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Problem solution · Python

Longest Substring of One Repeating Character

Longest Substring of One Repeating Character: 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
147 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 Substring of One Repeating Character, 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

  • 147 lines of Python from the credited upstream file longest-substring-of-one-repeating-character.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 Substring of One Repeating Character · PythonPython
Use this to learn the idea, then write your own version.
# Time:  O(nlogn)# Space: O(n) import itertools  # Template:# https://github.com/kamyu104/FacebookHackerCup-2021/blob/main/Round%203/auth_ore_ization.pyclass SegmentTree(object):    def __init__(self, N,                 build_fn=lambda _: float("inf"),                 query_fn=lambda x, y: x if y is None else min(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])  # segment treeclass Solution(object):    def longestRepeating(self, s, queryCharacters, queryIndices):        """        :type s: str        :type queryCharacters: str        :type queryIndices: List[int]        :rtype: List[int]        """        LEFT, RIGHT, LEFT_LEN, RIGHT_LEN, LEN, MAX_LEN, SIZE = xrange(7)        def build(i):            return update(s[i])         def update(y):            result = [0]*SIZE            result[LEFT] = result[RIGHT] = y            result[LEN] = result[LEFT_LEN] = result[RIGHT_LEN] = result[MAX_LEN] = 1            return result         def query(x, y):            return x if y is None else \                   [x[LEFT],                    y[RIGHT],                    x[LEFT_LEN]+(y[LEFT_LEN] if x[LEFT_LEN] == x[LEN] and x[RIGHT] == y[LEFT] else 0),                    y[RIGHT_LEN]+(x[RIGHT_LEN] if y[RIGHT_LEN] == y[LEN] and y[LEFT] == x[RIGHT] else 0),                    x[LEN]+y[LEN],                    max(x[MAX_LEN], y[MAX_LEN], x[RIGHT_LEN]+y[LEFT_LEN] if x[RIGHT] == y[LEFT] else 0)]                result = []        st = SegmentTree(len(s), build_fn=build, query_fn=query, update_fn=update)        for c, i in itertools.izip(queryCharacters, queryIndices):            st.update(i, c)            result.append(st.tree[1][MAX_LEN])        return result  # Time:  O(nlogn)# Space: O(n)import itertools  # Template:# https://github.com/kamyu104/FacebookHackerCup-2021/blob/main/Round%203/auth_ore_ization.pyclass SegmentTree2(object):    def __init__(self, N,                 build_fn=lambda _: float("inf"),                 query_fn=lambda x, y: y if x is None else x if y is None else min(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 None        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 treeclass Solution2(object):    def longestRepeating(self, s, queryCharacters, queryIndices):        """        :type s: str        :type queryCharacters: str        :type queryIndices: List[int]        :rtype: List[int]        """        LEFT, RIGHT, LEFT_LEN, RIGHT_LEN, LEN, MAX_LEN, SIZE = xrange(7)        def build(i):            return update(s[i])         def update(y):            result = [0]*SIZE            result[LEN] = result[LEFT_LEN] = result[RIGHT_LEN] = result[MAX_LEN] = 1            result[LEFT] = result[RIGHT] = y            return result         def query(x, y):            return y if x is None else x if y is None else \                   [x[LEFT],                    y[RIGHT],                    x[LEFT_LEN]+(y[LEFT_LEN] if x[LEFT_LEN] == x[LEN] and x[RIGHT] == y[LEFT] else 0),                    y[RIGHT_LEN]+(x[RIGHT_LEN] if y[RIGHT_LEN] == y[LEN] and y[LEFT] == x[RIGHT] else 0),                    x[LEN]+y[LEN],                    max(x[MAX_LEN], y[MAX_LEN], x[RIGHT_LEN]+y[LEFT_LEN] if x[RIGHT] == y[LEFT] else 0)]                result = []        st = SegmentTree2(len(s), build_fn=build, query_fn=query, update_fn=update)        for c, i in itertools.izip(queryCharacters, queryIndices):            st.update(i, c)            result.append(st.query(0, len(s)-1)[MAX_LEN])        return result

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