{ "data": { "question": { "questionId": "3648", "questionFrontendId": "3363", "categoryTitle": "Algorithms", "boundTopicId": 2996273, "title": "Find the Maximum Number of Fruits Collected", "titleSlug": "find-the-maximum-number-of-fruits-collected", "content": "
There is a game dungeon comprised of n x n
rooms arranged in a grid.
You are given a 2D array fruits
of size n x n
, where fruits[i][j]
represents the number of fruits in the room (i, j)
. Three children will play in the game dungeon, with initial positions at the corner rooms (0, 0)
, (0, n - 1)
, and (n - 1, 0)
.
The children will make exactly n - 1
moves according to the following rules to reach the room (n - 1, n - 1)
:
(0, 0)
must move from their current room (i, j)
to one of the rooms (i + 1, j + 1)
, (i + 1, j)
, and (i, j + 1)
if the target room exists.(0, n - 1)
must move from their current room (i, j)
to one of the rooms (i + 1, j - 1)
, (i + 1, j)
, and (i + 1, j + 1)
if the target room exists.(n - 1, 0)
must move from their current room (i, j)
to one of the rooms (i - 1, j + 1)
, (i, j + 1)
, and (i + 1, j + 1)
if the target room exists.When a child enters a room, they will collect all the fruits there. If two or more children enter the same room, only one child will collect the fruits, and the room will be emptied after they leave.
\n\nReturn the maximum number of fruits the children can collect from the dungeon.
\n\n\n
Example 1:
\n\nInput: fruits = [[1,2,3,4],[5,6,8,7],[9,10,11,12],[13,14,15,16]]
\n\nOutput: 100
\n\nExplanation:
\n\nIn this example:
\n\n(0,0) -> (1,1) -> (2,2) -> (3, 3)
.(0,3) -> (1,2) -> (2,3) -> (3, 3)
.(3,0) -> (3,1) -> (3,2) -> (3, 3)
.In total they collect 1 + 6 + 11 + 16 + 4 + 8 + 12 + 13 + 14 + 15 = 100
fruits.
Example 2:
\n\nInput: fruits = [[1,1],[1,1]]
\n\nOutput: 4
\n\nExplanation:
\n\nIn this example:
\n\n(0,0) -> (1,1)
.(0,1) -> (1,1)
.(1,0) -> (1,1)
.In total they collect 1 + 1 + 1 + 1 = 4
fruits.
\n
Constraints:
\n\n2 <= n == fruits.length == fruits[i].length <= 1000
0 <= fruits[i][j] <= 1000
有一个游戏,游戏由 n x n
个房间网格状排布组成。
给你一个大小为 n x n
的二位整数数组 fruits
,其中 fruits[i][j]
表示房间 (i, j)
中的水果数目。有三个小朋友 一开始 分别从角落房间 (0, 0)
,(0, n - 1)
和 (n - 1, 0)
出发。
每一位小朋友都会 恰好 移动 n - 1
次,并到达房间 (n - 1, n - 1)
:
(0, 0)
出发的小朋友每次移动从房间 (i, j)
出发,可以到达 (i + 1, j + 1)
,(i + 1, j)
和 (i, j + 1)
房间之一(如果存在)。(0, n - 1)
出发的小朋友每次移动从房间 (i, j)
出发,可以到达房间 (i + 1, j - 1)
,(i + 1, j)
和 (i + 1, j + 1)
房间之一(如果存在)。(n - 1, 0)
出发的小朋友每次移动从房间 (i, j)
出发,可以到达房间 (i - 1, j + 1)
,(i, j + 1)
和 (i + 1, j + 1)
房间之一(如果存在)。当一个小朋友到达一个房间时,会把这个房间里所有的水果都收集起来。如果有两个或者更多小朋友进入同一个房间,只有一个小朋友能收集这个房间的水果。当小朋友离开一个房间时,这个房间里不会再有水果。
\n\n请你返回三个小朋友总共 最多 可以收集多少个水果。
\n\n\n\n
示例 1:
\n\n输入:fruits = [[1,2,3,4],[5,6,8,7],[9,10,11,12],[13,14,15,16]]
\n\n输出:100
\n\n解释:
\n\n这个例子中:
\n\n(0,0) -> (1,1) -> (2,2) -> (3, 3)
。(0,3) -> (1,2) -> (2,3) -> (3, 3)
。(3,0) -> (3,1) -> (3,2) -> (3, 3)
。他们总共能收集 1 + 6 + 11 + 1 + 4 + 8 + 12 + 13 + 14 + 15 = 100
个水果。
示例 2:
\n\n输入:fruits = [[1,1],[1,1]]
\n\n输出:4
\n\n解释:
\n\n这个例子中:
\n\n(0,0) -> (1,1)
。(0,1) -> (1,1)
。(1,0) -> (1,1)
。他们总共能收集 1 + 1 + 1 + 1 = 4
个水果。
\n\n
提示:
\n\n2 <= n == fruits.length == fruits[i].length <= 1000
0 <= fruits[i][j] <= 1000
(0, 0)
has only one possible path.",
"The other two children won’t intersect its path.",
"Use Dynamic Programming."
],
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