Problem: We have N dice arranged in a line from left to right. The i-th die from the left shows p_i numbers from 1 to p_i with equal probability when thrown.  We will choose K adjacent dice, throw each of them independently, and compute the sum of the numbers shown. Find the maximum possible value of the expected value of this sum.

Submission attempts (in order):
import bisect,collections,copy,heapq,itertools,math,numpy,string,scipy
import sys
sys.setrecursionlimit(10**7)

def S(): return sys.stdin.readline().rstrip()
def I(): return int(sys.stdin.readline().rstrip())
def LI(): return list(map(int,sys.stdin.readline().rstrip().split()))
def LS(): return list(sys.stdin.readline().rstrip().split())


def main():
    N,K = LI()
    P = LI()
    
    
    
    print((numpy.max(scipy.convolve(P,numpy.ones(K,dtype='float'), mode='valid')/scipy.convolve(numpy.ones(len(P)),numpy.ones(K),mode='valid'))+1)*(K/2))
    
main()



import bisect,collections,copy,heapq,itertools,math,numpy,string,scipy
import sys
sys.setrecursionlimit(10**7)

def S(): return sys.stdin.readline().rstrip()
def I(): return int(sys.stdin.readline().rstrip())
def LI(): return list(map(int,sys.stdin.readline().rstrip().split()))
def LS(): return list(sys.stdin.readline().rstrip().split())


def main():
    N,K = LI()
    P = LI()
    Pe = [(v+1)/2 for v in P]
    P_ms = numpy.cumsum(Pe)
    ans = 0
    for i in range(K,N):
        ans = max(ans,P_ms[i]-P_ms[i-K])
    print(ans)
main()



import bisect,collections,copy,heapq,itertools,math,numpy,string
import sys
sys.setrecursionlimit(10**7)

def S(): return sys.stdin.readline().rstrip()
def I(): return int(sys.stdin.readline().rstrip())
def LI(): return list(map(int,sys.stdin.readline().rstrip().split()))
def LS(): return list(sys.stdin.readline().rstrip().split())


def main():
    N,K = LI()
    P = LI()
    
    
    
    print((numpy.max(numpy.convolve(P,numpy.ones(K)/K,mode="valid"))+1)*(K/2))

main()



import bisect,collections,copy,heapq,itertools,math,numpy,string
import sys
sys.setrecursionlimit(10**7)

def S(): return sys.stdin.readline().rstrip()
def I(): return int(sys.stdin.readline().rstrip())
def LI(): return list(map(int,sys.stdin.readline().rstrip().split()))
def LS(): return list(sys.stdin.readline().rstrip().split())


def main():
    N,K = LI()
    P = LI()
    Pk_max_idx = numpy.argmax([sum(P[i:i+K]) for i in range(len(P))])
    print((sum(P[Pk_max_idx:Pk_max_idx+K])+K)/2)

main()



import bisect,collections,copy,heapq,itertools,math,numpy,string
import sys
sys.setrecursionlimit(10**7)

def S(): return sys.stdin.readline().rstrip()
def I(): return int(sys.stdin.readline().rstrip())
def LI(): return list(map(int,sys.stdin.readline().rstrip().split()))
def LS(): return list(sys.stdin.readline().rstrip().split())


def main():
    N,K = LI()
    P = LI()
    Pk_max_idx = numpy.argmax(numpy.convolve(P,numpy.ones(K)/K,mode="valid"))
    print((sum(P[Pk_max_idx:Pk_max_idx+K])+K)/2)

main()



import bisect,collections,copy,heapq,itertools,math,numpy,string,scipy
import sys
sys.setrecursionlimit(10**7)

def S(): return sys.stdin.readline().rstrip()
def I(): return int(sys.stdin.readline().rstrip())
def LI(): return list(map(int,sys.stdin.readline().rstrip().split()))
def LS(): return list(sys.stdin.readline().rstrip().split())


def main():
    N,K = LI()
    P = LI()
    Pe = [(v+1)/2 for v in P]
    P_ms = numpy.cumsum(Pe)
    ans = 0
    for i in range(K,N):
        ans = max(ans,P_ms[i]-P_ms[i-K])
    print("{:f}".format(ans))
main()



import bisect,collections,copy,heapq,itertools,math,numpy,string,scipy
import sys
sys.setrecursionlimit(10**7)

def S(): return sys.stdin.readline().rstrip()
def I(): return int(sys.stdin.readline().rstrip())
def LI(): return list(map(int,sys.stdin.readline().rstrip().split()))
def LS(): return list(sys.stdin.readline().rstrip().split())


def main():
    N,K = LI()
    P = LI()
    Pe = [(v+1)/2 for v in P]
    P_ms = numpy.cumsum(Pe)
    if K==N:print("{:.12f}".format(sum(Pe)));exit(0)
    ans = 0
    for i in range(K,N):
        ans = max(ans,P_ms[i]-P_ms[i-K])
    print("{:.12f}".format(ans))
main()



Verdicts: Time Limit Exceeded

Wrong Answer

Time Limit Exceeded

Time Limit Exceeded

Time Limit Exceeded

Wrong Answer

Accepted