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Problem solution · Python

Longest Increasing Subsequence II

Longest Increasing Subsequence II: a Python solution using segment tree or range structure. Learn the idea, check the complexity, and read the full code, with credit to Kamyu LeetCode Solutions.

Technique
Segment tree or range structure
Source
Kamyu LeetCode Solutions
Length
62 lines
Start with the idea.

Try the problem first. If you get stuck, read the approach below, then write your own solution. The full code is at the bottom.

Approach

Segment tree or range structure

For Longest Increasing Subsequence II, the implementation stores interval information in a range-query data structure so updates and queries avoid rescanning the full input.

  1. Choose the aggregate stored for each interval or prefix.
  2. Build or initialize the structure from the input.
  3. Apply updates and combine the affected nodes to answer each query.

Code notes

  • 62 lines of Python from the credited upstream file longest-increasing-subsequence-ii.py.
  • The implementation visibly relies on sequence storage.
  • No explicit loop blocks detected.

Complexity

Count the build once, then multiply the logarithmic update or query path by the number of operations.

Check the problem constraints before deciding whether this complexity will pass.

Source

Code and credit

This code comes from Kamyu LeetCode Solutions by kamyu104 and is used under the MIT licence.

Open problem ↗Original source ↗
Full codeLongest Increasing Subsequence II · PythonPython
Use this to learn the idea, then write your own version.
# Time:  O(nlogn)# Space: O(n) import bisect  # Range Maximum Queryclass SegmentTree(object):    def __init__(self, N,                 build_fn=lambda _: 0,                 query_fn=lambda x, y: y if x is None else x if y is None else max(x, y),                 update_fn=lambda x: x):        self.tree = [None]*(2*2**((N-1).bit_length()))        self.base = len(self.tree)//2        self.query_fn = query_fn        self.update_fn = update_fn        for i in xrange(self.base, self.base+N):            self.tree[i] = build_fn(i-self.base)        for i in reversed(xrange(1, self.base)):            self.tree[i] = query_fn(self.tree[2*i], self.tree[2*i+1])     def update(self, i, h):        x = self.base+i        self.tree[x] = self.update_fn(h)        while x > 1:            x //= 2            self.tree[x] = self.query_fn(self.tree[x*2], self.tree[x*2+1])     def query(self, L, R):        if L > R:            return 0        L += self.base        R += self.base        left = right = None        while L <= R:            if L & 1:                left = self.query_fn(left, self.tree[L])                L += 1            if R & 1 == 0:                right = self.query_fn(self.tree[R], right)                R -= 1            L //= 2            R //= 2        return self.query_fn(left, right)  # segment tree with coordinate compressionclass Solution(object):    def lengthOfLIS(self, nums, k):        """        :type nums: List[int]        :type k: int        :rtype: int        """        sorted_nums = sorted({x-1 for x in nums})        num_to_idx = {x:i for i, x in enumerate(sorted_nums)}        st = SegmentTree(len(num_to_idx))        for x in nums:            x -= 1            st.update(num_to_idx[x], st.query(bisect.bisect_left(sorted_nums, x-k), num_to_idx[x]-1)+1)        return st.tree[1]  # st.query(0, len(num_to_idx)-1)

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