Problem:


Score : 400 points

Problem Statement

Your friend gave you a dequeue D as a birthday present.

D is a horizontal cylinder that contains a row of N jewels.

The values of the jewels are V_1, V_2, ..., V_N from left to right. There may be jewels with negative values.

In the beginning, you have no jewel in your hands.

You can perform at most K operations on D, chosen from the following, at most K times (possibly zero):

Operation A: Take out the leftmost jewel contained in D and have it in your hand. You cannot do this operation when D is empty.

Operation B: Take out the rightmost jewel contained in D and have it in your hand. You cannot do this operation when D is empty.

Operation C: Choose a jewel in your hands and insert it to the left end of D. You cannot do this operation when you have no jewel in your hand.

Operation D: Choose a jewel in your hands and insert it to the right end of D. You cannot do this operation when you have no jewel in your hand.

Find the maximum possible sum of the values of jewels in your hands after the operations.

Constraints

All values in input are integers.

1 \leq N \leq 50

1 \leq K \leq 100

-10^7 \leq V_i \leq 10^7

Input

Input is given from Standard Input in the following format:

N K
V_1 V_2 ... V_N

Output

Print the maximum possible sum of the values of jewels in your hands after the operations.

Sample Input 1

6 4
-10 8 2 1 2 6

Sample Output 1

14

After the following sequence of operations, you have two jewels of values 8 and 6 in your hands for a total of 14, which is the maximum result.

Do operation A. You take out the jewel of value -10 from the left end of D.

Do operation B. You take out the jewel of value 6 from the right end of D.

Do operation A. You take out the jewel of value 8 from the left end of D.

Do operation D. You insert the jewel of value -10 to the right end of D.

Sample Input 2

6 4
-6 -100 50 -2 -5 -3

Sample Output 2

44

Sample Input 3

6 3
-6 -100 50 -2 -5 -3

Sample Output 3

0

It is optimal to do no operation.



Sample input:
6 4
-10 8 2 1 2 6


Sample output:
14

Submission status: Time Limit Exceeded

Solution code:
N,K = map(int, input().split())
V = [int(v) for v in input().split()]


def f(L, i, n):
    if i == 0 or len(L) == 0:
        return 0
    if L[n] >= 0:
        t = L[n]
        if n >= 0:
            n += 1
        else:
            n -= 1
        return t+f(L,i-1,n)
    else:
        t = L[n]
        if n >= 0:
            n += 1
        else:
            n -= 1
        if i >= 2:
            return max(f(L, i-2, n), t+f(L, i-1, n))
        else:
            return t+f(L, i-1, n)
    

V_sort = sorted(V)
s = sum(V)
ans = 0
for i in range(1, K+1):
    if i >= N:
        c = s
        j = 0
        while j < N:
            if V_sort[j] < 0:
                c -= V_sort[j]
            else:
                j = N
            j += 1
        ans = max(ans, c)
    else:
        c = 0
        for j in range(i+1):
            c = max(c, f(V, j, 0)+f(V, i-j, -1))
        ans = max(ans, c)
        
print(ans)

Submission status: Time Limit Exceeded

Solution code:
N,K = map(int, input().split())
V = [int(v) for v in input().split()]


def f(L, i, n):
    if i == 0 or len(L) == 0:
        return 0
    if L[n] >= 0:
        t = L[n]
        if n >= 0:
            n += 1
        else:
            n -= 1
        return t+f(L,i-1,n)
    else:
        t = L[n]
        if n >= 0:
            n += 1
        else:
            n -= 1
        if i >= 2:
            return max(f(L, i-2, n), t+f(L, i-1, n))
        else:
            return t+f(L, i-1, n)
    
V_sort = sorted(V)
s = sum(V)
ans = 0
for i in range(1, K+1):
    if i >= N:
        c = s
        j = 0
        while j < N:
            if V_sort[j] < 0:
                c -= V_sort[j]
            else:
                j = N
            j += 1
        ans = max(ans, c)
    else:
        c = 0
        for j in range(i+1):
            c = max(c, f(V, j, 0)+f(V, i-j, -1))
        ans = max(ans, c)
        
print(ans)

