Card game

def solve(left, right, x, r):

    if (left, right) in r:
        return r[(left, right)]
    
    if right - left < 3:
        return 0
    elif right - left == 3:
        return x[left+1]
    else:
        output = 0
        
        for i in range(left, right-2):
            a, b = left, i
            val = x[i+1]
            c, d = i+3, right
            output = max(output, solve(a, b, x, r) + val + solve(c, d, x, r))

        r[(left, right)] = output
        return output

def solve2(left, right, x, r):

    if (left, right) in r:
        return r[(left, right)]
    
    if right - left < 3:
        return 0
    elif right - left == 3:
        return x[left+1]
    elif right - left == 4:
        return max(x[left+1], x[left+2])
    else:
        output = max(
            x[left+1] + solve2(left+3, right, x, r),
            x[left+2] + solve2(left+4, right, x, r),
            x[left+3] + solve2(left+5, right, x, r)
        )
        r[(left, right)] = output
        return output

def iterative(x):

    n = len(x)
    r = [0] * (n+1)
    r[3] = x[-2]
    r[4] = max(x[-3], x[-2])

    for i in range(5, n+1):
        r[i] = max(x[n-i+1] + r[i-3], x[n-i+2] + r[i-4], x[n-i+3] + r[i-5])

    return r[n]

# int(input(""))
# print(iterative([int(e) for e in input("").split(" ")]))

from random import randint

N = 5*10**2
X = [ randint(1, 10**3) for _ in range(N) ]

print(solve(0, N, X, {}))
print(solve2(0, N, X, {}))
print(iterative(X))

Test 1

Verdict: TIME LIMIT EXCEEDED

Test 2

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Test 3

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Test 4

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Test 5

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Test 6

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Test 7

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Test 8

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Test 9

Verdict: TIME LIMIT EXCEEDED

Test 10

Verdict: TIME LIMIT EXCEEDED

Test 11

Verdict: TIME LIMIT EXCEEDED

Test 12

Verdict: TIME LIMIT EXCEEDED

Test 13

Verdict: TIME LIMIT EXCEEDED

Test 14

Verdict: TIME LIMIT EXCEEDED

Test 15

Verdict: TIME LIMIT EXCEEDED