问题

### Instructions: You are an expert Python programmer. You will be given a question (problem specification) and the first lines of Python solution to this problem, and will write in Python the remaining lines of the program to produce a correct Python program that matches the specification and passes all tests. You will NOT return anything except for the second part of the program that you wrote.
### Question:
You are given a 0-indexed string s, a string a, a string b, and an integer k.
An index i is beautiful if:

0 <= i <= s.length - a.length
s[i..(i + a.length - 1)] == a
There exists an index j such that:

0 <= j <= s.length - b.length
s[j..(j + b.length - 1)] == b
|j - i| <= k



Return the array that contains beautiful indices in sorted order from smallest to largest.

Example 1:

Input: s = "isawsquirrelnearmysquirrelhouseohmy", a = "my", b = "squirrel", k = 15
Output: [16,33]
Explanation: There are 2 beautiful indices: [16,33].
- The index 16 is beautiful as s[16..17] == "my" and there exists an index 4 with s[4..11] == "squirrel" and |16 - 4| <= 15.
- The index 33 is beautiful as s[33..34] == "my" and there exists an index 18 with s[18..25] == "squirrel" and |33 - 18| <= 15.
Thus we return [16,33] as the result.

Example 2:

Input: s = "abcd", a = "a", b = "a", k = 4
Output: [0]
Explanation: There is 1 beautiful index: [0].
- The index 0 is beautiful as s[0..0] == "a" and there exists an index 0 with s[0..0] == "a" and |0 - 0| <= 4.
Thus we return [0] as the result.


Constraints:

1 <= k <= s.length <= 10^5
1 <= a.length, b.length <= 10
s, a, and b contain only lowercase English letters.

### Format: You will use the following starter code to write the solution to the problem and enclose your code within delimiters.
```python
class Solution(object):
def beautifulIndices(self, s, a, b, k):
"""
:type s: str
:type a: str
:type b: str
:type k: int
:rtype: List[int]
"""
def getPrefix(pattern):
prefix = [-1]*len(pattern)
j = -1
for i in range(1, len(pattern)):
while j+1 > 0 and pattern[j+1] != pattern[i]:
j = prefix[j]
if pattern[j+1] == pattern[i]:
j += 1
prefix[i] = j
return prefix

def KMP(text, pattern):
prefix = getPrefix(pattern)
j = -1
for i in range(len(text)):
while j+1 > 0 and pattern[j+1] != text[i]:
j = prefix[j]
if pattern[j+1] == text[i]:
j += 1
if j+1 == len(pattern):
yield i-j
j = prefix[j]

result = []
if not (len(a) <= len(s) and len(b) <= len(s)):
return result
lookup = list(KMP(s, b))
```

### Answer: (enclose your partial completion in backticks. Only write the missing portion of the code, not the entire code. Be very careful to match the appropriate indentation. Directly appending your code after the partial code should produce a correct completion solution.)

答案

模型 模型答案 正确答案
金声玉亮2.0 ```python
for i in KMP(s, a):
for j in lookup:
if abs(i - j) <= k:
result.append(i)
break
return sorted(result)
```		 class Solution(object): def beautifulIndices(self, s, a, b, k): """ :type s: str :type a: str :type b: str :type k: int :rtype: List[int] """ def getPrefix(pattern): prefix = [-1]*len(pattern) j = -1 for i in range(1, len(pattern)): while j+1 > 0 and pattern[j+1] != pattern[i]: j = prefix[j] if pattern[j+1] == pattern[i]: j += 1 prefix[i] = j return prefix def KMP(text, pattern): prefix = getPrefix(pattern) j = -1 for i in range(len(text)): while j+1 > 0 and pattern[j+1] != text[i]: j = prefix[j] if pattern[j+1] == text[i]: j += 1 if j+1 == len(pattern): yield i-j j = prefix[j] result = [] if not (len(a) <= len(s) and len(b) <= len(s)): return result lookup = list(KMP(s, b)) j = 0 for i in KMP(s, a): while j < len(lookup) and lookup[j] < i-k: j += 1 if j < len(lookup) and lookup[j] <= i+k: result.append(i) return result
deepseek-r1

