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93 lines
2.4 KiB
Plaintext
93 lines
2.4 KiB
Plaintext
---
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title: '74. Search a 2D Matrix'
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description: 'You are given an m x n integer matrix matrix with the following two properties:'
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icon: dot
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topics:
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- { name: "Array", slug: "array" }
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- { name: "Binary Search", slug: "binary-search" }
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- { name: "Matrix", slug: "matrix" }
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video: "Ber2pi2C0j0"
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issue: "https://github.com/prdlk/leetcode/issues/61"
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sidebar:
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label: 'Search a 2D Matrix'
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badge: 'Medium'
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---
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::::warning
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You must write a solution in O(log(m * n)) time complexity.
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::::
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### Example 1:
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- Input: `matrix = [[1,3,5,7],[10,11,16,20],[23,30,34,60]], target = 3`
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- Output: `true`
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### Example 2:
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- Input: `matrix = [[1,3,5,7],[10,11,16,20],[23,30,34,60]], target = 13`
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- Output: `false`
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### Constraints:
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- `m == matrix.length`
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- `n == matrix[i].length`
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- `1 <= m, n <= 100`
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- `-10^4 <= matrix[i][j], target <= 10^4`
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## Approach
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```mermaid
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flowchart TD
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S(["searchMatrix(matrix, target)"]) --> I["top = 0, bot = ROWS - 1"]
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I --> W1{"top <= bot?"}
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W1 -- yes --> R1["row = (top + bot) // 2"]
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R1 --> C1{"target vs that row's range"}
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C1 -- "above matrix[row][-1]" --> U["top = row + 1"]
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C1 -- "below matrix[row][0]" --> V["bot = row - 1"]
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C1 -- inside --> B(["break — row found"])
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U --> W1
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V --> W1
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W1 -- no --> F(["return False — no row can hold it"])
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B --> P["row = (top + bot) // 2; l = 0, r = COLS - 1"]
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P --> W2{"l <= r?"}
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W2 -- no --> G(["return False"])
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W2 -- yes --> M["m = (l + r) // 2"]
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M --> C2{"target vs matrix[row][m]"}
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C2 -- greater --> X["l = m + 1"]
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C2 -- smaller --> Y["r = m - 1"]
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C2 -- equal --> T(["return True"])
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X --> W2
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Y --> W2
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```
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## Solution
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```py
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class Solution:
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def searchMatrix(self, matrix: List[List[int]], target: int) -> bool:
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ROWS, COLS = len(matrix), len(matrix[0])
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top, bot = 0, ROWS - 1
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while top <= bot:
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row = (top + bot) // 2
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if target > matrix[row][-1]:
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top = row + 1
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elif target < matrix[row][0]:
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bot = row - 1
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else:
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break
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if not (top <= bot):
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return False
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row = (top + bot) // 2
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l, r = 0, COLS - 1
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while l <= r:
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m = (l + r) // 2
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if target > matrix[row][m]:
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l = m + 1
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elif target < matrix[row][m]:
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r = m - 1
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else:
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return True
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return False
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```
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