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Master essential array techniques including two pointers, sliding window, and prefix sums for efficient problem solving with O(n) patterns.
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| name | array-techniques |
| description | Master essential array techniques including two pointers, sliding window, and prefix sums for efficient problem solving with O(n) patterns. |
| sasmp_version | 1.3.0 |
| bonded_agent | 01-arrays-lists |
| bond_type | PRIMARY_BOND |
| atomic_responsibility | array_pattern_execution |
| version | 2.0.0 |
| parameter_validation | {"strict":true,"rules":[{"name":"array_input","type":"list","required":true,"constraints":{"min_length":0,"max_length":100000}},{"name":"target","type":"integer","required":false},{"name":"window_size","type":"integer","required":false,"constraints":{"min_value":1}}]} |
| retry_logic | {"max_attempts":3,"backoff_ms":[100,200,400],"retryable_errors":["timeout","memory_exceeded"]} |
| logging_hooks | {"on_start":true,"on_complete":true,"on_error":true,"log_format":"[ARR-SKILL] {timestamp} | {operation} | {status}"} |
| complexity_annotations | {"two_pointers":{"time":"O(n)","space":"O(1)"},"sliding_window":{"time":"O(n)","space":"O(1)"},"prefix_sum":{"time":"O(n) build, O(1) query","space":"O(n)"}} |
Atomic Responsibility: Execute array manipulation patterns with optimal complexity.
from typing import List
def remove_element(nums: List[int], val: int) -> int:
"""
Remove all occurrences of val in-place.
Time: O(n), Space: O(1)
Args:
nums: Input array (modified in-place)
val: Value to remove
Returns:
New length of array
Raises:
ValueError: If nums is None
"""
if nums is None:
raise ValueError("Input array cannot be None")
write_ptr = 0
for read_ptr in range(len(nums)):
if nums[read_ptr] != val:
nums[write_ptr] = nums[read_ptr]
write_ptr += 1
return write_ptr
def two_sum_sorted(arr: List[int], target: int) -> List[int]:
"""
Find two indices in sorted array that sum to target.
Time: O(n), Space: O(1)
Args:
arr: Sorted input array
target: Target sum
Returns:
List of two indices, or empty list if not found
"""
if not arr or len(arr) < 2:
return []
left, right = , (arr) -
left < right:
total = arr[left] + arr[right]
total == target:
[left, right]
total < target:
left +=
:
right -=
[]
def max_sum_subarray(nums: List[int], k: int) -> int:
"""
Find maximum sum of contiguous subarray of size k.
Time: O(n), Space: O(1)
Args:
nums: Input array
k: Window size
Returns:
Maximum sum, or 0 if invalid input
Raises:
ValueError: If k > len(nums) or k <= 0
"""
if not nums or k <= 0:
raise ValueError("Invalid input: empty array or k <= 0")
if k > len(nums):
raise ValueError(f"Window size {k} exceeds array length {len(nums)}")
window_sum = sum(nums[:k])
max_sum = window_sum
for i in range(k, len(nums)):
window_sum = window_sum - nums[i - k] + nums[i]
max_sum = max(max_sum, window_sum)
return max_sum
def min_subarray_len(target: int, nums: List[int]) -> int:
"""
Find minimal length of subarray with sum >= target.
Time: O(n), Space: O(1)
Args:
target: Minimum sum required
nums: Input array of positive integers
Returns:
Minimum length, or 0 if no valid subarray
"""
if not nums:
return 0
left = 0
current_sum = 0
min_len = float('inf')
for right in range(len(nums)):
current_sum += nums[right]
while current_sum >= target:
min_len = min(min_len, right - left + 1)
current_sum -= nums[left]
left += 1
return min_len if min_len != float('inf') else 0
class PrefixSum:
"""
Precompute cumulative sums for O(1) range queries.
Time: O(n) initialization, O(1) query
Space: O(n)
"""
def __init__(self, nums: List[int]):
if nums is None:
raise ValueError("Input array cannot be None")
self.prefix = [0]
for num in nums:
self.prefix.append(self.prefix[-1] + num)
def range_sum(self, left: int, right: int) -> int:
"""Get sum of elements from left to right (inclusive)."""
if left < 0 or right >= len(self.prefix) - 1:
raise IndexError(f"Indices out of bounds: [{left}, {right}]")
return self.prefix[right + 1] - self.prefix[left]
import pytest
class TestArrayTechniques:
def test_two_sum_sorted_found(self):
assert two_sum_sorted([1, 2, 3, 4, 5], 9) == [3, 4]
def test_two_sum_sorted_not_found(self):
assert two_sum_sorted([1, 2, 3], 10) == []
def test_sliding_window_basic(self):
assert max_sum_subarray([1, 2, 3, 4, 5], 2) == 9
def test_prefix_sum_range(self):
ps = PrefixSum([1, 2, 3, 4, 5])
assert ps.range_sum(1, 3) == 9
def test_min_subarray_len(self):
assert min_subarray_len(7, [2, 3, 1, 2, 4, 3]) == 2
| Issue | Cause | Solution |
|---|---|---|
| Off-by-one error | Wrong index bounds | Use len(arr) - 1 for last valid index |
| Infinite loop | Window never shrinks | Ensure left pointer advances |
| Wrong sum | Missing edge case | Handle empty array, single element |
□ Input validation (None, empty, invalid k)?
□ Pointer bounds checked (left < right)?
□ Window sum updated correctly?
□ Edge cases: single element, all same values?