add(coding/1980): find-unique-binary-string

source/coding/1980-find-unique-binary-string.md

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+---
+title: 1980. Find Unique Binary String
+notebook: coding
+tags:
+- medium
+date: 2025-02-20 09:57:26
+updated: 2025-02-20 09:57:26
+---
+## Problem
+
+Given an array of strings `nums` containing `n` **unique** binary strings each of length `n`, return _a binary string of length_ `n` _that **does not appear** in_ `nums`_. If there are multiple answers, you may return **any** of them_.
+
+<https://leetcode.com/problems/find-unique-binary-string/>
+
+**Example 1:**
+
+> Input: `nums = ["01","10"]`
+> Output: `"11"`
+> Explanation: `"11"` does not appear in nums. `"00"` would also be correct.
+
+**Example 2:**
+
+> Input: `nums = ["00","01"]`
+> Output: `"11"`
+> Explanation: `"11"` does not appear in nums. `"10"` would also be correct.
+
+**Example 3:**
+
+> Input: `nums = ["111","011","001"]`
+> Output: `"101"`
+> Explanation: `"101"` does not appear in nums. `"000"`, `"010"`, `"100"`, and `"110"` would also be correct.
+
+**Constraints:**
+
+- `n == nums.length`
+- `1 <= n <= 16`
+- `nums[i].length == n`
+- `nums[i]` is either `'0'` or `'1'`.
+- All the strings of `nums` are **unique**.
+
+## Test Cases
+
+``` python
+class Solution:
+    def findDifferentBinaryString(self, nums: List[str]) -> str:
+```
+
+{% asset_code coding/1980-find-unique-binary-string/solution_test.py %}
+
+## Thoughts
+
+取 0 到 n（包含）的所有整数（共 `n + 1` 个），这些数字都可以表达成长度为 n 的二进制形式（左补零），且根据鸽笼原理，这 `n + 1` 个整数中，至少有一个不在 `nums` 中。
+
+用一个集合记录 `[0, n]` 区间内所有整数，遍历 nums，对于 nums 中的每一个二进制串，转成整数后从集合中删除该数字。最后集合中至少会剩余一个数字。从集合剩余的数字中任取一个，格式化为长度为 n 的二进制字符串，返回即可。
+
+时间复杂度 `O(n²)`，空间复杂度 `O(n)`。
+
+## Code
+
+{% asset_code coding/1980-find-unique-binary-string/solution.py %}

source/coding/1980-find-unique-binary-string/solution.py

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+class Solution:
+    def findDifferentBinaryString(self, nums: list[str]) -> str:
+        n = len(nums[0])
+        candidates = set(range(n + 1))
+        for num in nums:
+            candidates.discard(int(num, 2))
+
+        return format(candidates.pop(), f'0{n}b')

source/coding/1980-find-unique-binary-string/solution_test.py

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+import pytest
+
+from solution import Solution
+
+
+def verify(res: str, nums: list[str]):
+    assert res not in nums
+    assert len(res) == len(nums[0])
+    for d in res:
+        assert d in '01'
+
+
+@pytest.mark.parametrize('nums, expected', [
+    (["01","10"], "11"),
+    (["00","01"], "11"),
+    (["111","011","001"], "101"),
+])
+@pytest.mark.parametrize('sol', [Solution()])
+def test_solution(sol, nums, expected):
+    res = sol.findDifferentBinaryString(nums)
+    if res != expected:
+        verify(res, nums)