Coin change varient,Perfect Sqaures add to sum 2d dp to 1d dp

'''
Try to make 1D dp possible

This gave TLE. Since I used 2d dp in python.
Both are kind of coin change varient either add or dont add type. Whats the difference. WHy method 2 gave TLE why other didnot?
What diff between method 1 and method 2 varient.
Method 1:can only give min no of denominations
Method 2:can give min no of denominations and also tells which are the denominations that adds up to given sum value
'''
class Solution:
    def numSquares(self, n: int) -> int:
        q=[]
        for i in range(1,int(n**0.5)+1):
            if i*i<=n:
                q.append(i*i)
            else:
                break
        @cache
        def find(s):
            if s==0:return 0
            if s<0:return 0
            ans=float('inf')
            for sq in q:
                if s-sq>=0:
                    ans=min(ans,1+find(s-sq))
            return ans
        return find(n)

class Solution:
    def numSquares(self, n: int) -> int:
        q=[]
        for i in range(1,n+1):
            if i*i<=n:
                q.append(i*i)
            else:
                break
        #print(q)
        @cache
        def find(x,i):

            if x==0:
                return 0
            if x<0 or  i>=len(q) or q[i]>x :
                return float('inf')
            else:
                return min(1+find(x-q[i],i),find(x,i+1))
        return find(n,0)