“N -й каталонский номер” Ответ

N -й каталонский номер

Recursion :

def findCatalan(n):
    def recur(n):
        if n == 0 or n == 1:
            return 1
        res = 0
        for i in range(n):
            res += recur(i) * recur(n-i-1)
        return res
    return recur(n)

Top down :

def findCatalan(n): 
    def top_down(n,dp):
        if dp[n] != -1:
            return dp[n]
        res = 0
        for i in range(n):
            res += top_down(i,dp) * top_down(n-i-1,dp)
        dp[n] = res
        return dp[n]
    
    dp = [-1] * (n+1)
    dp[0] = 1
    dp[1] = 1
    return top_down(n,dp)

Bottom Up:

def findCatalan(n): 
    def bottom_up(n,dp):
        for i in range(2,n+1):
            for j in range(i):
                dp[i]  += dp[j] * dp[i-j-1]
    
    dp = [0] * (n+1)
    dp[0] = 1
    dp[1] = 1
    bottom_up(n,dp) # Calling function
    return dp[n]