Problem:
Score : 700 points

Problem Statement

We have a tree with N vertices. Vertex 1 is the root of the tree, and the parent of Vertex i (2 \leq i \leq N) is Vertex P_i.

To each vertex in the tree, Snuke will allocate a color, either black or white, and a non-negative integer weight.

Snuke has a favorite integer sequence, X_1, X_2, ..., X_N, so he wants to allocate colors and weights so that the following condition is satisfied for all v.

The total weight of the vertices with the same color as v among the vertices contained in the subtree whose root is v, is X_v.

Here, the subtree whose root is v is the tree consisting of Vertex v and all of its descendants.

Determine whether it is possible to allocate colors and weights in this way.

Constraints

1 \leq N \leq 1 000

1 \leq P_i \leq i - 1

0 \leq X_i \leq 5 000

Inputs

Input is given from Standard Input in the following format:

N
P_2 P_3 ... P_N
X_1 X_2 ... X_N

Outputs

If it is possible to allocate colors and weights to the vertices so that the condition is satisfied, print POSSIBLE; otherwise, print IMPOSSIBLE.

Sample Input 1

3
1 1
4 3 2

Sample Output 1

POSSIBLE

For example, the following allocation satisfies the condition:

Set the color of Vertex 1 to white and its weight to 2.

Set the color of Vertex 2 to black and its weight to 3.

Set the color of Vertex 3 to white and its weight to 2.

There are also other possible allocations.

Sample Input 2

3
1 2
1 2 3

Sample Output 2

IMPOSSIBLE

If the same color is allocated to Vertex 2 and Vertex 3, Vertex 2 cannot be allocated a non-negative weight.

If different colors are allocated to Vertex 2 and 3, no matter which color is allocated to Vertex 1, it cannot be allocated a non-negative weight.

Thus, there exists no allocation of colors and weights that satisfies the condition.

Sample Input 3

8
1 1 1 3 4 5 5
4 1 6 2 2 1 3 3

Sample Output 3

POSSIBLE

Sample Input 4

1

0

Sample Output 4

POSSIBLE

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)


import java.util.Arrays;

public class Main {
  private static void solve() {
    int n = ni();
    
    
    int[] p = na(n - 1);
    int[] x = na(n);
    int[] par = new int[n];
    par[0] = -1;
    for (int i = 0; i < n - 1; i ++) {
      par[i + 1] = p[i] - 1;
    }
    int[][] g = parentToG(par);
    
    int[] ret = dfs(0, -1, g, x);
    System.out.println(ret[0] >= 0 ? "POSSIBLE" : "IMPOSSIBLE");
  }
  
  private static int[] dfs(int now, int pre, int[][] g, int[] x) {
    int m = g[now].length + (now == 0 ? 0 : -1);
    if (m == 0) {
      return new int[] {0, x[now]};
    }

    int[] w = new int[m];
    int total = 0;
    int ptr = 0;

    int min = 0;
    for (int next : g[now]) {
      if (next != pre) {
        int[] y = dfs(next, now, g, x);
        if (y[0] < 0) {
          return y;
        }
        min += y[0];
        w[ptr ++] = y[1] - y[0];
        total += y[0] + y[1];
      }
    }
    
    int v = x[now] - min;
    if (v < 0) {
      return new int[] {-1, -1};
    }

    boolean[][] dp = new boolean[2][v + 1];
    dp[0][0] = true;
    for (int i = 0; i < m; i ++) {
      int from = i % 2;
      int to = (i + 1) % 2;
      Arrays.fill(dp[to], false);
      for (int j = 0; j <= v; j ++) {
        dp[to][j] |= dp[from][j];
        if (j + w[i] <= v)
          dp[to][j + w[i]] |= dp[from][j];
      }
    }
    int np = m % 2;
    
    for (int i = v; i >= 0; i --) {
      if (dp[np][i]) {
        int z = v - i;
        return new int[] { Math.min(z, total - i), Math.max(z,  total - i)};
      }
    }
    return new int[] {-1, -1};
  }
  
  public static int[][] parentToG(int[] par)
  {
      int n = par.length;
      int[] ct = new int[n];
      for(int i = 0;i < n;i++){
          if(par[i] >= 0){
              ct[i]++;
              ct[par[i]]++;
          }
      }
      int[][] g = new int[n][];
      for(int i = 0;i < n;i++){
          g[i] = new int[ct[i]];
      }
      for(int i = 0;i < n;i++){
          if(par[i] >= 0){
              g[par[i]][--ct[par[i]]] = i;
              g[i][--ct[i]] = par[i];
          }
      }
      return g;
  }
  


  public static void main(String[] args) {
    new Thread(null, new Runnable() {
      @Override
      public void run() {
        long start = System.currentTimeMillis();
        String debug = System.getProperty("debug");
        if (debug != null) {
          try {
            is = java.nio.file.Files.newInputStream(java.nio.file.Paths.get(debug));
          } catch (Exception e) {
            throw new RuntimeException(e);
          }
        }
        reader = new java.io.BufferedReader(new java.io.InputStreamReader(is), 32768);
        solve();
        out.flush();
        tr((System.currentTimeMillis() - start) + "ms");
      }
    }, "", 64000000).start();
  }

  private static java.io.InputStream is = System.in;
  private static java.io.PrintWriter out = new java.io.PrintWriter(System.out);
  private static java.util.StringTokenizer tokenizer = null;
  private static java.io.BufferedReader reader;

  public static String next() {
    while (tokenizer == null || !tokenizer.hasMoreTokens()) {
      try {
        tokenizer = new java.util.StringTokenizer(reader.readLine());
      } catch (Exception e) {
        throw new RuntimeException(e);
      }
    }
    return tokenizer.nextToken();
  }

  private static double nd() {
    return Double.parseDouble(next());
  }

  private static long nl() {
    return Long.parseLong(next());
  }

  private static int[] na(int n) {
    int[] a = new int[n];
    for (int i = 0; i < n; i++)
      a[i] = ni();
    return a;
  }

  private static char[] ns() {
    return next().toCharArray();
  }

  private static long[] nal(int n) {
    long[] a = new long[n];
    for (int i = 0; i < n; i++)
      a[i] = ni();
    return a;
  }

  private static int[][] ntable(int n, int m) {
    int[][] table = new int[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[i][j] = ni();
      }
    }
    return table;
  }

  private static int[][] nlist(int n, int m) {
    int[][] table = new int[m][n];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[j][i] = ni();
      }
    }
    return table;
  }

  private static int ni() {
    return Integer.parseInt(next());
  }

  private static void tr(Object... o) {
    if (is != System.in)
      System.out.println(java.util.Arrays.deepToString(o));
  }
}