Submission status: Time Limit Exceeded

Solution code:
import sys

sys.setrecursionlimit(10 ** 8)

n, k = map(int, input().split())
d = list(map(int, input().split()))


def put_queue(dd, l, v):
    if l == k:
        return 0

    if len(dd) > 0:
        a = dd[0] + put_queue(dd[1:], l + 1, v + [dd[0]])
        b = dd[-1] + put_queue(dd[:-1], l + 1, v + [dd[-1]])
    else:
        a = 0
        b = 0
    if len(v) > 0:
        vs = sorted(v)
        minv = vs[0]
        c = -minv + put_queue([minv] + dd, l + 1, vs[1:])
        d = -minv + put_queue(dd + [minv], l + 1, vs[1:])
        return max(a, b, c, d)
    return max(a, b)


print(max(0, put_queue(d, 0, [])))

Submission status: Time Limit Exceeded

Solution code:
from collections import deque
import copy

N,K = map(int,input().split(" "))

V = deque(map(int,input().split(" ")))

def search(N,K,V,score,a,b):
    if a+b < min(N,K):
        Vb = copy.copy(V)
        scoreA = copy.copy(score)
        scoreB=copy.copy(score)
        scoreA.append(V.popleft())
        A = search(N,K,V,scoreA,a+1,b)
        scoreB.append(Vb.pop())
        B = search(N,K,Vb,scoreB,a,b+1)
    score = sorted(score)
    counter = 0
    while(counter < K-a-b):
        if len(score)== 0:
            break;
        if score[0]<0:
            score.pop(0)
            counter +=1
        else:
            break;
    ans = sum(score)
    if a+b < min(N,K):
        return max(0,ans,A,B)
    else:
        return max(0,ans)

score = []
a = 0
b= 0
ans = search(N,K,V,score,a,b)
print(ans)

Submission status: Time Limit Exceeded

Solution code:
from collections import deque
import copy

N,K = map(int,input().split(" "))

V = deque(map(int,input().split(" ")))

def search(N,K,V,score,a,b):
    if a+b < min(N,K):
        Vb = copy.copy(V)
        scoreA = copy.copy(score)
        scoreB=copy.copy(score)
        scoreA.append(V.popleft())
        A = search(N,K,V,scoreA,a+1,b)
        scoreB.append(Vb.pop())
        B = search(N,K,Vb,scoreB,a,b+1)
    score=sorted(score)
    counter = 0
    while(counter < K-a-b):
        if len(score)== 0:
            break;
        if score[0]<0:
            score.pop(0)
            counter +=1
        else:
            break;
    ans = sum(score)
    if a+b < min(N,K):
        return max(0,ans,A,B)
    else:
        return max(0,ans)

score = []
a = 0
b= 0
ans = search(N,K,V,score,a,b)
print(ans)

Submission status: Time Limit Exceeded

Solution code:
from collections import deque
import copy

N,K = map(int,input().split(" "))

V = deque(map(int,input().split(" ")))

def search(N,K,V,score,a,b):
    if a+b < min(N,K):
        Vb = copy.copy(V)
        Va = copy.copy(V)
        scoreA = copy.copy(score)
        scoreB=copy.copy(score)
        scoreA.append(Va.popleft())
        A = search(N,K,Va,scoreA,a+1,b)
        scoreB.append(Vb.pop())
        B = search(N,K,Vb,scoreB,a,b+1)
    score=sorted(score)
    counter = 0
    while(counter < K-a-b):
        if len(score)== 0:
            break;
        if score[0]<0:
            score.pop(0)
            counter +=1
        else:
            break;
    ans = sum(score)
    if a+b < min(N,K):
        return max(0,ans,A,B)
    else:
        return max(0,ans)

score = []
a = 0
b= 0
ans = search(N,K,V,score,a,b)
print(ans)

Submission status: Time Limit Exceeded

Solution code:
n, k = map(int, input().split())
vs = list(map(int, input().split()))

from collections import deque
from heapq import heappush, heappop
from itertools import product

res = 0

for comb in product([1, 2, 3, 4], repeat=k):
    dq = deque(vs)
    hq = []
    valid = True
    for i in range(k):
        s = comb[i]
        if s == 1:
            if len(dq) > 0:
                heappush(hq, dq.popleft())
            else:
                valid = False
                break
        elif s == 2:
            if len(dq) > 0:
                heappush(hq, dq.pop())
            else:
                valid = False
                break
        elif s == 3:
            if len(hq) > 0:
                dq.appendleft(heappop(hq))
            else:
                valid = False
                break
        else:
            if len(hq) > 0:
                dq.append(heappop(hq))
            else:
                valid = False
                break
    if valid:
        res = max(res, sum(hq))

print(res)