```python
list_a = list(KMP(s, a))
import bisect
for i in list_a:
left = i - k
right = i + k
pos = bisect.bisect_left(lookup, left)
if pos < len(lookup) and lookup[pos] <= right:
result.append(i)
return result
```		 class Solution(object): def beautifulIndices(self, s, a, b, k): """ :type s: str :type a: str :type b: str :type k: int :rtype: List[int] """ def getPrefix(pattern): prefix = [-1]*len(pattern) j = -1 for i in range(1, len(pattern)): while j+1 > 0 and pattern[j+1] != pattern[i]: j = prefix[j] if pattern[j+1] == pattern[i]: j += 1 prefix[i] = j return prefix def KMP(text, pattern): prefix = getPrefix(pattern) j = -1 for i in range(len(text)): while j+1 > 0 and pattern[j+1] != text[i]: j = prefix[j] if pattern[j+1] == text[i]: j += 1 if j+1 == len(pattern): yield i-j j = prefix[j] result = [] if not (len(a) <= len(s) and len(b) <= len(s)): return result lookup = list(KMP(s, b)) j = 0 for i in KMP(s, a): while j < len(lookup) and lookup[j] < i-k: j += 1 if j < len(lookup) and lookup[j] <= i+k: result.append(i) return result
gpto1 ```python
import bisect
indices_a = list(KMP(s, a))
result = []
for i in indices_a:
left = bisect.bisect_left(lookup, i - k)
right = bisect.bisect_right(lookup, i + k)
if left < right:
result.append(i)
return result
```		 class Solution(object): def beautifulIndices(self, s, a, b, k): """ :type s: str :type a: str :type b: str :type k: int :rtype: List[int] """ def getPrefix(pattern): prefix = [-1]*len(pattern) j = -1 for i in range(1, len(pattern)): while j+1 > 0 and pattern[j+1] != pattern[i]: j = prefix[j] if pattern[j+1] == pattern[i]: j += 1 prefix[i] = j return prefix def KMP(text, pattern): prefix = getPrefix(pattern) j = -1 for i in range(len(text)): while j+1 > 0 and pattern[j+1] != text[i]: j = prefix[j] if pattern[j+1] == text[i]: j += 1 if j+1 == len(pattern): yield i-j j = prefix[j] result = [] if not (len(a) <= len(s) and len(b) <= len(s)): return result lookup = list(KMP(s, b)) j = 0 for i in KMP(s, a): while j < len(lookup) and lookup[j] < i-k: j += 1 if j < len(lookup) and lookup[j] <= i+k: result.append(i) return result
gpt-4o-2024-08-06 ```python
for i in KMP(s, a):
for j in lookup:
if abs(j - i) <= k:
result.append(i)
break
return sorted(result)
```		 class Solution(object): def beautifulIndices(self, s, a, b, k): """ :type s: str :type a: str :type b: str :type k: int :rtype: List[int] """ def getPrefix(pattern): prefix = [-1]*len(pattern) j = -1 for i in range(1, len(pattern)): while j+1 > 0 and pattern[j+1] != pattern[i]: j = prefix[j] if pattern[j+1] == pattern[i]: j += 1 prefix[i] = j return prefix def KMP(text, pattern): prefix = getPrefix(pattern) j = -1 for i in range(len(text)): while j+1 > 0 and pattern[j+1] != text[i]: j = prefix[j] if pattern[j+1] == text[i]: j += 1 if j+1 == len(pattern): yield i-j j = prefix[j] result = [] if not (len(a) <= len(s) and len(b) <= len(s)): return result lookup = list(KMP(s, b)) j = 0 for i in KMP(s, a): while j < len(lookup) and lookup[j] < i-k: j += 1 if j < len(lookup) and lookup[j] <= i+k: result.append(i) return result
