|
| 1 | +from typing import List |
| 2 | +import sys |
| 3 | + |
| 4 | + |
| 5 | +# N ** 3으로 작성된 코드 |
| 6 | +# def maxCoins(self, nums: List[int]) -> int: |
| 7 | +# n = len(nums) |
| 8 | +# nums = [1] + nums + [1] |
| 9 | +# dp = [[0] * (n + 2) for _ in range(n + 2)] |
| 10 | +# |
| 11 | +# for i in range(n, 0, -1): |
| 12 | +# for j in range(i, n + 1): |
| 13 | +# for k in range(i, j + 1): |
| 14 | +# dp[i][j] = max(dp[i][j], dp[i][k - 1] + dp[k + 1][j] + nums[k] * nums[i - 1] * nums[j + 1]) |
| 15 | +# |
| 16 | +# return dp[1][n] |
| 17 | + |
| 18 | +class Solution: |
| 19 | + def maxCoins(self, nums: List[int]) -> int: |
| 20 | + nums = [1] + nums + [1] |
| 21 | + l = len(nums) |
| 22 | + dp = [[-1] * l for _ in range(l)] |
| 23 | + |
| 24 | + def dp_d_c(i_left, i_right): |
| 25 | + if i_right - i_left < 0: |
| 26 | + return 0 |
| 27 | + |
| 28 | + if dp[i_left][i_right] > -1: |
| 29 | + return dp[i_left][i_right] |
| 30 | + |
| 31 | + coins_mx = 0 |
| 32 | + |
| 33 | + for i in range(i_left, i_right + 1): |
| 34 | + coins_i = nums[i_left - 1] * nums[i] * nums[i_right + 1] |
| 35 | + coins_lr = 0 |
| 36 | + coins_lr += dp_d_c(i_left, i - 1) |
| 37 | + coins_lr += dp_d_c(i + 1, i_right) |
| 38 | + |
| 39 | + coins_mx = max(coins_mx, coins_i + coins_lr) |
| 40 | + |
| 41 | + dp[i_left][i_right] = coins_mx |
| 42 | + |
| 43 | + return dp[i_left][i_right] |
| 44 | + |
| 45 | + coins = dp_d_c(1, l - 2) |
| 46 | + return coins |
| 47 | + |
| 48 | +# DP (Naive) |
| 49 | +# def maxCoins(self, nums: List[int]) -> int: |
| 50 | +# memo: dict = {} |
| 51 | +# nums = [1] + nums + [1] |
| 52 | +# coins = self.dp(nums, memo) |
| 53 | +# |
| 54 | +# return coins |
| 55 | +# |
| 56 | +# def dp(self, nums: List[int], memo: dict): |
| 57 | +# if tuple(nums) in memo.keys(): |
| 58 | +# return memo[tuple(nums)] |
| 59 | +# |
| 60 | +# if len(nums) == 3: |
| 61 | +# memo[tuple(nums)] = nums[0] * nums[1] * nums[2] |
| 62 | +# return memo[tuple(nums)] |
| 63 | +# |
| 64 | +# coins = 0 |
| 65 | +# mx = -sys.maxsize - 1 |
| 66 | +# |
| 67 | +# for i in range(1, len(nums) - 1): |
| 68 | +# coins = nums[i - 1] * nums[i] * nums[i + 1] |
| 69 | +# coins_2 = self.dp(nums[:i] + nums[i + 1:], memo) |
| 70 | +# |
| 71 | +# mx = max(mx, coins + coins_2) |
| 72 | +# |
| 73 | +# memo[tuple(nums)] = mx |
| 74 | +# |
| 75 | +# return mx |
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