Submission status: Time Limit Exceeded

Solution code:
def main():
    import collections
    import copy
    N,K = map(int, input().split())
    V = collections.deque(map(int, input().split()))

    answer = [[0]*(K+1) for _ in range(K+1)]


    for i in range(1,K+1):
        for j in range(1,min(i+1,N+1)):
            opt = 0
            for k in range(j+1):
                tmp = copy.deepcopy(V)
                tmp2 = collections.deque()
                for _ in range(k):
                    tmp2.append(tmp.popleft())
                for _ in range(j-k):
                    tmp2.append(tmp.pop())
                tmp2 = list(tmp2)
                tmp2.sort()
                for l in range(min(i-j,j)):
                    if tmp2[l] < 0:
                        tmp2[l] = 0
                S = sum(tmp2)
                if S > opt:
                    opt = S
            answer[i][j] = opt
    print(max(max(answer)))

main()

Submission status: Time Limit Exceeded

Solution code:
import collections
import copy
N,K = map(int, input().split())
V = collections.deque(map(int, input().split()))

answer = [[0]*(K+1) for _ in range(K+1)]


for i in range(1,K+1):
    for j in range(1,min(i+1,N+1)):
        opt = 0
        for k in range(j+1):
            tmp = copy.deepcopy(V)
            tmp2 = []
            for _ in range(k):
                tmp2.append(tmp.popleft())
            for _ in range(j-k):
                tmp2.append(tmp.pop())
            tmp2.sort()
            for l in range(min(i-j,j)):
                if tmp2[l] < 0:
                    tmp2[l] = 0
            S = sum(tmp2)
            if S > opt:
                opt = S
        answer[i][j] = opt
print(max(max(answer)))

Submission status: Time Limit Exceeded

Solution code:
import heapq

n, k = map(int, input().split())
lst = list(map(int, input().split()))

def heap_push(my_lst, a):
    heapq.heappush(my_lst, a)
    return my_lst


def dfs(k, lst, my_lst):
    if k == 0:
        return max(sum(my_lst), 0)
    
    if len(my_lst) == 0:
        a = dfs(k-1, lst[1:], heap_push(my_lst[:], lst[0]))
        b = dfs(k-1, lst[:-1], heap_push(my_lst[:], lst[-1]))
        return max(a, b)
                
    if len(lst) == 0:
        return dfs(k-1, lst + heapq.nsmallest(1,my_lst), my_lst[1:])
                
    else:
        a = dfs(k-1, lst[1:], heap_push(my_lst[:], lst[0]))
        b = dfs(k-1, lst[:-1], heap_push(my_lst[:], lst[-1]))
        
        c = dfs(k-1, lst + heapq.nsmallest(1,my_lst), my_lst[1:])
        d = dfs(k-1, heapq.nsmallest(1,my_lst) + lst, my_lst[1:])
        return max(a,b,c,d)
    
my_lst = []
heapq.heapify(my_lst)
print(dfs(k, lst, []))

Submission status: Time Limit Exceeded

Solution code:
n, k = map(int, input().split())
lst = list(map(int, input().split()))

def dfs(k, lst, my_lst):
    if k == 0:
        return max(sum(my_lst), 0)
    if len(my_lst) == 0:
        a = dfs(k-1, lst[1:], my_lst + [lst[0]])
        b = dfs(k-1, lst[:-1], my_lst + [lst[-1]])
        return max(a, b)
    if len(lst) == 0:
        return dfs(k-1, lst + [min(my_lst)], sorted(my_lst)[1:])
    else:
        a = dfs(k-1, lst[1:], my_lst + [lst[0]])
        b = dfs(k-1, lst[:-1], my_lst + [lst[-1]])
        c = dfs(k-1, lst + [min(my_lst)], sorted(my_lst)[1:])
        d = dfs(k-1, [min(my_lst)] + lst, sorted(my_lst)[1:])
        return max(a,b,c,d)
    
print(dfs(k, lst, []))

