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Problem solution · C++

Kth Smallest Product of Two Sorted Arrays

Kth Smallest Product of Two Sorted Arrays: a C++ solution using sliding window or two pointers. Learn the idea, check the complexity, and read the full code, with credit to walkccc LeetCode Solutions.

Technique
Sliding window or two pointers
Source
walkccc LeetCode Solutions
Length
64 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 Kth Smallest Product of Two Sorted Arrays, 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

  • 64 lines of C++ from the credited upstream file 2040.cpp.
  • The implementation visibly relies on sequence storage.
  • 4 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 walkccc LeetCode Solutions by P.-Y. Chen (walkccc) and is used under the MIT licence.

Open problem ↗Original source ↗
Full codeKth Smallest Product of Two Sorted Arrays · C++C++
Use this to learn the idea, then write your own version.
class Solution { public:  long long kthSmallestProduct(vector<int>& nums1, vector<int>& nums2,                               long long k) {    vector<int> A1;    vector<int> A2;    vector<int> B1;    vector<int> B2;     seperate(nums1, A1, A2);    seperate(nums2, B1, B2);     const long negCount = A1.size() * B2.size() + A2.size() * B1.size();    int sign = 1;     if (k > negCount) {      k -= negCount;  //  Find the (k - negCount)-th positive.    } else {      k = negCount - k + 1;  // Find the (negCount - k + 1)-th abs(negative).      sign = -1;      swap(B1, B2);    }     long l = 0;    long r = 1e10;     while (l < r) {      const long m = (l + r) / 2;      if (numProductNoGreaterThan(A1, B1, m) +              numProductNoGreaterThan(A2, B2, m) >=          k)        r = m;      else        l = m + 1;    }     return sign * l;  }  private:  void seperate(const vector<int>& arr, vector<int>& A1, vector<int>& A2) {    for (const int a : arr)      if (a < 0)        A1.push_back(-a);      else        A2.push_back(a);    ranges::reverse(A1);  // Reverse to sort ascending  }   long numProductNoGreaterThan(const vector<int>& A, const vector<int>& B,                               long m) {    long count = 0;    int j = B.size() - 1;    // For each a, find the first index j s.t. a * B[j] <= m    // So numProductNoGreaterThan m for this row will be j + 1    for (const long a : A) {      while (j >= 0 && a * B[j] > m)        --j;      count += j + 1;    }    return count;  }};

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