{ "data": { "question": { "questionId": "3391", "questionFrontendId": "3148", "categoryTitle": "Algorithms", "boundTopicId": 2773143, "title": "Maximum Difference Score in a Grid", "titleSlug": "maximum-difference-score-in-a-grid", "content": "
You are given an m x n
matrix grid
consisting of positive integers. You can move from a cell in the matrix to any other cell that is either to the bottom or to the right (not necessarily adjacent). The score of a move from a cell with the value c1
to a cell with the value c2
is c2 - c1
.
You can start at any cell, and you have to make at least one move.
\n\nReturn the maximum total score you can achieve.
\n\n\n
Example 1:
\n\nInput: grid = [[9,5,7,3],[8,9,6,1],[6,7,14,3],[2,5,3,1]]
\n\nOutput: 9
\n\nExplanation: We start at the cell (0, 1)
, and we perform the following moves:
\n- Move from the cell (0, 1)
to (2, 1)
with a score of 7 - 5 = 2
.
\n- Move from the cell (2, 1)
to (2, 2)
with a score of 14 - 7 = 7
.
\nThe total score is 2 + 7 = 9
.
Example 2:
\n\n\n\nInput: grid = [[4,3,2],[3,2,1]]
\n\nOutput: -1
\n\nExplanation: We start at the cell (0, 0)
, and we perform one move: (0, 0)
to (0, 1)
. The score is 3 - 4 = -1
.
\n
Constraints:
\n\nm == grid.length
n == grid[i].length
2 <= m, n <= 1000
4 <= m * n <= 105
1 <= grid[i][j] <= 105
给你一个由 正整数 组成、大小为 m x n
的矩阵 grid
。你可以从矩阵中的任一单元格移动到另一个位于正下方或正右侧的任意单元格(不必相邻)。从值为 c1
的单元格移动到值为 c2
的单元格的得分为 c2 - c1
。
你可以从 任一 单元格开始,并且必须至少移动一次。
\n\n返回你能得到的 最大 总得分。
\n\n\n\n
示例 1:
\n\n输入:grid = [[9,5,7,3],[8,9,6,1],[6,7,14,3],[2,5,3,1]]
\n\n输出:9
\n\n解释:从单元格 (0, 1)
开始,并执行以下移动:
\n- 从单元格 (0, 1)
移动到 (2, 1)
,得分为 7 - 5 = 2
。
\n- 从单元格 (2, 1)
移动到 (2, 2)
,得分为 14 - 7 = 7
。
\n总得分为 2 + 7 = 9
。
示例 2:
\n\n\n\n输入:grid = [[4,3,2],[3,2,1]]
\n\n输出:-1
\n\n解释:从单元格 (0, 0)
开始,执行一次移动:从 (0, 0)
到 (0, 1)
。得分为 3 - 4 = -1
。
\n\n
提示:
\n\nm == grid.length
n == grid[i].length
2 <= m, n <= 1000
4 <= m * n <= 105
1 <= grid[i][j] <= 105
(x1, y1)
to another cell (x2, y2)
will always have a score of grid[x2][y2] - grid[x1][y1]
.",
"Let’s say we fix the starting cell (x1, y1)
, how to the find a cell (x2, y2)
such that the value grid[x2][y2] - grid[x1][y1]
is the maximum possible?"
],
"solution": null,
"status": null,
"sampleTestCase": "[[9,5,7,3],[8,9,6,1],[6,7,14,3],[2,5,3,1]]",
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