Submission status: Time Limit Exceeded

Solution code:
n, k = map(int, input().split())
li = list(map(int, input().split()))
global ans
#m残り捜査回数, hand 手に持っている宝石 board :残っている宝石
ans = 0
def get(n, plus_hand, mainus_hand, board):
    global ans
    mainus_hand.sort()
    ans = max(ans, sum(plus_hand) + sum(mainus_hand[n:]))
    if n > 0 and len(board) > 0:
        if board[0] > 0:
            temp = plus_hand[:]
            temp.append(board[0])
            get(n-1, temp,  mainus_hand, board[1:])
        else:  
            temp = mainus_hand[:]
            temp.append(board[0])
            get(n-1, plus_hand,  temp, board[1:])
        if board[-1] > 0:
            temp = plus_hand[:]
            temp.append(board[-1])
            get(n-1, temp,  mainus_hand, board[:-1])
        else:  
            temp = mainus_hand[:]
            temp.append(board[-1])
            get(n-1, plus_hand,  temp, board[:-1])

get(k, [], [], li)
print(ans)

Submission status: Time Limit Exceeded

Solution code:
import sys
from collections import deque
from copy import copy

N,K = list(map(int, input().split()))
V = deque(list(map(int, input().split())))

max_value = 0

def calc_max_value(V, k, l, r):
    store = deque([])
    for i in range(l):
        if len(V)>0:
            store.append(V.popleft())
            continue
        else:
            break
    for i in range(r):
        if len(V)>0:
            store.append(V.pop())
            continue
        else:
            break
    store = deque(sorted(store))
    for i in range(k-l-r):
        if len(store)>0:
            e = store.popleft()
            if e < 0:
                continue
            else:
                store.appendleft(e)
                break
        else:
            break
    max_value = sum(store)
    return max_value

    
for k in range(K+1):
    for l in range(K+1):
        for r in range(K+1-l):
            max_value = max(max_value, calc_max_value(copy(V), k, l, r))

print(max_value)

Submission status: Time Limit Exceeded

Solution code:
import sys
from collections import deque
from copy import copy

N,K = list(map(int, input().split()))
V = deque(list(map(int, input().split())))

max_value = 0

def calc_max_value(V, k, l, r):
    store = deque([])
    for i in range(l):
        if len(V)>0:
            store.append(V.popleft())
            continue
        else:
            break
    for i in range(r):
        if len(V)>0:
            store.append(V.pop())
            continue
        else:
            break
    store = deque(sorted(store))
    max_value = sum(store)
    for i in range(k-l-r):
        if len(store)>0:
            e = store.popleft()
            if e < 0:
                max_value -= e
            else:
                break
        else:
            break
    return max_value

    
for k in range(K+1):
    for l in range(K+1):
        for r in range(K+1-l):
            max_value = max(max_value, calc_max_value(copy(V), k, l, r))

print(max_value)

Submission status: Time Limit Exceeded

Solution code:
import sys
from collections import deque
from copy import copy

N,K = list(map(int, input().split()))
V = deque(list(map(int, input().split())))

max_value = 0

def calc_max_value(V, k, l, r):
    store = []
    for i in range(l):
        if len(V)>0:
            store.append(V.popleft())
            continue
        else:
            break
    for i in range(r):
        if len(V)>0:
            store.append(V.pop())
            continue
        else:
            break
    store.sort()
    store = deque(store)
    max_value = sum(store)
    for i in range(k-l-r):
        if len(store)>0:
            e = store.popleft()
            if e < 0:
                max_value -= e
            else:
                break
        else:
            break
    return max_value

    
for k in range(K+1):
    for l in range(K+1):
        for r in range(K+1-l):
            max_value = max(max_value, calc_max_value(copy(V), k, l, r))

print(max_value)

Submission status: Time Limit Exceeded

Solution code:
import sys
from collections import deque
from copy import copy

N,K = list(map(int, input().split()))
V = deque(list(map(int, input().split())))

max_value = 0

def calc_max_value(V, k, l, r):
    store = []
    for i in range(l):
        if len(V)>0:
            store.append(V.popleft())
            continue
        else:
            break
    for i in range(r):
        if len(V)>0:
            store.append(V.pop())
            continue
        else:
            break
    store.sort()
    max_value = sum(store)
    for i in range(k-l-r):
        if len(store)>0:
            store.pop(0)
            max_value = max(max_value, sum(store))
        else:
            break
    return max_value

    
for k in range(K+1):
    for l in range(K+1):
        for r in range(K+1-l):
            max_value = max(max_value, calc_max_value(copy(V), k, l, r))

print(max_value)

