;
for (int v : nodes[nodeNumber]) {
dp[nodeNumber] += dp[v];
}
}
}
}
static class InputReader {
public BufferedReader reader;
public StringTokenizer tokenizer;
public InputReader(InputStream stream) {
reader = new BufferedReader(new InputStreamReader(stream), 32768);
tokenizer = null;
}
public String next() {
while (tokenizer == null || !tokenizer.hasMoreTokens()) {
try {
tokenizer = new StringTokenizer(reader.readLine());
} catch (IOException e) {
throw new RuntimeException(e);
}
}
return tokenizer.nextToken();
}
public int nextInt() {
return Integer.parseInt(next());
}
public long nextLong() {
return Long.parseLong(next());
}
}
}