Meta-Llama-3.1-405B-Instruct-Turbo ```python
for i in KMP(s, a):
for j in lookup:
if abs(i - j) <= k:
result.append(i)
break
return result
```		 class Solution(object): def beautifulIndices(self, s, a, b, k): """ :type s: str :type a: str :type b: str :type k: int :rtype: List[int] """ def getPrefix(pattern): prefix = [-1]*len(pattern) j = -1 for i in range(1, len(pattern)): while j+1 > 0 and pattern[j+1] != pattern[i]: j = prefix[j] if pattern[j+1] == pattern[i]: j += 1 prefix[i] = j return prefix def KMP(text, pattern): prefix = getPrefix(pattern) j = -1 for i in range(len(text)): while j+1 > 0 and pattern[j+1] != text[i]: j = prefix[j] if pattern[j+1] == text[i]: j += 1 if j+1 == len(pattern): yield i-j j = prefix[j] result = [] if not (len(a) <= len(s) and len(b) <= len(s)): return result lookup = list(KMP(s, b)) j = 0 for i in KMP(s, a): while j < len(lookup) and lookup[j] < i-k: j += 1 if j < len(lookup) and lookup[j] <= i+k: result.append(i) return result
Meta-Llama-3.1-70B-Instruct-Turbo ```python
for i in KMP(s, a):
for j in lookup:
if abs(i - j) <= k:
result.append(i)
break
return sorted(set(result))
```		 class Solution(object): def beautifulIndices(self, s, a, b, k): """ :type s: str :type a: str :type b: str :type k: int :rtype: List[int] """ def getPrefix(pattern): prefix = [-1]*len(pattern) j = -1 for i in range(1, len(pattern)): while j+1 > 0 and pattern[j+1] != pattern[i]: j = prefix[j] if pattern[j+1] == pattern[i]: j += 1 prefix[i] = j return prefix def KMP(text, pattern): prefix = getPrefix(pattern) j = -1 for i in range(len(text)): while j+1 > 0 and pattern[j+1] != text[i]: j = prefix[j] if pattern[j+1] == text[i]: j += 1 if j+1 == len(pattern): yield i-j j = prefix[j] result = [] if not (len(a) <= len(s) and len(b) <= len(s)): return result lookup = list(KMP(s, b)) j = 0 for i in KMP(s, a): while j < len(lookup) and lookup[j] < i-k: j += 1 if j < len(lookup) and lookup[j] <= i+k: result.append(i) return result
DeepSeek-Coder-V2-Lite-Instruct ```python
for i in range(len(s) - len(a) + 1):
if s[i:i+len(a)] == a:
for j in lookup:
if abs(i - j) <= k:
result.append(i)
break
return sorted(result)
```		 class Solution(object): def beautifulIndices(self, s, a, b, k): """ :type s: str :type a: str :type b: str :type k: int :rtype: List[int] """ def getPrefix(pattern): prefix = [-1]*len(pattern) j = -1 for i in range(1, len(pattern)): while j+1 > 0 and pattern[j+1] != pattern[i]: j = prefix[j] if pattern[j+1] == pattern[i]: j += 1 prefix[i] = j return prefix def KMP(text, pattern): prefix = getPrefix(pattern) j = -1 for i in range(len(text)): while j+1 > 0 and pattern[j+1] != text[i]: j = prefix[j] if pattern[j+1] == text[i]: j += 1 if j+1 == len(pattern): yield i-j j = prefix[j] result = [] if not (len(a) <= len(s) and len(b) <= len(s)): return result lookup = list(KMP(s, b)) j = 0 for i in KMP(s, a): while j < len(lookup) and lookup[j] < i-k: j += 1 if j < len(lookup) and lookup[j] <= i+k: result.append(i) return result
Qwen2-72B-Instruct ```python