Submission status: Time Limit Exceeded

Solution code:
import bisect


def do_action(Vs, Vs_in_D, rest):
    if rest == 0:  # もう操作できないとき
        return 0

    if Vs_in_D:  # Dが空ではないとき
        Vs_A = Vs[:]
        bisect.insort_left(Vs_A, Vs_in_D[0])
        patternA = do_action(Vs_A, Vs_in_D[1:], rest-1) + Vs_in_D[0]  # 操作A
        Vs_B = Vs[:]
        bisect.insort_left(Vs_B, Vs_in_D[-1])
        patternB = do_action(Vs_B, Vs_in_D[:-1], rest-1) + Vs_in_D[-1]  # 操作B
    else:
        patternA = 0  # 操作A
        patternB = 0  # 操作B

    if Vs:  # 宝石を持っていたら
        patternC = do_action(Vs[1:], [Vs[0]]+Vs_in_D, rest-1) - Vs[0]   # 操作C
        patternD = do_action(Vs[1:], Vs_in_D+[Vs[0]], rest-1) - Vs[0]  # 操作D
    else:
        patternC = 0  # 操作C
        patternD = 0  # 操作D
    return max(max(patternA, patternB), max(patternC, patternD))


N, K = map(int, input().split())
V_list = list(map(int, input().split()))

print(do_action([], V_list, K))

Submission status: Time Limit Exceeded

Solution code:
#coding:utf-8



def main():
    
    def dbg(*something):
        if DEBUG:
            print(*something)


    #正の宝石を戻すことはない
    #負の宝石を戻すのは後半
    from sys import stdin
    from math import ceil,floor
    DEBUG = False
    N,K = list(map(int,stdin.readline().split()))
    V = list(map(int,stdin.readline().split()))


    #残りk回のとき深さk以下の場所に正の宝石がない→終了
    #i回の操作で取れる石>それまでにとるi-1個の石の和
    #深さiにある石vの価値：v - (それまでにとるi-1個の石の和　except (k-i)個の負の石)
    '''
    '''




    def tansaku(left,right,rK,N,score):
        dbg(V[left:right+1],rK,N,score)

        N.sort()
        # max_v = score + sum(N[rK:])
        max_v = score
        for i in range(rK,len(N)):
            max_v += N[i]
        


        # n = []
        for i in range(left,min(rK+left, ceil((right - left +1)/2)+left)):
            
            if V[i] <= 0:
                continue


            next_rK = rK - 1 - (i - left)
            next_tmp_v = tansaku(i+1,right,  next_rK, N+V[left:i], score+V[i])
            #max_v = max(next_tmp_v , max_v)
            if max_v < next_tmp_v:
                max_v = next_tmp_v


            break

        # n = []
        for i in range(right ,max(right - ceil((right-left+1)/2)  ,right-rK)  ,-1 ):
            
            if V[i] <= 0:
                continue

            next_rK = rK - 1 - (right - i)
            next_tmp_v = tansaku(   left,   i-1  ,next_rK,N+V[i+1:right+1],score+V[i])
            #max_v = max(next_tmp_v , max_v)
            if max_v < next_tmp_v:
                max_v = next_tmp_v
            break


        return max_v

    print(tansaku(0,len(V)-1,K,[],0))





if __name__ == '__main__':
    main()

Submission status: Time Limit Exceeded

Solution code:
#coding:utf-8



def main():
    
    def dbg(*something):
        if DEBUG:
            print(*something)


    #正の宝石を戻すことはない
    #負の宝石を戻すのは後半
    from sys import stdin
    from math import ceil,floor
    DEBUG = False
    N,K = list(map(int,stdin.readline().split()))
    V = list(map(int,stdin.readline().split()))


    #残りk回のとき深さk以下の場所に正の宝石がない→終了
    #i回の操作で取れる石>それまでにとるi-1個の石の和
    #深さiにある石vの価値：v - (それまでにとるi-1個の石の和　except (k-i)個の負の石)
    '''
    '''




    def tansaku(left,right,rK,N,score):
        dbg(V[left:right+1],rK,N,score)

        N.sort()
        max_v = score + sum(N[rK:])
        


