{ "data": { "question": { "questionId": "2801", "questionFrontendId": "2711", "categoryTitle": "Algorithms", "boundTopicId": 2284417, "title": "Difference of Number of Distinct Values on Diagonals", "titleSlug": "difference-of-number-of-distinct-values-on-diagonals", "content": "
Given a 2D grid
of size m x n
, you should find the matrix answer
of size m x n
.
The cell answer[r][c]
is calculated by looking at the diagonal values of the cell grid[r][c]
:
leftAbove[r][c]
be the number of distinct values on the diagonal to the left and above the cell grid[r][c]
not including the cell grid[r][c]
itself.rightBelow[r][c]
be the number of distinct values on the diagonal to the right and below the cell grid[r][c]
, not including the cell grid[r][c]
itself.answer[r][c] = |leftAbove[r][c] - rightBelow[r][c]|
.A matrix diagonal is a diagonal line of cells starting from some cell in either the topmost row or leftmost column and going in the bottom-right direction until the end of the matrix is reached.
\n\n(2, 3)
colored gray:\n\n\tReturn the matrix answer
.
\n
Example 1:
\n\nInput: grid = [[1,2,3],[3,1,5],[3,2,1]]
\n\nOutput: Output: [[1,1,0],[1,0,1],[0,1,1]]
\n\nExplanation:
\n\nTo calculate the answer
cells:
answer | \n\t\t\tleft-above elements | \n\t\t\tleftAbove | \n\t\t\tright-below elements | \n\t\t\trightBelow | \n\t\t\t|leftAbove - rightBelow| | \n\t\t
---|---|---|---|---|---|
[0][0] | \n\t\t\t[] | \n\t\t\t0 | \n\t\t\t[grid[1][1], grid[2][2]] | \n\t\t\t|{1, 1}| = 1 | \n\t\t\t1 | \n\t\t
[0][1] | \n\t\t\t[] | \n\t\t\t0 | \n\t\t\t[grid[1][2]] | \n\t\t\t|{5}| = 1 | \n\t\t\t1 | \n\t\t
[0][2] | \n\t\t\t[] | \n\t\t\t0 | \n\t\t\t[] | \n\t\t\t0 | \n\t\t\t0 | \n\t\t
[1][0] | \n\t\t\t[] | \n\t\t\t0 | \n\t\t\t[grid[2][1]] | \n\t\t\t|{2}| = 1 | \n\t\t\t1 | \n\t\t
[1][1] | \n\t\t\t[grid[0][0]] | \n\t\t\t|{1}| = 1 | \n\t\t\t[grid[2][2]] | \n\t\t\t|{1}| = 1 | \n\t\t\t0 | \n\t\t
[1][2] | \n\t\t\t[grid[0][1]] | \n\t\t\t|{2}| = 1 | \n\t\t\t[] | \n\t\t\t0 | \n\t\t\t1 | \n\t\t
[2][0] | \n\t\t\t[] | \n\t\t\t0 | \n\t\t\t[] | \n\t\t\t0 | \n\t\t\t0 | \n\t\t
[2][1] | \n\t\t\t[grid[1][0]] | \n\t\t\t|{3}| = 1 | \n\t\t\t[] | \n\t\t\t0 | \n\t\t\t1 | \n\t\t
[2][2] | \n\t\t\t[grid[0][0], grid[1][1]] | \n\t\t\t|{1, 1}| = 1 | \n\t\t\t[] | \n\t\t\t0 | \n\t\t\t1 | \n\t\t
Example 2:
\n\nInput: grid = [[1]]
\n\nOutput: Output: [[0]]
\n\n
Constraints:
\n\nm == grid.length
n == grid[i].length
1 <= m, n, grid[i][j] <= 50
给你一个下标从 0
开始、大小为 m x n
的二维矩阵 grid
,请你求解大小同样为 m x n
的答案矩阵 answer
。
矩阵 answer
中每个单元格 (r, c)
的值可以按下述方式进行计算:
topLeft[r][c]
为矩阵 grid
中单元格 (r, c)
左上角对角线上 不同值 的数量。bottomRight[r][c]
为矩阵 grid
中单元格 (r, c)
右下角对角线上 不同值 的数量。然后 answer[r][c] = |topLeft[r][c] - bottomRight[r][c]|
。
返回矩阵 answer
。
矩阵对角线 是从最顶行或最左列的某个单元格开始,向右下方向走到矩阵末尾的对角线。
\n\n如果单元格 (r1, c1)
和单元格 (r, c)
属于同一条对角线且 r1 < r
,则单元格 (r1, c1)
属于单元格 (r, c)
的左上对角线。类似地,可以定义右下对角线。
\n\n
示例 1:
\n\n输入:grid = [[1,2,3],[3,1,5],[3,2,1]]\n输出:[[1,1,0],[1,0,1],[0,1,1]]\n解释:第 1 个图表示最初的矩阵 grid 。 \n第 2 个图表示对单元格 (0,0) 计算,其中蓝色单元格是位于右下对角线的单元格。\n第 3 个图表示对单元格 (1,2) 计算,其中红色单元格是位于左上对角线的单元格。\n第 4 个图表示对单元格 (1,1) 计算,其中蓝色单元格是位于右下对角线的单元格,红色单元格是位于左上对角线的单元格。\n- 单元格 (0,0) 的右下对角线包含 [1,1] ,而左上对角线包含 [] 。对应答案是 |1 - 0| = 1 。\n- 单元格 (1,2) 的右下对角线包含 [] ,而左上对角线包含 [2] 。对应答案是 |0 - 1| = 1 。\n- 单元格 (1,1) 的右下对角线包含 [1] ,而左上对角线包含 [1] 。对应答案是 |1 - 1| = 0 。\n其他单元格的对应答案也可以按照这样的流程进行计算。\n\n\n
示例 2:
\n\n\n输入:grid = [[1]]\n输出:[[0]]\n解释:- 单元格 (0,0) 的右下对角线包含 [] ,左上对角线包含 [] 。对应答案是 |0 - 0| = 0 。\n\n\n
\n\n
提示:
\n\nm == grid.length
n == grid[i].length
1 <= m, n, grid[i][j] <= 50
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