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  • HDU How Many Trees

    How Many Trees?

    Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
    Total Submission(s): 163 Accepted Submission(s): 102
    Problem Description
    A binary search tree is a binary tree with root k such that any node v reachable from its left has label (v) <label (k) and any node w reachable from its right has label (w) > label (k). It is a search structure which can find a node with label x in O(n log n) average time, where n is the size of the tree (number of vertices).

    Given a number n, can you tell how many different binary search trees may be constructed with a set of numbers of size n such that each element of the set will be associated to the label of exactly one node in a binary search tree?
     
    Input
    The input will contain a number 1 <= i <= 100 per line representing the number of elements of the set.
     
    Output
    You have to print a line in the output for each entry with the answer to the previous question.
     
    Sample Input
    1
    2
    3
     
    Sample Output
    1
    2
    5
     
    卡特兰数
     
    import java.math.BigDecimal;
    import
    java.util.*;
    public class
    Main {
      public static
    void main(String[] args){
      BigDecimal
    []t = new BigDecimal[101];
      BigDecimal
    n,b;
      int
    k;
      Scanner
    cin = new Scanner(System.in);

      t[1] = BigDecimal.valueOf(1);
      for
    (int i = 2;i< 101;i++){

      n = BigDecimal.valueOf(i);
      b = BigDecimal.valueOf(4).multiply(n);
      b = b.subtract(BigDecimal.valueOf(2));
      n = n.add(BigDecimal.valueOf(1));
      b = b.multiply(t[i-1]);
      t[i] = b.divide(n);
      //System.out.println(t[i]);
      }
      while
    (cin.hasNext()){

      k = cin.nextInt();
      System
    .out.println(t[k]);
      }
      }
    }
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  • 原文地址:https://www.cnblogs.com/newpanderking/p/2122523.html
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