        # n = []
        for i in range(left,min(rK+left, ceil((right - left +1)/2)+left)):
            
            if V[i] <= 0:
                continue


            next_rK = rK - 1 - (i - left)
            next_tmp_v = tansaku(i+1,right,  next_rK, N+V[left:i], score+V[i])
            #max_v = max(next_tmp_v , max_v)
            if max_v < next_tmp_v:
                max_v = next_tmp_v


            break

        # n = []
        for i in range(right ,max(right - ceil((right-left+1)/2)  ,right-rK)  ,-1 ):
            
            if V[i] <= 0:
                continue

            next_rK = rK - 1 - (right - i)
            next_tmp_v = tansaku(   left,   i-1  ,next_rK,N+V[i+1:right+1],score+V[i])
            #max_v = max(next_tmp_v , max_v)
            if max_v < next_tmp_v:
                max_v = next_tmp_v
            break


        return max_v

    print(tansaku(0,len(V)-1,K,[],0))





if __name__ == '__main__':
    main()

Submission status: Time Limit Exceeded

Solution code:
#coding:utf-8



def main():
    
    def dbg(*something):
        if DEBUG:
            print(*something)


    #正の宝石を戻すことはない
    #負の宝石を戻すのは後半
    from sys import stdin
    from math import ceil,floor
    DEBUG = False
    N,K = list(map(int,stdin.readline().split()))
    V = list(map(int,stdin.readline().split()))


    #残りk回のとき深さk以下の場所に正の宝石がない→終了
    #i回の操作で取れる石>それまでにとるi-1個の石の和
    #深さiにある石vの価値：v - (それまでにとるi-1個の石の和　except (k-i)個の負の石)
    '''
    '''




    def tansaku(left,right,rK,N,score):
        dbg(V[left:right+1],rK,N,score)

        N.sort()
        max_v = score + sum(N[rK:])
        


        # n = []
        for i in range(left,min(rK+left, ceil((right - left +1)/2)+left)):
            
            if V[i] <= 0:
                #n.append(V[i])
                continue


            next_rK = rK - 1 - (i - left)
            next_tmp_v = tansaku(i+1,right,  next_rK, N+V[left:i], score+V[i])
            #next_tmp_v = tansaku(i+1,right,  next_rK, newN, score+V[i])
            max_v = max(next_tmp_v , max_v)


            break

        # n = []
        for i in range(right ,max(right - ceil((right-left+1)/2)  ,right-rK)  ,-1 ):
            
            if V[i] <= 0:
                #n.append(V[i])
                continue

            #next_V = V[:i]
            next_rK = rK - 1 - (right - i)
            #next_tmp_v = tansaku(   left,   i- left -1  ,next_rK,N+n,score+V[i])
            next_tmp_v = tansaku(   left,   i-1  ,next_rK,N+V[i+1:right+1],score+V[i])
            max_v = max(next_tmp_v , max_v)
            break


        return max_v

    print(tansaku(0,len(V)-1,K,[],0))





if __name__ == '__main__':
    main()

Submission status: Time Limit Exceeded

Solution code:
#coding:utf-8



def main():
    
    def dbg(*something):
        if DEBUG:
            print(*something)


    #正の宝石を戻すことはない
    #負の宝石を戻すのは後半
    from sys import stdin
    from math import ceil,floor
    DEBUG = False
    N,K = list(map(int,stdin.readline().split()))
    V = list(map(int,stdin.readline().split()))


    #残りk回のとき深さk以下の場所に正の宝石がない→終了
    #i回の操作で取れる石>それまでにとるi-1個の石の和
    #深さiにある石vの価値：v - (それまでにとるi-1個の石の和　except (k-i)個の負の石)
    '''
    '''




    def tansaku(left,right,rK,N,score):
        dbg(V[left:right+1],rK,N,score)

        N.sort()
        # max_v = score + sum(N[rK:])
        max_v = score
        for n in N[rK:]:
            max_v += n


