DDSA Solutions

1438. Longest Continuous Subarray With Absolute Diff Less Than or Equal to Limit

MediumView on LeetCode
ArrayQueueSliding WindowHeap (Priority Queue)Monotonic Queue

Problem Overview

Sliding window with a monotone deque tracking min and max.

Intuition

Sliding window with a monotone deque tracking min and max. Window is valid when max-min <= limit.

Algorithm

  1. 1Two deques: max-deque (decreasing) and min-deque (increasing).
  2. 2Expand right. When max-min > limit, shrink left (remove from fronts of deques if index out of window).
  3. 3Track max window size.

Common Pitfalls

  • •Two separate deques for min and max. Shrink window when constraint violated.
1438.cpp
C++
class Solution {
 public:
  int longestSubarray(vector<int>& nums, int limit) {
    int ans = 1;
    deque<int> minQ;
    deque<int> maxQ;

    for (int l = 0, r = 0; r < nums.size(); ++r) {
      while (!minQ.empty() && minQ.back() > nums[r])
        minQ.pop_back();
      minQ.push_back(nums[r]);
      while (!maxQ.empty() && maxQ.back() < nums[r])
        maxQ.pop_back();
      maxQ.push_back(nums[r]);
      while (maxQ.front() - minQ.front() > limit) {
        if (minQ.front() == nums[l])
          minQ.pop_front();
        if (maxQ.front() == nums[l])
          maxQ.pop_front();
        ++l;
      }
      ans = max(ans, r - l + 1);
    }

    return ans;
  }
};
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