Time: 1363 ms (65.95%), Space: 30 MB (89.22%) - LeetHub

1286-constrained-subsequence-sum/1286-constrained-subsequence-sum.py

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+class Solution:
+  def constrainedSubsetSum(self, nums: List[int], k: int) -> int:
+    # dp[i] := max sum of non-empty subsequence in nums[0..i]
+    dp = [0] * len(nums)
+    # dq stores dp[i - k], dp[i - k + 1], ..., dp[i - 1] whose values are > 0
+    # in decreasing order.
+    dq = collections.deque()
+
+    for i, num in enumerate(nums):
+      if dq:
+        dp[i] = max(dq[0], 0) + num
+      else:
+        dp[i] = num
+      while dq and dq[-1] < dp[i]:
+        dq.pop()
+      dq.append(dp[i])
+      if i >= k and dp[i - k] == dq[0]:
+        dq.popleft()
+
+    return max(dp)