        # n = []
        for i in range(left,min(rK+left, ceil((right - left +1)/2)+left)):
            
            if V[i] <= 0:
                #n.append(V[i])
                continue


            next_rK = rK - 1 - (i - left)
            next_tmp_v = tansaku(i+1,right,  next_rK, N+V[left:i], score+V[i])
            #next_tmp_v = tansaku(i+1,right,  next_rK, newN, score+V[i])
            max_v = max(next_tmp_v , max_v)


            break

        # n = []
        for i in range(right ,max(right - ceil((right-left+1)/2)  ,right-rK)  ,-1 ):
            
            if V[i] <= 0:
                #n.append(V[i])
                continue

            #next_V = V[:i]
            next_rK = rK - 1 - (right - i)
            #next_tmp_v = tansaku(   left,   i- left -1  ,next_rK,N+n,score+V[i])
            next_tmp_v = tansaku(   left,   i-1  ,next_rK,N+V[i+1:right+1],score+V[i])
            max_v = max(next_tmp_v , max_v)
            break


        return max_v

    print(tansaku(0,len(V)-1,K,[],0))





if __name__ == '__main__':
    main()

Submission status: Time Limit Exceeded

Solution code:
#coding:utf-8



def main():
    
    def dbg(*something):
        if DEBUG:
            print(*something)


    #正の宝石を戻すことはない
    #負の宝石を戻すのは後半
    from sys import stdin
    from math import ceil,floor
    DEBUG = False
    N,K = list(map(int,stdin.readline().split()))
    V = list(map(int,stdin.readline().split()))


    #残りk回のとき深さk以下の場所に正の宝石がない→終了
    #i回の操作で取れる石>それまでにとるi-1個の石の和
    #深さiにある石vの価値：v - (それまでにとるi-1個の石の和　except (k-i)個の負の石)
    '''
    '''




    def tansaku(left,right,rK,N,score):
        dbg(V[left:right+1],rK,N,score)

        N.sort()
        # max_v = score + sum(N[rK:])
        max_v = score
        for i in range(rK,len(N)):
            max_v += N[i]


        # n = []
        for i in range(left,min(rK+left, ceil((right - left +1)/2)+left)):
            
            if V[i] <= 0:
                #n.append(V[i])
                continue

            #next_V = V[i+1:left+lenV]
            next_rK = rK - 1 - (i - left)
            next_tmp_v = tansaku(i+1,right,  next_rK, N+V[left:i], score+V[i])
            max_v = max(next_tmp_v , max_v)


            break

        # n = []
        for i in range(right ,max(right - ceil((right-left+1)/2)  ,right-rK)  ,-1 ):
            
            if V[i] <= 0:
                #n.append(V[i])
                continue

            #next_V = V[:i]
            next_rK = rK - 1 - (right - i)
            #next_tmp_v = tansaku(   left,   i- left -1  ,next_rK,N+n,score+V[i])
            next_tmp_v = tansaku(   left,   i-1  ,next_rK,N+V[i+1:right+1],score+V[i])
            max_v = max(next_tmp_v , max_v)
            break


        return max_v

    print(tansaku(0,len(V)-1,K,[],0))





if __name__ == '__main__':
    main()

Submission status: Time Limit Exceeded

Solution code:
#coding:utf-8



def main():
    
    def dbg(*something):
        if DEBUG:
            print(*something)


    #正の宝石を戻すことはない
    #負の宝石を戻すのは後半
    from sys import stdin
    from math import ceil,floor
    DEBUG = False
    N,K = list(map(int,stdin.readline().split()))
    V = list(map(int,stdin.readline().split()))


    #残りk回のとき深さk以下の場所に正の宝石がない→終了
    #i回の操作で取れる石>それまでにとるi-1個の石の和
    #深さiにある石vの価値：v - (それまでにとるi-1個の石の和　except (k-i)個の負の石)
    '''
    '''




    def tansaku(left,right,rK,N,score):
        dbg(V[left:right+1],rK,N,score)

        N.sort()
        max_v = score + sum(N[rK:])


        # n = []
        for i in range(left,min(rK+left, ceil((right - left +1)/2)+left)):
            
            if V[i] <= 0:
                #n.append(V[i])
                continue

            #next_V = V[i+1:left+lenV]
            next_rK = rK - 1 - (i - left)
            next_tmp_v = tansaku(i+1,right,  next_rK, N+V[left:i], score+V[i])
            max_v = max(next_tmp_v , max_v)


            break

        # n = []
        for i in range(right ,max(right - ceil((right-left+1)/2)  ,right-rK)  ,-1 ):
            
            if V[i] <= 0:
                #n.append(V[i])
                continue

            #next_V = V[:i]
            next_rK = rK - 1 - (right - i)
            #next_tmp_v = tansaku(   left,   i- left -1  ,next_rK,N+n,score+V[i])
            next_tmp_v = tansaku(   left,   i-1  ,next_rK,N+V[i+1:right+1],score+V[i])
            max_v = max(next_tmp_v , max_v)
            break


        return max_v

    print(tansaku(0,len(V)-1,K,[],0))





if __name__ == '__main__':
    main()

