import time
start = time.perf_counter()

def con(H):
    J = []
    Q = []
    W = []
    for i in H:
        for j in range(len(i)-1):
            Cop = i[::]
            y = i[j]+i[j+1]
            del Cop[j:j+2]
            Cop.insert(j,y)
            J.append(Cop)
    for i in J:
        y =(sorted("".join(str(j) for j in i)))
        Q.append("".join(y))
    T = list(set(Q))
    for i in T:
        y = [int(j) for j in i]
        W.append(y)
    return W
    
num = 5
K = [[1 for i in range(num)]]
count = 0
for i in range(len(K[0])-2):
    K = con(K)
    print(K)
    count = count + len(K)
print(count+1)
end = time.perf_counter()
print(end-start,"second")

Here what this code does, For example, let us say num = 4. Then it creates an array of

[[1,1,1,1]]. Then it sums the consecutive numbers so our result becomes (from line 9-14)

[[2,1,1],[1,2,1],[1,1,2]] Since they are all same my code (from line 15-18) makes them just one function and returns ["112"] and then from 18-21 turns ["112"] to [[1,1,2]] and then I do this whole process again for the [[1,1,2]] and then I count the number of these arrays (from 25-29). The problem is its fast up to num = 20-30 but then it really slows down. Is there a way to increase the speed of my code or should I try a different algorithm?

Thanks.

For num = 5 the number should be 6

(1,1,1,1,1)

(2,1,1,1)

(2,2,1)

(3,2)

(3,1,1)

(4,1)

The question asks us to try this idea for 100. Or there are how many ways to write 100.

My code is correct bu just works slow.

Project Euler Problem 76 asks:

How many different ways can one hundred be written as a sum of at least two positive integers?

My code is correct but just works slowly.

import time
start = time.perf_counter()

def con(H):
    J = []
    Q = []
    W = []
    for i in H:
        for j in range(len(i)-1):
            Cop = i[::]
            y = i[j]+i[j+1]
            del Cop[j:j+2]
            Cop.insert(j,y)
            J.append(Cop)
    for i in J:
        y =(sorted("".join(str(j) for j in i)))
        Q.append("".join(y))
    T = list(set(Q))
    for i in T:
        y = [int(j) for j in i]
        W.append(y)
    return W
    
num = 5
K = [[1 for i in range(num)]]
count = 0
for i in range(len(K[0])-2):
    K = con(K)
    print(K)
    count = count + len(K)
print(count+1)
end = time.perf_counter()
print(end-start,"second")

Here what this code does. For example, let us say num = 4. Then it creates an array of

[[1,1,1,1]]. Then it sums the consecutive numbers so our result becomes (from line 9-14)

[[2,1,1],[1,2,1],[1,1,2]] Since they are all same my code (from line 15-18) makes them just one function and returns ["112"] and then from 18-21 turns ["112"] to [[1,1,2]] and then I do this whole process again for the [[1,1,2]] and then I count the number of these arrays (from 25-29). The problem is its fast up to num = 20-30 but then it really slows down. Is there a way to increase the speed of my code or should I try a different algorithm?