Problem:


Score : 500 points

Problem Statement

There are N children standing in a line from left to right. The activeness of the i-th child from the left is A_i.

You can rearrange these children just one time in any order you like.

When a child who originally occupies the x-th position from the left in the line moves to the y-th position from the left, that child earns A_x \times |x-y| happiness points.

Find the maximum total happiness points the children can earn.

Constraints

2 \leq N \leq 2000

1 \leq A_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the maximum total happiness points the children can earn.

Sample Input 1

4
1 3 4 2

Sample Output 1

20

If we move the 1-st child from the left to the 3-rd position from the left, the 2-nd child to the 4-th position, the 3-rd child to the 1-st position, and the 4-th child to the 2-nd position, the children earns 1 \times |1-3|+3 \times |2-4|+4 \times |3-1|+2 \times |4-2|=20 happiness points in total.

Sample Input 2

6
5 5 6 1 1 1

Sample Output 2

58

Sample Input 3

6
8 6 9 1 2 1

Sample Output 3

85



Sample input:
4
1 3 4 2


Sample output:
20

Submission status: Time Limit Exceeded

Solution code:
# -*- coding: utf-8 -*-

# 整数の入力
a = int(input())
# # スペース区切りの整数の入力
# strs = input().split()

nums = list(map(int, input().split()))

vilist = []
for i in range(a):
    vilist.append((nums[i], i))
vilist = sorted(vilist, key=lambda vi: vi[0], reverse=True)

# dp[x][y]をx人を左から活性度順に並べて、y人を右から活性度順に並べた状態のスコア最大値とする
dp = []
for i in range(a + 1):
    ls = []
    for j in range(a + 1):
        ls.append(0)
    dp.append(ls)

# dp[i][j]を考える
for k in range(a):
    for i in range(k + 2):
        j = k - i + 1
        if i == 0 and j == 0:
            continue
        if j == 0:
            dp[i][0] = dp[i-1][0] + vilist[k][0] * abs(vilist[k][1] - i + 1)
        elif i == 0:
            dp[0][j] = dp[0][j-1] + vilist[k][0] * abs(a - j - vilist[k][1])
        else:
            dp[i][j] = max(dp[i-1][j] + vilist[k][0] * abs(vilist[k][1] - i + 1),
                           dp[i][j-1] + vilist[k][0] * abs(a - j - vilist[k][1]))

print(max([max(x) for x in dp]))

Submission status: Time Limit Exceeded

Solution code:
# -*- coding: utf-8 -*-

# 整数の入力
a = int(input())
# # スペース区切りの整数の入力
# strs = input().split()

nums = list(map(int, input().split()))

vilist = []
for i in range(a):
    vilist.append((nums[i], i))
vilist = sorted(vilist, key=lambda vi: vi[0], reverse=True)

# dp[x][y]をx人を左から活性度順に並べて、y人を右から活性度順に並べた状態のスコア最大値とする
dp = []
for i in range(a + 1):
    ls = []
    for j in range(a + 1):
        ls.append(0)
    dp.append(ls)

# dp[i][j]を考える
for i in range(a+1):
    for j in range(a+1-i):
        if i == 0 and j == 0:
            continue
        # k = (i + j - 1)番目の人
        k = i + j - 1

        if j == 0:
            dp[i][0] = dp[i-1][0] + vilist[k][0] * abs(vilist[k][1] - i + 1)
        elif i == 0:
            dp[0][j] = dp[0][j-1] + vilist[k][0] * abs(a - j - vilist[k][1])
        else:
            dp[i][j] = max(dp[i-1][j] + vilist[k][0] * abs(vilist[k][1] - i + 1),
                           dp[i][j-1] + vilist[k][0] * abs(a - j - vilist[k][1]))

max_v = 0
for x in dp:
    max_x = max(x)
    if max_v < max_x:
        max_v = max_x

print(max_v)

Submission status: Time Limit Exceeded

Solution code:
# -*- coding: utf-8 -*-

# 整数の入力
a = int(input())
# スペース区切りの整数の入力
strs = input().split()

vilist = []
for i in range(a):
    vilist.append((int(strs[i]), i))
vilist = sorted(vilist, key=lambda vi: vi[0], reverse=True)