for i in KMP(s, a):
for j in lookup:
if abs(i - j) <= k:
result.append(i)
break
return sorted(list(set(result)))
```		 class Solution(object): def beautifulIndices(self, s, a, b, k): """ :type s: str :type a: str :type b: str :type k: int :rtype: List[int] """ def getPrefix(pattern): prefix = [-1]*len(pattern) j = -1 for i in range(1, len(pattern)): while j+1 > 0 and pattern[j+1] != pattern[i]: j = prefix[j] if pattern[j+1] == pattern[i]: j += 1 prefix[i] = j return prefix def KMP(text, pattern): prefix = getPrefix(pattern) j = -1 for i in range(len(text)): while j+1 > 0 and pattern[j+1] != text[i]: j = prefix[j] if pattern[j+1] == text[i]: j += 1 if j+1 == len(pattern): yield i-j j = prefix[j] result = [] if not (len(a) <= len(s) and len(b) <= len(s)): return result lookup = list(KMP(s, b)) j = 0 for i in KMP(s, a): while j < len(lookup) and lookup[j] < i-k: j += 1 if j < len(lookup) and lookup[j] <= i+k: result.append(i) return result
baichuan4 ```python
for i in range(len(s) - len(a) + 1):
if s[i:i+len(a)] == a:
for j in lookup:
if abs(i - j) <= k:
result.append(i)
break
return result
```		 class Solution(object): def beautifulIndices(self, s, a, b, k): """ :type s: str :type a: str :type b: str :type k: int :rtype: List[int] """ def getPrefix(pattern): prefix = [-1]*len(pattern) j = -1 for i in range(1, len(pattern)): while j+1 > 0 and pattern[j+1] != pattern[i]: j = prefix[j] if pattern[j+1] == pattern[i]: j += 1 prefix[i] = j return prefix def KMP(text, pattern): prefix = getPrefix(pattern) j = -1 for i in range(len(text)): while j+1 > 0 and pattern[j+1] != text[i]: j = prefix[j] if pattern[j+1] == text[i]: j += 1 if j+1 == len(pattern): yield i-j j = prefix[j] result = [] if not (len(a) <= len(s) and len(b) <= len(s)): return result lookup = list(KMP(s, b)) j = 0 for i in KMP(s, a): while j < len(lookup) and lookup[j] < i-k: j += 1 if j < len(lookup) and lookup[j] <= i+k: result.append(i) return result
doubao ```python
for i in range(len(s) - len(a) + 1):
if s[i:i + len(a)] == a:
for j in lookup:
if abs(i - j) <= k:
result.append(i)
break
return sorted(result)
```		 class Solution(object): def beautifulIndices(self, s, a, b, k): """ :type s: str :type a: str :type b: str :type k: int :rtype: List[int] """ def getPrefix(pattern): prefix = [-1]*len(pattern) j = -1 for i in range(1, len(pattern)): while j+1 > 0 and pattern[j+1] != pattern[i]: j = prefix[j] if pattern[j+1] == pattern[i]: j += 1 prefix[i] = j return prefix def KMP(text, pattern): prefix = getPrefix(pattern) j = -1 for i in range(len(text)): while j+1 > 0 and pattern[j+1] != text[i]: j = prefix[j] if pattern[j+1] == text[i]: j += 1 if j+1 == len(pattern): yield i-j j = prefix[j] result = [] if not (len(a) <= len(s) and len(b) <= len(s)): return result lookup = list(KMP(s, b)) j = 0 for i in KMP(s, a): while j < len(lookup) and lookup[j] < i-k: j += 1 if j < len(lookup) and lookup[j] <= i+k: result.append(i) return result
gpto1 ```python
import bisect
indices_a = list(KMP(s, a))
result = []
for i in indices_a:
left = bisect.bisect_left(lookup, i - k)
right = bisect.bisect_right(lookup, i + k)
if left < right:
result.append(i)
return result
```		 class Solution(object): def beautifulIndices(self, s, a, b, k): """ :type s: str :type a: str :type b: str :type k: int :rtype: List[int] """ def getPrefix(pattern): prefix = [-1]*len(pattern) j = -1 for i in range(1, len(pattern)): while j+1 > 0 and pattern[j+1] != pattern[i]: j = prefix[j] if pattern[j+1] == pattern[i]: j += 1 prefix[i] = j return prefix def KMP(text, pattern): prefix = getPrefix(pattern) j = -1 for i in range(len(text)): while j+1 > 0 and pattern[j+1] != text[i]: j = prefix[j] if pattern[j+1] == text[i]: j += 1 if j+1 == len(pattern): yield i-j j = prefix[j] result = [] if not (len(a) <= len(s) and len(b) <= len(s)): return result lookup = list(KMP(s, b)) j = 0 for i in KMP(s, a): while j < len(lookup) and lookup[j] < i-k: j += 1 if j < len(lookup) and lookup[j] <= i+k: result.append(i) return result
kimi ```python
for i in KMP(s, a):
j = 0
while j < len(lookup) and abs(lookup[j] - i) > k:
j += 1
if j < len(lookup):
result.append(i)
return sorted(result)
```		 class Solution(object): def beautifulIndices(self, s, a, b, k): """ :type s: str :type a: str :type b: str :type k: int :rtype: List[int] """ def getPrefix(pattern): prefix = [-1]*len(pattern) j = -1 for i in range(1, len(pattern)): while j+1 > 0 and pattern[j+1] != pattern[i]: j = prefix[j] if pattern[j+1] == pattern[i]: j += 1 prefix[i] = j return prefix def KMP(text, pattern): prefix = getPrefix(pattern) j = -1 for i in range(len(text)): while j+1 > 0 and pattern[j+1] != text[i]: j = prefix[j] if pattern[j+1] == text[i]: j += 1 if j+1 == len(pattern): yield i-j j = prefix[j] result = [] if not (len(a) <= len(s) and len(b) <= len(s)): return result lookup = list(KMP(s, b)) j = 0 for i in KMP(s, a): while j < len(lookup) and lookup[j] < i-k: j += 1 if j < len(lookup) and lookup[j] <= i+k: result.append(i) return result
minimax ```python
for i in range(len(a)):
for j in range(len(s) - len(a) + 1):
if s[j:j+len(a)] == a:
for idx in lookup:
if abs(j - idx) <= k:
result.append(j)
break
return sorted(set(result))
```		 class Solution(object): def beautifulIndices(self, s, a, b, k): """ :type s: str :type a: str :type b: str :type k: int :rtype: List[int] """ def getPrefix(pattern): prefix = [-1]*len(pattern) j = -1 for i in range(1, len(pattern)): while j+1 > 0 and pattern[j+1] != pattern[i]: j = prefix[j] if pattern[j+1] == pattern[i]: j += 1 prefix[i] = j return prefix def KMP(text, pattern): prefix = getPrefix(pattern) j = -1 for i in range(len(text)): while j+1 > 0 and pattern[j+1] != text[i]: j = prefix[j] if pattern[j+1] == text[i]: j += 1 if j+1 == len(pattern): yield i-j j = prefix[j] result = [] if not (len(a) <= len(s) and len(b) <= len(s)): return result lookup = list(KMP(s, b)) j = 0 for i in KMP(s, a): while j < len(lookup) and lookup[j] < i-k: j += 1 if j < len(lookup) and lookup[j] <= i+k: result.append(i) return result
wenxinyiyan ```python
a_indices = list(KMP(s, a))

