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Problem solution · Python

Number of Pairs After Increment

Number of Pairs After Increment: 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
51 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 Number of Pairs After Increment, 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

  • 51 lines of Python from the credited upstream file number-of-pairs-after-increment.py.
  • The implementation visibly relies on sequence storage, hash lookup.
  • 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 codeNumber of Pairs After Increment · PythonPython
Use this to learn the idea, then write your own version.
# Time:  O(n + m + q * sqrt(m * n)), n = len(nums1), m = len(nums2)# Space: O(n + m) import collections  # freq table, sqrt decompositionclass Solution(object):    def numberOfPairs(self, nums1, nums2, queries):        """        :type nums1: List[int]        :type nums2: List[int]        :type queries: List[List[int]]        :rtype: List[int]        """        def ceil_divide(a, b):            return (a+b-1)//b         def update(cnt, left, right, val):            for i in xrange(left, right+1):                cnt[nums2[i]] -= 1                if not cnt[nums2[i]]:                    del cnt[nums2[i]]                nums2[i] += val                cnt[nums2[i]] += 1            cnt1 = collections.defaultdict(int)        for x in nums1:            cnt1[x] += 1        B = int((len(cnt1)*len(nums2))**0.5)+1        cnt2 = [collections.defaultdict(int) for _ in xrange(ceil_divide(len(nums2), B))]        for i in xrange(len(cnt2)):             for j in xrange(i*B, min(i*B+B, len(nums2))):                cnt2[i][nums2[j]] += 1        lazy = [0]*len(cnt2)        result = []        for q in queries:            if q[0] == 2:                tot = q[1]                result.append(sum(cnt2[i][(tot-x)-lazy[i]]*c for x, c in cnt1.iteritems() for i in xrange(len(cnt2)) if (tot-x)-lazy[i] in cnt2[i]))                continue            x, y, val = q[1], q[2], q[3]            if x//B == y//B:                update(cnt2[x//B], x, y, val)                continue            update(cnt2[x//B], x, ((x//B)+1)*B-1, val)            for i in xrange((x//B)+1, y//B):                lazy[i] += val            update(cnt2[y//B], (y//B)*B, y, val)        return result

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