# dp[x][y]をx人を左から活性度順に並べて、y人を右から活性度順に並べた状態のスコア最大値とする
dp = []
for i in range(a + 1):
    ls = []
    for j in range(a + 1):
        ls.append(0)
    dp.append(ls)

# dp[i][j]を考える
for i in range(a+1):
    for j in range(a+1-i):
        # k = (i + j - 1)番目の人
        k = i + j - 1
        if i == 0 and j == 0:
            continue

        if j == 0 and i > 0:
            dp[i][0] = dp[i-1][0] + vilist[k][0] * abs(vilist[k][1] - i + 1)
        elif i == 0 and j > 0:
            dp[0][j] = dp[0][j-1] + vilist[k][0] * abs(a - j - vilist[k][1])
        else:
            # dp[i][j] = max(dp[i][j],
            #                dp[i-1][j] + vilist[k][0] * abs(vilist[k][1] - i + 1),
            #                dp[i][j-1] + vilist[k][0] * abs(a - j - vilist[k][1]))
            dp[i][j] = max(dp[i-1][j] + vilist[k][0] * abs(vilist[k][1] - i + 1),
                           dp[i][j-1] + vilist[k][0] * abs(a - j - vilist[k][1]))

max_v = 0
for x in dp:
    max_x = max(x)
    if max_v < max_x:
        max_v = max_x

print(max_v)

Submission status: Time Limit Exceeded

Solution code:
# -*- coding: utf-8 -*-
from collections import deque


def create_tmp_list(dq1: deque, dq2: deque):
    tmp1 = dq1.copy()
    for x in dq2:
        if tmp1[0] == x:
            tmp1.popleft()
        elif tmp1[-1] == x:
            tmp1.pop()
    return tmp1


# 整数の入力
a = int(input())
# スペース区切りの整数の入力
strs = input().split()

vilist = []
for i in range(a):
    vilist.append((int(strs[i]), i))
vilist = sorted(vilist, key=lambda vi: vi[0], reverse=True)

# # dp[x][y]をx人を左から活性度順に並べて、y人を右から活性度順に並べた状態の(スコア最大値, 移動済のindexを記述したリスト)とする
# dp = []
# for i in range(a + 1):
#     ls = []
#     for j in range(a + 1):
#         ls.append((0, []))
#     dp.append(ls)
# 
# # 0番目の人
# # dp[1][0] 左につめる
# dp[1][0] = (vilist[0][0] * abs(vilist[0][1] - 0), [vilist[0][1]])
# # dp[0][1] 右につめる
# dp[0][1] = (vilist[0][0] * abs(a - 1 - vilist[0][1]), [vilist[0][1]])
# 
# # 1番目の人
# # dp[2][0] 左につめる
# dp[1][0] = (vilist[0][0] * abs(vilist[0][1] - 0), [vilist[0][1]])
# # dp[0][1] 右につめる
# dp[0][1] = (vilist[0][0] * abs(a - 1 - vilist[0][1]), [vilist[0][1]])

# dp[x][y]をx人を左から活性度順に並べて、y人を右から活性度順に並べた状態のスコア最大値とする
dp = []
for i in range(a + 1):
    ls = []
    for j in range(a + 1):
        ls.append(0)
    dp.append(ls)