for idx in a_indices:
for lookup_idx in lookup:
if abs(lookup_idx - idx) <= k:
result.append(idx)
break

return sorted(set(result))
```
**Note**: The provided solution uses the Knuth-Morris-Pratt (KMP) algorithm to efficiently find all occurrences of substrings `a` and `b` within the string `s`. However, the solution has a potential efficiency issue due to the nested loop used to check the condition `|j - i| <= k` for each occurrence of `a`. This approach may not be optimal for very long strings or large values of `k`.

To optimize the solution further, you could consider using additional data structures, such as interval trees or sorted sets, to efficiently query the existence of indices `j` within the range `[i - k, i + k]` for each occurrence `i` of substring `a`. However, implementing such data structures is beyond the scope of this simple completion task.

The provided solution should work correctly for most cases and is sufficient to demonstrate the basic idea of solving the problem.		 class Solution(object): def beautifulIndices(self, s, a, b, k): """ :type s: str :type a: str :type b: str :type k: int :rtype: List[int] """ def getPrefix(pattern): prefix = [-1]*len(pattern) j = -1 for i in range(1, len(pattern)): while j+1 > 0 and pattern[j+1] != pattern[i]: j = prefix[j] if pattern[j+1] == pattern[i]: j += 1 prefix[i] = j return prefix def KMP(text, pattern): prefix = getPrefix(pattern) j = -1 for i in range(len(text)): while j+1 > 0 and pattern[j+1] != text[i]: j = prefix[j] if pattern[j+1] == text[i]: j += 1 if j+1 == len(pattern): yield i-j j = prefix[j] result = [] if not (len(a) <= len(s) and len(b) <= len(s)): return result lookup = list(KMP(s, b)) j = 0 for i in KMP(s, a): while j < len(lookup) and lookup[j] < i-k: j += 1 if j < len(lookup) and lookup[j] <= i+k: result.append(i) return result
zhipu ```
for i in KMP(s, a):
left = bisect.bisect_left(lookup, i - k)
right = bisect.bisect_right(lookup, i + k)
if left < right:
result.append(i)
return result
```		 class Solution(object): def beautifulIndices(self, s, a, b, k): """ :type s: str :type a: str :type b: str :type k: int :rtype: List[int] """ def getPrefix(pattern): prefix = [-1]*len(pattern) j = -1 for i in range(1, len(pattern)): while j+1 > 0 and pattern[j+1] != pattern[i]: j = prefix[j] if pattern[j+1] == pattern[i]: j += 1 prefix[i] = j return prefix def KMP(text, pattern): prefix = getPrefix(pattern) j = -1 for i in range(len(text)): while j+1 > 0 and pattern[j+1] != text[i]: j = prefix[j] if pattern[j+1] == text[i]: j += 1 if j+1 == len(pattern): yield i-j j = prefix[j] result = [] if not (len(a) <= len(s) and len(b) <= len(s)): return result lookup = list(KMP(s, b)) j = 0 for i in KMP(s, a): while j < len(lookup) and lookup[j] < i-k: j += 1 if j < len(lookup) and lookup[j] <= i+k: result.append(i) return result
deepseek-v3 ```python
a_indices = list(KMP(s, a))
if not lookup:
return result

for i in a_indices:
low = max(0, i - k)
high = min(len(s) - len(b), i + k)
left = bisect.bisect_left(lookup, low)
right = bisect.bisect_right(lookup, high)
if left < right:
result.append(i)

return result
```		 class Solution(object): def beautifulIndices(self, s, a, b, k): """ :type s: str :type a: str :type b: str :type k: int :rtype: List[int] """ def getPrefix(pattern): prefix = [-1]*len(pattern) j = -1 for i in range(1, len(pattern)): while j+1 > 0 and pattern[j+1] != pattern[i]: j = prefix[j] if pattern[j+1] == pattern[i]: j += 1 prefix[i] = j return prefix def KMP(text, pattern): prefix = getPrefix(pattern) j = -1 for i in range(len(text)): while j+1 > 0 and pattern[j+1] != text[i]: j = prefix[j] if pattern[j+1] == text[i]: j += 1 if j+1 == len(pattern): yield i-j j = prefix[j] result = [] if not (len(a) <= len(s) and len(b) <= len(s)): return result lookup = list(KMP(s, b)) j = 0 for i in KMP(s, a): while j < len(lookup) and lookup[j] < i-k: j += 1 if j < len(lookup) and lookup[j] <= i+k: result.append(i) return result