Submission status: Time Limit Exceeded

Solution code:
#coding:utf-8



def main():
    
    def dbg(*something):
        if DEBUG:
            print(*something)


    #正の宝石を戻すことはない
    #負の宝石を戻すのは後半
    from sys import stdin
    from math import ceil,floor
    DEBUG = False
    N,K = list(map(int,stdin.readline().split()))
    V = list(map(int,stdin.readline().split()))


    #残りk回のとき深さk以下の場所に正の宝石がない→終了
    #i回の操作で取れる石>それまでにとるi-1個の石の和
    #深さiにある石vの価値：v - (それまでにとるi-1個の石の和　except (k-i)個の負の石)
    '''
    '''




    def tansaku(left,right,rK,N,score):
        dbg(V[left:right+1],rK,N,score)


        max_v = score + sum(sorted(N)[rK:])


        # n = []
        for i in range(left,min(rK+left, ceil((right - left +1)/2)+left)):
            
            if V[i] <= 0:
                #n.append(V[i])
                continue

            #next_V = V[i+1:left+lenV]
            next_rK = rK - 1 - (i - left)
            next_tmp_v = tansaku(i+1,right,  next_rK, N+V[left:i], score+V[i])
            max_v = max(next_tmp_v , max_v)


            break

        # n = []
        for i in range(right ,max(right - ceil((right-left+1)/2)  ,right-rK)  ,-1 ):
            
            if V[i] <= 0:
                #n.append(V[i])
                continue

            #next_V = V[:i]
            next_rK = rK - 1 - (right - i)
            #next_tmp_v = tansaku(   left,   i- left -1  ,next_rK,N+n,score+V[i])
            next_tmp_v = tansaku(   left,   i-1  ,next_rK,N+V[i+1:right+1],score+V[i])
            max_v = max(next_tmp_v , max_v)
            break


        return max_v

    print(tansaku(0,len(V)-1,K,[],0))





if __name__ == '__main__':
    main()

Submission status: Time Limit Exceeded

Solution code:
#coding:utf-8
def dbg(*something):
    if DEBUG:
        print(*something)






#正の宝石を戻すことはない
#負の宝石を戻すのは後半
from sys import stdin
from math import ceil,floor
DEBUG = False
N,K = list(map(int,stdin.readline().split()))
V = list(map(int,stdin.readline().split()))


#残りk回のとき深さk以下の場所に正の宝石がない→終了
#i回の操作で取れる石>それまでにとるi-1個の石の和
#深さiにある石vの価値：v - (それまでにとるi-1個の石の和　except (k-i)個の負の石)
'''
'''




def tansaku(left,right,rK,N,score):
    dbg(V[left:right+1],rK,N,score)


    max_v = score + sum(sorted(N)[rK:])


    # n = []
    for i in range(left,min(rK+left, ceil((right - left +1)/2)+left)):
        
        if V[i] <= 0:
            #n.append(V[i])
            continue

        #next_V = V[i+1:left+lenV]
        next_rK = rK - 1 - (i - left)
        next_tmp_v = tansaku(i+1,right,  next_rK, N+V[left:i], score+V[i])
        max_v = max(next_tmp_v , max_v)


        break

    # n = []
    for i in range(right ,max(right - ceil((right-left+1)/2)  ,right-rK)  ,-1 ):
        
        if V[i] <= 0:
            #n.append(V[i])
            continue

        #next_V = V[:i]
        next_rK = rK - 1 - (right - i)
        #next_tmp_v = tansaku(   left,   i- left -1  ,next_rK,N+n,score+V[i])
        next_tmp_v = tansaku(   left,   i-1  ,next_rK,N+V[i+1:right+1],score+V[i])
        max_v = max(next_tmp_v , max_v)
        break


    return max_v

print(tansaku(0,len(V)-1,K,[],0))