# # 0番目の人
# # dp[1][0] 左につめる
# dp[1][0] = max(dp[1][0], vilist[0][0] * abs(vilist[0][1] - 0))
# # dp[0][1] 右につめる
# dp[0][1] = max(dp[0][1], vilist[0][0] * abs(a - 1 - vilist[0][1]))
#
# # 1番目の人
# # dp[2][0] 左につめる
# dp[2][0] = max(dp[2][0], dp[1][0] + vilist[1][0] * abs(vilist[1][1] - 1))
# # dp[1][1] 左につめる or 右につめる
# dp[1][1] = max(dp[1][1],
#                dp[0][1] + vilist[1][0] * abs(vilist[1][1] - 0),
#                dp[1][0] + vilist[1][0] * abs(a - 1 - vilist[1][1]))
# # dp[0][2] 右につめる
# dp[0][2] = max(dp[0][2], dp[0][1] + vilist[1][0] * abs(a - 2 - vilist[1][1]))
#
# # 2番目の人
# # dp[3][0] 左につめる
# dp[3][0] = max(dp[3][0], dp[2][0] + vilist[2][0] * abs(vilist[2][1] - 2))
# # dp[2][1] 左につめる or 右につめる
# dp[2][1] = max(dp[2][1],
#                dp[1][1] + vilist[2][0] * abs(vilist[2][1] - 1),
#                dp[2][0] + vilist[2][0] * abs(a - 1 - vilist[2][1]))
# # dp[1][2] 左につめる or 右につめる
# dp[1][2] = max(dp[1][2],
#                dp[0][2] + vilist[2][0] * abs(vilist[2][1] - 0),
#                dp[1][1] + vilist[2][0] * abs(a - 2 - vilist[2][1]))
# # dp[0][3] 右につめる
# dp[0][3] = max(dp[0][3], dp[0][2] + vilist[2][0] * abs(a - 3 - vilist[2][1]))
#
# # 3番目の人
# # dp[4][0] 左につめる
# dp[4][0] = max(dp[4][0], dp[3][0] + vilist[3][0] * abs(vilist[3][1] - 3))
# # dp[3][1] 左につめる or 右につめる
# dp[3][1] = max(dp[3][1],
#                dp[2][1] + vilist[3][0] * abs(vilist[3][1] - 2),
#                dp[3][0] + vilist[3][0] * abs(a - 1 - vilist[3][1]))
# # dp[2][2] 左につめる or 右につめる
# dp[2][2] = max(dp[2][1],
#                dp[1][2] + vilist[3][0] * abs(vilist[3][1] - 1),
#                dp[2][1] + vilist[3][0] * abs(a - 2 - vilist[3][1]))
# # dp[1][3] 左につめる or 右につめる
# dp[1][3] = max(dp[1][2],
#                dp[0][3] + vilist[3][0] * abs(vilist[3][1] - 0),
#                dp[1][2] + vilist[3][0] * abs(a - 3 - vilist[3][1]))
# # dp[0][4] 右につめる
# dp[0][4] = max(dp[0][3], dp[0][3] + vilist[3][0] * abs(a - 4 - vilist[3][1]))
#
# print(max(dp[4][0], dp[3][1], dp[2][2], dp[1][3], dp[0][4]))

# dp[i][j]を考える
for i in range(a+1):
    for j in range(a+1-i):
        # k = (i + j - 1)番目の人
        k = i + j - 1
        if i == 0 and j == 0:
            continue

        if j == 0 and i > 0:
            dp[i][0] = max(dp[i][0], dp[i-1][0] + vilist[k][0] * abs(vilist[k][1] - i + 1))
        elif i == 0 and j > 0:
            dp[0][j] = max(dp[0][j], dp[0][j-1] + vilist[k][0] * abs(a - j - vilist[k][1]))
        else:
            dp[i][j] = max(dp[i][j],
                           dp[i-1][j] + vilist[k][0] * abs(vilist[k][1] - i + 1),
                           dp[i][j-1] + vilist[k][0] * abs(a - j - vilist[k][1]))

max_v = 0
for x in dp:
    max_x = max(x)
    if max_v < max_x:
        max_v = max_x

print(max_v)

Submission status: Time Limit Exceeded

Solution code:
# -*- coding: utf-8 -*-
from collections import deque


def create_tmp_list(dq1: deque, dq2: deque):
    tmp1 = dq1.copy()
    for x in dq2:
        if tmp1[0] == x:
            tmp1.popleft()
        elif tmp1[-1] == x:
            tmp1.pop()
    return tmp1


# 整数の入力
a = int(input())
# スペース区切りの整数の入力
strs = input().split()

# nums = []
only_nums = []
dic = {}
for i in range(a):
    v = int(strs[i])
    v_list = dic.setdefault(v, deque())
    v_list.append(i)
    only_nums.append(v)

sorted_nums = sorted(only_nums, reverse=True)
# print(sorted_nums)

