Buggy python submission (verdict: Time Limit Exceeded):
import sys
sys.setrecursionlimit(5000)
def max(a,b):
    if a >= b:
        return a
    return b
def min(a,b):
    if a <= b:
        return a
    return b

def main():

    n = int(input())
    a = list(map(int, input().split()))

    dp = [[-1]*(n+1) for i in range(n)]
    def rec(i=0, j=n):
        if i == j:
            return 0
        if dp[i][j] != -1:
            return dp[i][j]
        # 太郎
        if (n - (j-i))%2==0:
            dp[i][j] = max(a[i] + rec(i+1,j), a[j-1] +rec(i,j-1))
        else:
            dp[i][j] = min(-a[i] + rec(i+1,j), -a[j-1] +rec(i,j-1))
        return dp[i][j]
    print(rec())

main()

Fixed submission:
n = int(input())
a = list(map(int, input().split()))

dp = [[0]*(n+1) for i in range(n+1)]
for l in range(1,n+1):
    for i in range(n+1-l):
        j = i+l
        if (n-l)%2 == 0:
            dp[i][j] = max(dp[i+1][j]+a[i], dp[i][j-1]+a[j-1])
        else:
            dp[i][j] = min(dp[i+1][j]-a[i], dp[i][j-1]-a[j-1])
print(dp[0][-1])

Buggy python submission (verdict: Time Limit Exceeded):
import sys
sys.setrecursionlimit(5000)
def max(a,b):
    if a >= b:
        return a
    return b
def min(a,b):
    if a <= b:
        return a
    return b

n = int(input())
a = list(map(int, input().split()))

dp = [[-1]*(n+1) for i in range(n)]

def rec(i=0, j=n):
    if i == j:
        return 0
    if dp[i][j] != -1:
        return dp[i][j]
    # 太郎
    if (n - (j-i))%2==0:
        dp[i][j] = max(a[i] + rec(i+1,j), a[j-1] +rec(i,j-1))
    else:
        dp[i][j] = min(-a[i] + rec(i+1,j), -a[j-1] +rec(i,j-1))
    return dp[i][j]
print(rec())

Fixed submission:
n = int(input())
a = list(map(int, input().split()))

dp = [[0]*(n+1) for i in range(n+1)]
for l in range(1,n+1):
    for i in range(n+1-l):
        j = i+l
        if (n-l)%2 == 0:
            dp[i][j] = max(dp[i+1][j]+a[i], dp[i][j-1]+a[j-1])
        else:
            dp[i][j] = min(dp[i+1][j]-a[i], dp[i][j-1]-a[j-1])
print(dp[0][-1])

Buggy python submission (verdict: Time Limit Exceeded):
import sys
sys.setrecursionlimit(5000)
n = int(input())
a = list(map(int, input().split()))

dp = [[-1]*(n+1) for i in range(n)]
for i in range(n):
    dp[i][i] = 0

def rec(i=0, j=n):
    if i == j:
        return 0
    if dp[i][j] != -1:
        return dp[i][j]
    # 太郎
    if (n - (j-i))%2==0:
        dp[i][j] = max(a[i] + rec(i+1,j), a[j-1] +rec(i,j-1))
    else:
        dp[i][j] = min(-a[i] + rec(i+1,j), -a[j-1] +rec(i,j-1))
    return dp[i][j]
print(rec())

Fixed submission:
n = int(input())
a = list(map(int, input().split()))

dp = [[0]*(n+1) for i in range(n+1)]
for l in range(1,n+1):
    for i in range(n+1-l):
        j = i+l
        if (n-l)%2 == 0:
            dp[i][j] = max(dp[i+1][j]+a[i], dp[i][j-1]+a[j-1])
        else:
            dp[i][j] = min(dp[i+1][j]-a[i], dp[i][j-1]-a[j-1])
print(dp[0][-1])

Buggy python submission (verdict: Time Limit Exceeded):
import sys
sys.setrecursionlimit(5000)
n = int(input())
a = list(map(int, input().split()))

dp = [[-1]*(n+1) for i in range(n)]
for i in range(n):
    dp[i][i] = 0

def rec(i=0, j=n):
    if i == j:
        return 0
    if dp[i][j] != -1:
        return dp[i][j]
    # 太郎
    if (n - (j-i))%2==0:
        dp[i][j] = max(a[i] + rec(i+1,j), a[j-1] +rec(i,j-1))
    else:
        dp[i][j] = min(-a[i] + rec(i+1,j), -a[j-1] +rec(i,j-1))
    return dp[i][j]
print(rec())

Fixed submission:
n = int(input())
a = list(map(int, input().split()))

dp = [[0]*(n+1) for i in range(n+1)]
for l in range(1,n+1):
    for i in range(n+1-l):
        j = i+l
        if (n-l)%2 == 0:
            dp[i][j] = max(dp[i+1][j]+a[i], dp[i][j-1]+a[j-1])
        else:
            dp[i][j] = min(dp[i+1][j]-a[i], dp[i][j-1]-a[j-1])
print(dp[0][-1])

Buggy python submission (verdict: Runtime Error):
n = int(input())
a = list(map(int, input().split()))

dp = [[-1]*(n+1) for i in range(n)]
for i in range(n):
    dp[i][i] = 0

def rec(i=0, j=n):
    if i == j:
        return 0
    if dp[i][j] != -1:
        return dp[i][j]
    # 太郎
    if (n - (j-i))%2==0:
        dp[i][j] = max(a[i] + rec(i+1,j), a[j-1] +rec(i,j-1))
    else:
        dp[i][j] = min(-a[i] + rec(i+1,j), -a[j-1] +rec(i,j-1))
    return dp[i][j]
print(rec())

Fixed submission:
n = int(input())
a = list(map(int, input().split()))

dp = [[0]*(n+1) for i in range(n+1)]
for l in range(1,n+1):
    for i in range(n+1-l):
        j = i+l
        if (n-l)%2 == 0:
            dp[i][j] = max(dp[i+1][j]+a[i], dp[i][j-1]+a[j-1])
        else:
            dp[i][j] = min(dp[i+1][j]-a[i], dp[i][j-1]-a[j-1])
print(dp[0][-1])