题目链接：点击打开链接

给定多叉树的先序遍历结果，求多叉树的同构数

思路:区间dp

import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Scanner;

public class Main {
	int min(int a,int b){return a>b?b:a;}
	int max(int a,int b){return a>b?a:b;}
	long min(long a,long b){return a>b?b:a;}
	long max(long a,long b){return a>b?a:b;}
	int abs(int x){return x>0?x:-x;}
	static long mod = 1000 * 1000 * 1000;
	static int N = 1005;
	String s;
	long[][] dp = new long[N][N];
	long dfs(int l, int r){
		if(dp[l][r]!=-1)return dp[l][r];
		if(l == r)return dp[l][r] = 1;
		if(s.charAt(l)!=s.charAt(r))return dp[l][r] = 0;
		dp[l][r] = 0;
		for(int i = l+2; i <= r; i++)
			if(s.charAt(i) == s.charAt(l))
				dp[l][r] += dfs(l+1, i-1)*dfs(i,r)%mod;	
		dp[l][r] %= mod;
		return dp[l][r];
	}
	void work() {	
		while(cin.hasNext()){
			s = cin.next();
			for(int i = 0; i <= s.length(); i++)
				for(int j = i; j <= s.length(); j++)
					dp[i][j] = -1;
			out.println(dfs(0, s.length()-1));
		}
	}

	Main() {
		cin = new Scanner(System.in);
		out = new PrintWriter(System.out);
	}

	public static void main(String[] args) {
		Main e = new Main();
		e.work();
		out.close();
	}

	public Scanner cin;
	public static PrintWriter out;
}

UVALive 3516 Exploring Pyramids 区间dp+计数原理