# print(nums)

# res[x][y]をx人を左から活性度順に並べて、y人を右から活性度順に並べた状態の(スコア最大値, 移動済のindexを記述したリスト)とする
res = []
for i in range(a + 1):
    ls = []
    for j in range(a + 1):
        ls.append((0, deque()))
    res.append(ls)

max_num_changed = True
max_num = sorted_nums[0]
for i in range(a + 1):
    # print("i in range(a)")
    # print(i)
    # print(a)
    # print("i in range(a)")
    if i == 0:
        continue
    if i == 1:
        sorted_nums = sorted_nums[1:]
        # x,y = 0,1にした場合
        max_num_idx_min = dic[max_num][0]
        res[0][1] = (max_num * (a - 1 - max_num_idx_min), deque([max_num_idx_min]))

        # x,y = 1,0にした場合
        max_num_idx_max = dic[max_num][-1]
        res[1][0] = (max_num * max_num_idx_max, deque([max_num_idx_max]))

    else:
        target_val = sorted_nums[0]
        sorted_nums = sorted_nums[1:]
        if target_val == max_num:
            max_num_changed = False
        else:
            max_num_changed = True
            max_num = target_val

        # print(sorted_nums)

        score_right = -1
        # x,y = i-j,j(0 ≤ j ≤ i)にした場合を考える
        # i - 1のresについてそれぞれ次の状態を考えていく
        # res[i-1][0], res[i-2][1], res[i-3][2], ... , res[i-1-j][j], ... , res[0][i-1]
        ls_j = []
        for j in range(i):
            if max_num_changed:
                already_used_max_num_index = deque()
                max_num_idx_max = dic[max_num][-1]
                max_num_idx_min = dic[max_num][0]
            else:
                already_used_max_num_index = res[i-j-1][j][1]
                tmp_list = create_tmp_list(dic[max_num], already_used_max_num_index)
                max_num_idx_max = tmp_list[-1]
                max_num_idx_min = tmp_list[0]

            # from i-j-1,j to i-j,j (最大活性のものを左に移動)
            score_left = max_num * abs(max_num_idx_max - (i - j - 1)) + res[i - j - 1][j][0]

            # 左端はその値をそのまま利用。右側に移動したものよりも大きい場合はleftの値を設定
            if j == 0 or score_right < score_left:
                res_list = already_used_max_num_index.copy()
                res_list.append(max_num_idx_max)
                res[i - j][j] = (score_left, res_list)

            # from i-j-1,j to i-j-1,j+1 (最大活性のものを右に移動)
            score_right = max_num * abs(a - 1 - max_num_idx_min - j) + res[i - j - 1][j][0]
            # 右側に移動の場合は一旦その値を暫定値として設定してしまう（必要があれば次のループで上書きされるので問題ない）
            # res_list = already_used_max_num_index.copy()
            res_list = already_used_max_num_index
            res_list.append(max_num_idx_min)
            res[i - j - 1][j + 1] = (score_right, res_list)

    if i == a:
        max_v = 0
        for j in range(a + 1):
            v = res[j][i - j][0]
            if max_v < v:
                max_v = v
        # print(result)
        print(max_v)

Submission status: Time Limit Exceeded

Solution code:
# -*- coding: utf-8 -*-


# 整数の入力
a = int(input())
# スペース区切りの整数の入力
strs = input().split()

# nums = []
only_nums = []
dic = {}
for i in range(a):
    v = int(strs[i])
    v_list = dic.setdefault(v, set([]))
    v_list.add(i)
    only_nums.append(v)

sorted_nums = sorted(only_nums, reverse=True)
# print(sorted_nums)

# print(nums)

# res[x][y]をx人を左から活性度順に並べて、y人を右から活性度順に並べた状態の(スコア最大値, 移動済のindexを記述したリスト)とする
res = []
for i in range(a + 1):
    ls = []
    for j in range(a + 1):
        ls.append((0, set([])))
    res.append(ls)

max_num_changed = True
max_num = sorted_nums[0]
for i in range(a + 1):
    # print("i in range(a)")
    # print(i)
    # print(a)
    # print("i in range(a)")
    if i == 0:
        continue
    if i == 1:
        sorted_nums = sorted_nums[1:]
        # x,y = 0,1にした場合
        max_num_idx_min = min(dic[max_num])
        res[0][1] = (max_num * (a - 1 - max_num_idx_min), {max_num_idx_min})

