Buggy python submission (verdict: Time Limit Exceeded):
def f(a,p1,p2):
    if p1>p2:
        return 0
   
    return max(a[p1]+min(f(a,p1+2,p2),f(a,p1+1,p2-1))
                      ,a[p2]+min(f(a,p1+1,p2-1),f(a,p1,p2-2)))
n=int(input())
a=list(map(int,input().split()))
s=sum(a)
first=f(a,0,n-1)
print(first-(s-first))
                             


Fixed submission:
def f(a,i,j,dp):
    if dp[i][j]==-1:
        if i>j:
            return 0

        dp[i][j]=max(a[i]+min(f(a,i+2,j,dp),f(a,i+1,j-1,dp)),
                                a[j]+min(f(a,i+1,j-1,dp),f(a,i,j-2,dp)))
    return dp[i][j]
        
n=int(input())
dp=[[-1 for i in range(n)] for j in range(n)]
a=list(map(int,input().split()))
for i in range(n):
    dp[i][i]=a[i]

for i in range(n-1):
    dp[i][i+1]=max(a[i],a[i+1])

s1=f(a,0,n-1,dp)

print(s1-sum(a)+s1)

Buggy python submission (verdict: Runtime Error):
def f(a,p1,p2):
    if p1>p2:
        return 0
   
    return max(a[p1]+min(f(a,p1+2,p2),f(a,p1+1,p2-1))
                      ,a[p2]+min(f(a,p1+1,p2-1),f(a,p1,p2-2)))
n=int(input())
a=list(map(int,input().split()))
s=sum(a)
p1=0
p2=n-1
first=f(a,n,0,p1,p2,2)
print(first-(s-first))
                             


Fixed submission:
def f(a,i,j,dp):
    if dp[i][j]==-1:
        if i>j:
            return 0

        dp[i][j]=max(a[i]+min(f(a,i+2,j,dp),f(a,i+1,j-1,dp)),
                                a[j]+min(f(a,i+1,j-1,dp),f(a,i,j-2,dp)))
    return dp[i][j]
        
n=int(input())
dp=[[-1 for i in range(n)] for j in range(n)]
a=list(map(int,input().split()))
for i in range(n):
    dp[i][i]=a[i]

for i in range(n-1):
    dp[i][i+1]=max(a[i],a[i+1])

s1=f(a,0,n-1,dp)

print(s1-sum(a)+s1)

Buggy python submission (verdict: Time Limit Exceeded):
def f(a,n,ans1,p1,p2,flag):
    if p1>p2:
        return 0
   
    return max(a[p1]+min(f(a,n,ans1,p1+2,p2,flag+1),f(a,n,ans1,p1+1,p2-1,flag+1))
                      ,a[p2]+min(f(a,n,ans1,p1+1,p2-1,flag+1),f(a,n,ans1,p1,p2-2,flag+1)))
n=int(input())
a=list(map(int,input().split()))
s=sum(a)
p1=0
p2=n-1
first=f(a,n,0,p1,p2,2)
print(first-(s-first))
                             


Fixed submission:
def f(a,i,j,dp):
    if dp[i][j]==-1:
        if i>j:
            return 0

        dp[i][j]=max(a[i]+min(f(a,i+2,j,dp),f(a,i+1,j-1,dp)),
                                a[j]+min(f(a,i+1,j-1,dp),f(a,i,j-2,dp)))
    return dp[i][j]
        
n=int(input())
dp=[[-1 for i in range(n)] for j in range(n)]
a=list(map(int,input().split()))
for i in range(n):
    dp[i][i]=a[i]

for i in range(n-1):
    dp[i][i+1]=max(a[i],a[i+1])

s1=f(a,0,n-1,dp)

print(s1-sum(a)+s1)

Buggy python submission (verdict: Runtime Error):
def f(a,n,ans1,p1,p2,flag):
    if p1>p2:
        return ans1
    if flag&1==0:
        return max(f(a,n,ans1+a[p1],p1+1,p2,flag+1),
                   f(a,n,ans1+a[p2],p1,p2-1,flag+1))
    return min(f(a,n,ans1,p1+1,p2,flag+1),f(a,n,ans1,p1,p2-1,flag+1))
n=int(input())
a=list(map(int,input().split()))
s=sum(a)
p1=0
p2=n-1
first=f(a,n,0,p1,p2,2)
print(first-(s-first))


Fixed submission:
def f(a,i,j,dp):
    if dp[i][j]==-1:
        if i>j:
            return 0

        dp[i][j]=max(a[i]+min(f(a,i+2,j,dp),f(a,i+1,j-1,dp)),
                                a[j]+min(f(a,i+1,j-1,dp),f(a,i,j-2,dp)))
    return dp[i][j]
        
n=int(input())
dp=[[-1 for i in range(n)] for j in range(n)]
a=list(map(int,input().split()))
for i in range(n):
    dp[i][i]=a[i]

for i in range(n-1):
    dp[i][i+1]=max(a[i],a[i+1])

s1=f(a,0,n-1,dp)

print(s1-sum(a)+s1)

Buggy python submission (verdict: Runtime Error):
def f(a,n,ans1,p1,p2,flag):
    if p1>p2:
        return ans1
    if flag&1==0:
        return max(f(a,n,ans1+a[p1],p1+1,p2,flag+1),
                   f(a,n,ans1+a[p2],p1,p2-1,flag+1))
    return min(f(a,n,ans1,p1+1,p2,flag+1),f(a,n,ans1,p1,p2-1,flag+1))
n=int(input())
a=list(map(int,input().split()))
s=sum(a)
p1=0
p2=n-1
first=f(a,n,0,p1,p2,2)
print(first-(s-first))


Fixed submission:
def f(a,i,j,dp):
    if dp[i][j]==-1:
        if i>j:
            return 0

        dp[i][j]=max(a[i]+min(f(a,i+2,j,dp),f(a,i+1,j-1,dp)),
                                a[j]+min(f(a,i+1,j-1,dp),f(a,i,j-2,dp)))
    return dp[i][j]
        
n=int(input())
dp=[[-1 for i in range(n)] for j in range(n)]
a=list(map(int,input().split()))
for i in range(n):
    dp[i][i]=a[i]

for i in range(n-1):
    dp[i][i+1]=max(a[i],a[i+1])

s1=f(a,0,n-1,dp)

print(s1-sum(a)+s1)