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Problem solution · Python

Query Kth Smallest Trimmed Number

Query Kth Smallest Trimmed Number: a Python solution using sliding window or two pointers. Learn the idea, check the complexity, and read the full code, with credit to Kamyu LeetCode Solutions.

Technique
Sliding window or two pointers
Source
Kamyu LeetCode Solutions
Length
122 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

Sliding window or two pointers

For Query Kth Smallest Trimmed Number, the implementation maintains a moving interval and updates only the information that enters or leaves the window.

  1. Choose the invariant that makes a window valid or useful.
  2. Advance the right boundary and add the new element.
  3. Move the left boundary only as needed while maintaining the invariant and updating the answer.

Code notes

  • 122 lines of Python from the credited upstream file query-kth-smallest-trimmed-number.py.
  • The implementation visibly relies on sequence storage.
  • No explicit loop blocks detected.

Complexity

Confirm that neither pointer moves backwards; if so, the scan is usually linear apart from the window’s data-structure 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 codeQuery Kth Smallest Trimmed Number · PythonPython
Use this to learn the idea, then write your own version.
# Time:  O(q + n * t)# Space: O(t + n + q) # radix sortclass Solution(object):    def smallestTrimmedNumbers(self, nums, queries):        """        :type nums: List[str]        :type queries: List[List[int]]        :rtype: List[int]        """        max_t = max(t for _, t in queries)        lookup = [[] for _ in xrange(max_t+1)]        for i, (k, t) in enumerate(queries):            lookup[t].append((k, i))        result = [0]*len(queries)        idxs = range(len(nums))        for l in xrange(1, max_t+1):            cnt = [0]*10            for i in idxs:                d = int(nums[i][-l])                cnt[d] += 1            for d in xrange(9):                cnt[d+1] += cnt[d]            new_idxs = [0]*len(nums)            for i in reversed(idxs):                d = int(nums[i][-l])                cnt[d] -= 1                new_idxs[cnt[d]] = i            idxs = new_idxs            for k, i in lookup[l]:                result[i] = idxs[k-1]        return result             # Time:  O(q * n * t) on average# Space: O(n + q)import random  # quick selectclass Solution2(object):    def smallestTrimmedNumbers(self, nums, queries):        """        :type nums: List[str]        :type queries: List[List[int]]        :rtype: List[int]        """        def nth_element(nums, n, compare=lambda a, b: a < b):            def tri_partition(nums, left, right, target, compare):                mid = left                while mid <= right:                    if nums[mid] == target:                        mid += 1                    elif compare(nums[mid], target):                        nums[left], nums[mid] = nums[mid], nums[left]                        left += 1                        mid += 1                    else:                        nums[mid], nums[right] = nums[right], nums[mid]                        right -= 1                return left, right             left, right = 0, len(nums)-1            while left <= right:                pivot_idx = random.randint(left, right)                pivot_left, pivot_right = tri_partition(nums, left, right, nums[pivot_idx], compare)                if pivot_left <= n <= pivot_right:                    return                elif pivot_left > n:                    right = pivot_left-1                else:  # pivot_right < n.                    left = pivot_right+1         def compare(a, b):            for i in xrange(len(nums[a])-t, len(nums[a])):                if nums[a][i] < nums[b][i]:                    return True                if nums[a][i] > nums[b][i]:                    return False            return cmp(a, b) < 0         result = []        idxs = range(len(nums))        for k, t in queries:            nth_element(idxs, k-1, compare=compare)            result.append(idxs[k-1])        return result  # Time:  O(q + nlogn * t)# Space: O(t + n + q)# sortclass Solution3(object):    def smallestTrimmedNumbers(self, nums, queries):        """        :type nums: List[str]        :type queries: List[List[int]]        :rtype: List[int]        """        def compare(a, b):            for i in xrange(len(nums[a])-t, len(nums[a])):                if nums[a][i] < nums[b][i]:                    return -1                if nums[a][i] > nums[b][i]:                    return 1            return cmp(a, b)         max_t = max(t for _, t in queries)        lookup = [[] for _ in xrange(max_t+1)]        for i, (k, t) in enumerate(queries):            lookup[t].append((k, i))        result = [0]*len(queries)        idxs = range(len(nums))        for t in xrange(1, max_t+1):            if not lookup[t]:                continue            idxs.sort(cmp=compare)            for k, i in lookup[t]:                result[i] = idxs[k-1]        return result

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