        # x,y = 1,0にした場合
        max_num_idx_max = max(dic[max_num])
        res[1][0] = (max_num * max_num_idx_max, {max_num_idx_max})

    else:
        target_val = sorted_nums[0]
        sorted_nums = sorted_nums[1:]
        if target_val == max_num:
            max_num_changed = False
        else:
            max_num_changed = True
            max_num = target_val

        # print(sorted_nums)

        score_right = -1
        # x,y = i-j,j(0 ≤ j ≤ i)にした場合を考える
        # i - 1のresについてそれぞれ次の状態を考えていく
        # res[i-1][0], res[i-2][1], res[i-3][2], ... , res[i-1-j][j], ... , res[0][i-1]
        ls_j = []
        for j in range(i):
            if max_num_changed:
                already_used_max_num_index = set([])
                max_num_idx_max = max(dic[max_num])
                max_num_idx_min = min(dic[max_num])
            else:
                already_used_max_num_index = res[i-j-1][j][1]
                tmp_list = dic[max_num] - already_used_max_num_index
                max_num_idx_max = max(tmp_list)
                max_num_idx_min = min(tmp_list)

            # from i-j-1,j to i-j,j (最大活性のものを左に移動)
            score_left = max_num * abs(max_num_idx_max - (i - j - 1)) + res[i - j - 1][j][0]

            # 左端はその値をそのまま利用。右側に移動したものよりも大きい場合はleftの値を設定
            if j == 0 or score_right < score_left:
                res_list = already_used_max_num_index.copy()
                res_list.add(max_num_idx_max)
                res[i - j][j] = (score_left, res_list)

            # from i-j-1,j to i-j-1,j+1 (最大活性のものを右に移動)
            score_right = max_num * abs(a - 1 - max_num_idx_min - j) + res[i - j - 1][j][0]
            # 右側に移動の場合は一旦その値を暫定値として設定してしまう（必要があれば次のループで上書きされるので問題ない）
            # res_list = already_used_max_num_index.copy()
            res_list = already_used_max_num_index
            res_list.add(max_num_idx_min)
            res[i - j - 1][j + 1] = (score_right, res_list)

    if i == a:
        result = []
        for j in range(a + 1):
            result.append(res[j][i - j][0])
        # print(result)
        print(max(result))

Submission status: Time Limit Exceeded

Solution code:
# -*- coding: utf-8 -*-


# 整数の入力
a = int(input())
# スペース区切りの整数の入力
strs = input().split()

# nums = []
only_nums = []
dic = {}
for i in range(a):
    v = int(strs[i])
    v_list = dic.setdefault(v, set([]))
    v_list.add(i)
    only_nums.append(v)

sorted_nums = sorted(only_nums, reverse=True)
# print(sorted_nums)

# print(nums)

# res[x][y]をx人を左から活性度順に並べて、y人を右から活性度順に並べた状態の(スコア最大値, 移動済のindexを記述したリスト)とする
res = []
for i in range(a + 1):
    ls = []
    for j in range(a + 1):
        ls.append((0, set([])))
    res.append(ls)

max_num_changed = True
max_num = sorted_nums[0]
for i in range(a + 1):
    # print("i in range(a)")
    # print(i)
    # print(a)
    # print("i in range(a)")
    if i == 0:
        continue
    if i == 1:
        sorted_nums = sorted_nums[1:]
        # x,y = 0,1にした場合
        max_num_idx_min = min(dic[max_num])
        res[0][1] = (max_num * (a - 1 - max_num_idx_min), {max_num_idx_min})

        # x,y = 1,0にした場合
        max_num_idx_max = max(dic[max_num])
        res[1][0] = (max_num * max_num_idx_max, {max_num_idx_max})

    else:
        target_val = sorted_nums[0]
        sorted_nums = sorted_nums[1:]
        if target_val == max_num:
            max_num_changed = False
        else:
            max_num_changed = True
            max_num = target_val

        # print(sorted_nums)

        score_right = -1
        # x,y = i-j,j(0 ≤ j ≤ i)にした場合を考える
        # i - 1のresについてそれぞれ次の状態を考えていく
        # res[i-1][0], res[i-2][1], res[i-3][2], ... , res[i-1-j][j], ... , res[0][i-1]
        ls_j = []
        for j in range(i):
            if max_num_changed:
                already_used_max_num_index = set([])
                max_num_idx_max = max(dic[max_num])
                max_num_idx_min = min(dic[max_num])
            else:
                already_used_max_num_index = res[i-j-1][j][1]
                tmp_list = dic[max_num] - already_used_max_num_index
                max_num_idx_max = max(tmp_list)
                max_num_idx_min = min(tmp_list)

