Codeforces 509F Progress Monitoring 给定dfs序求树的同构数 区间dp

题目链接：点击打开链接

==说同构数有点不对。。反正就是这个意思，对于某个点的所有儿子，先访问标号小的，再访问标号大的。

dp[l][r]表示 区间[l,r] 构成一棵树的方法数。

对于一个区间[l, r] 构成一棵树，则点l一定是根，然后枚举2个区间相乘即可

dp[l][r] = dp[l+1][i] * dp[i+1][r] ( i = [l+1, r] )

当然 a[i+1] > a[l+1] ，这样才会满足题目中的暴力代码。

import java.io.PrintWriter;import java.text.DecimalFormat;import java.util.ArrayList;import java.util.Arrays;import java.util.Collections;import java.util.Comparator;import java.util.HashMap;import java.util.Iterator;import java.util.LinkedList;import java.util.Map;import java.util.PriorityQueue;import java.util.Scanner;import java.util.Stack;import java.util.TreeMap;import java.util.TreeSet;import java.util.Queue;public class Main {int n;int[] a = new int[N];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;long ans = 0;for(int i = l+1; i <= r; i++)if(i == r || a[i + 1] > a[l + 1])ans = (dfs(l+1, i) * dfs(i, r)+ans)%mod;return dp[l][r] = ans;}void work() {while(cin.hasNext()){n = cin.nextInt(); for(int i = 1; i <= n; i++)a[i] = cin.nextInt();for(int i = 1; i <= n; i++){for(int j = i; j <= n; j++)dp[i][j] = -1;}System.out.println(dfs(1, n));}}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;static int N = 505;static int mod = 1000000007 ;}