            # from i-j-1,j to i-j,j (最大活性のものを左に移動)
            score_left = max_num * abs(max_num_idx_max - (i - j - 1)) + res[i - j - 1][j][0]

            # 左端はその値をそのまま利用。右側に移動したものよりも大きい場合はleftの値を設定
            if j == 0 or score_right < score_left:
                res_list = already_used_max_num_index.copy()
                res_list.add(max_num_idx_max)
                res[i - j][j] = (score_left, res_list)

            # from i-j-1,j to i-j-1,j+1 (最大活性のものを右に移動)
            score_right = max_num * abs(a - 1 - max_num_idx_min - j) + res[i - j - 1][j][0]
            # 右側に移動の場合は一旦その値を暫定値として設定してしまう（必要があれば次のループで上書きされるので問題ない）
            res_list = already_used_max_num_index.copy()
            res_list.add(max_num_idx_min)
            res[i - j - 1][j + 1] = (score_right, res_list)

    if i == a:
        result = []
        for j in range(a + 1):
            result.append(res[j][i - j][0])
        # print(result)
        print(max(result))

Submission status: Time Limit Exceeded

Solution code:
# -*- coding: utf-8 -*-


# 整数の入力
a = int(input())
# スペース区切りの整数の入力
strs = input().split()

# nums = []
only_nums = []
dic = {}
for i in range(a):
    v = int(strs[i])
    v_list = dic.setdefault(v, [])
    v_list.append(i)
    only_nums.append(v)

sorted_nums = sorted(only_nums, reverse=True)
# print(sorted_nums)

# print(nums)

# res[x][y]をx人を左から活性度順に並べて、y人を右から活性度順に並べた状態の(スコア最大値, 移動済のindexを記述したリスト)とする
res = []
for i in range(a + 1):
    ls = []
    for j in range(a + 1):
        ls.append((0, []))
    res.append(ls)

max_num_changed = True
max_num = sorted_nums[0]
for i in range(a + 1):
    # print("i in range(a)")
    # print(i)
    # print(a)
    # print("i in range(a)")
    if i == 0:
        continue
    if i == 1:
        sorted_nums = sorted_nums[1:]
        # x,y = 0,1にした場合
        max_num_idx_min = dic[max_num][0]
        res[0][1] = (max_num * (a - 1 - max_num_idx_min), [max_num_idx_min])

        # x,y = 1,0にした場合
        max_num_idx_max = dic[max_num][-1]
        res[1][0] = (max_num * max_num_idx_max, [max_num_idx_max])

    else:
        target_val = sorted_nums[0]
        sorted_nums = sorted_nums[1:]
        if target_val == max_num:
            max_num_changed = False
        else:
            max_num_changed = True
            max_num = target_val

        # print(sorted_nums)

        score_right = -1
        # x,y = i-j,j(0 ≤ j ≤ i)にした場合を考える
        # i - 1のresについてそれぞれ次の状態を考えていく
        # res[i-1][0], res[i-2][1], res[i-3][2], ... , res[i-1-j][j], ... , res[0][i-1]
        ls_j = []
        for j in range(i):
            if max_num_changed:
                already_used_max_num_index = []
                max_num_idx_max = dic[max_num][-1]
                max_num_idx_min = dic[max_num][0]
            else:
                already_used_max_num_index = res[i-j-1][j][1]
                tmp_list = [x for x in dic[max_num][:] if x not in already_used_max_num_index]
                max_num_idx_max = tmp_list[-1]
                max_num_idx_min = tmp_list[0]

            # from i-j-1,j to i-j,j (最大活性のものを左に移動)
            score_left = max_num * abs(max_num_idx_max - (i - j - 1)) + res[i - j - 1][j][0]

            # 左端はその値をそのまま利用。右側に移動したものよりも大きい場合はleftの値を設定
            if j == 0 or score_right < score_left:
                res_list = already_used_max_num_index[:]
                res_list.append(max_num_idx_max)
                res[i - j][j] = (score_left, res_list)

            # from i-j-1,j to i-j-1,j+1 (最大活性のものを右に移動)
            score_right = max_num * abs(a - 1 - max_num_idx_min - j) + res[i - j - 1][j][0]
            # 右側に移動の場合は一旦その値を暫定値として設定してしまう（必要があれば次のループで上書きされるので問題ない）
            res_list = already_used_max_num_index[:]
            res_list.append(max_num_idx_min)
            res[i - j - 1][j + 1] = (score_right, res_list)

    if i == a:
        result = []
        for j in range(a + 1):
            result.append(res[j][i - j][0])
        # print(result)
        print(max(result))

Submission status: Time Limit Exceeded

Solution code:
from heapq import heappush, heappop

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

dp = [[0 for _ in range(n+1)] for _ in range(n+1)]
dp[0][0] = 0

hq = []
for i in range(n):
    heappush(hq, (-A[i], i))

for i in range(n):
    x, pi = heappop(hq)
    for l in range(i+1):
        r = i-l
        dp[i+1][l+1] = max(dp[i+1][l+1], dp[i][l] + (pi-l)*A[pi])
        dp[i+1][l] = max(dp[i+1][l], dp[i][l] + ((n-r-1)-pi)*A[pi])

ans = 0
for i in range(n+1):
    ans = max(ans, dp[n][i])
print(ans)

Submission status: Time Limit Exceeded

Solution code:
from heapq import heappush, heappop

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

MX = 2005
f_inf = float('inf')
dp = [[0 for _ in range(MX)] for _ in range(MX)]
dp[0][0] = 0

hq = []
for i in range(n):
    heappush(hq, (-A[i], i))

ans = 0
for i in range(n):
    x, pi = heappop(hq)
    for l in range(i+1):
        r = i-l
        dp[i+1][l+1] = max(dp[i+1][l+1], dp[i][l] + (pi-l)*A[pi])
        dp[i+1][l] = max(dp[i+1][l], dp[i][l] + ((n-r-1)-pi)*A[pi])

ans = 0
for i in range(n+1):
    ans = max(ans, dp[n][i])
print(ans)

Submission status: Time Limit Exceeded

Solution code:
N = int(input())
S = list(map(int, input().split()))

data = [0]*N
for i, item in enumerate(S):
    data[i] = [item, i]
data.sort(reverse=True)

dp = [[0]*(N+1) for _ in range(N+1)]
# dp[i][j] i+j-1番目までの幼児がi人0から、j人N-1から並んだ時の最大値

for i in range(N):
    for j in range(N):
        if i+j >= N:
            break
        dp[i+1][j] = max(dp[i+1][j], dp[i][j]+data[i+j][0]*(data[i+j][1]-(i)))
        dp[i][j+1] = max(dp[i][j+1], dp[i][j]+data[i+j][0]*((N-1-j)-data[i+j][1]))

ans = 0
for i in range(N+1):
    ans = max(ans, dp[i][N-i])

print(ans)

Submission status: Time Limit Exceeded

Solution code:
# -*- coding: utf-8 -*-

N = int(input())
A = list(map(int, input().split()))
A = sorted([(a, p) for p, a in enumerate(A)], reverse=True)


# dp[i][j] := i番目の幼児まで見て、左に詰める選択をj回行った場合のうれしさの最大値
dp = [[0] * (N + 1) for _ in range(N + 1)]
for i, (a, p) in enumerate(A):
    for j in range(i + 1):
        # 左に詰める場合
        dp[i + 1][j + 1] = max(dp[i + 1][j + 1], dp[i][j] + (p - j) * a)

        # 右に詰める場合
        dp[i + 1][j] = max(dp[i + 1][j], dp[i][j] + ((N - (i - j) - 1) - p) * a)
#print(dp)
print(max(dp[-1]))

Submission status: Time Limit Exceeded

Solution code:
# -*- coding: utf-8 -*-
# 整数の入力
a = int(input())
# スペース区切りの整数の入力
strs = input().split()

nums = []
only_nums = []
for i in range(a):
    v = int(strs[i])
    nums.append((i, v, True))
    only_nums.append(v)

sorted_nums = sorted(only_nums, reverse=True)
# print(sorted_nums)

# print(nums)

# res[x][y]をx人を左から活性度順に並べて、y人を右から活性度順に並べた状態の(スコア最大値, 移動済のものを除いたnums)とする
res = []
for i in range(a + 1):
    ls = []
    for j in range(a + 1):
        ls.append((0, []))
    res.append(ls)

for i in range(a + 1):
    # print("i in range(a)")
    # print(i)
    # print(a)
    # print("i in range(a)")
    if i == 0:
        continue
    if i == 1:
        max_num = sorted_nums[0]
        sorted_nums = sorted_nums[1:]
        # x,y = 0,1にした場合
        max_num_idx_min = -1
        nums_clone = nums.copy()
        for x in nums_clone:
            if x[1] == max_num:
                max_num_idx_min = x[0]
                break
        nums_clone[max_num_idx_min] = (nums_clone[max_num_idx_min][0], nums_clone[max_num_idx_min][1], False)
        res[0][1] = (max_num * (a - 1 - max_num_idx_min), nums_clone)

        # x,y = 1,0にした場合
        max_num_idx_max = -1
        nums_clone = nums.copy()
        for y in range(len(nums_clone)):
            x = nums_clone[len(nums_clone) - 1 - y]
            if x[1] == max_num:
                max_num_idx_max = x[0]
                break
        nums_clone[max_num_idx_max] = (nums_clone[max_num_idx_max][0], nums_clone[max_num_idx_max][1], False)
        res[1][0] = (max_num * max_num_idx_max, nums_clone)

    else:
        # print(sorted_nums)
        max_num = sorted_nums[0]
        sorted_nums = sorted_nums[1:]
        # x,y = i-j,j(0 ≤ j ≤ i)にした場合を考える
        # i - 1のresについてそれぞれ次の状態を考えていく
        # res[i-1][0], res[i-2][1], res[i-3][2], ... , res[i-1-j][j], ... , res[0][i-1]
        ls_j = []
        for j in range(i):
            # from i-j-1,j to i-j,j (最大活性のものを左に移動)
            max_num_idx_max = -1
            nums_clone = res[i - j - 1][j][1].copy()
            for y in range(len(nums_clone)):
                x = nums_clone[len(nums_clone) - 1 - y]
                if x[1] == max_num and x[2]:
                    max_num_idx_max = x[0]
                    break
            score_left = max_num * abs(max_num_idx_max - (i - j - 1)) + res[i - j - 1][j][0]
            nums_clone[max_num_idx_max] = (nums_clone[max_num_idx_max][0], nums_clone[max_num_idx_max][1], False)
            left = (score_left, nums_clone)
            # res[j-1][i-j+1] = (score_left, nums_clone)

            # from i-j-1,j to i-j-1,j+1 (最大活性のものを右に移動)
            max_num_idx_min = -1
            nums_clone = res[i - j - 1][j][1].copy()
            for x in nums_clone:
                if x[1] == max_num and x[2]:
                    max_num_idx_min = x[0]
                    break
            score_right = max_num * abs(a - 1 - max_num_idx_min - j) + res[i - j - 1][j][0]
            nums_clone[max_num_idx_min] = (nums_clone[max_num_idx_min][0], nums_clone[max_num_idx_min][1], False)
            right = (score_right, nums_clone)
            # res[j-1][i-j+1] = (score_right, nums_clone)

            ls_j.append((left, right))

        # iのres (res[i-j][j]) についてそれぞれleftとrightのどちらがより高いスコアかを考えて値を決定する
        for j in range(i + 1):
            # i,0は決定済
            if j == 0:
                res[i - j][j] = ls_j[0][0]
            # 0,iは決定済
            elif j == i:
                res[i - j][j] = ls_j[i - 1][1]
            else:
                # 木のイメージで左側から伸びてきた枝
                from_left = ls_j[j - 1][1]
                # 木のイメージで右側から伸びてきた枝
                from_right = ls_j[j][0]
                if from_left[0] < from_right[0]:
                    res[i - j][j] = from_right
                else:
                    res[i - j][j] = from_left

    if i == a:
        result = []
        for j in range(a + 1):
            result.append(res[j][i - j][0])
        # print(result)
        print(max(result))