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Problem solution · C++

Kth Smallest Amount With Single Denomination Combination

Kth Smallest Amount With Single Denomination Combination: 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
48 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 Amount With Single Denomination Combination, 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

  • 48 lines of C++ from the credited upstream file 3116.cpp.
  • The implementation visibly relies on sequence storage.
  • 5 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 Amount With Single Denomination Combination · C++C++
Use this to learn the idea, then write your own version.
class Solution { public:  long long findKthSmallest(vector<int>& coins, int k) {    const vector<vector<long>> sizeToLcms = getSizeToLcms(coins);    long l = 0;    long r = static_cast<long>(k) * ranges::min(coins);     while (l < r) {      const long m = (l + r) / 2;      if (numDenominationsNoGreaterThan(sizeToLcms, m) >= k)        r = m;      else        l = m + 1;    }     return l;  }  private:  // Returns the number of denominations <= m.  long numDenominationsNoGreaterThan(const vector<vector<long>>& sizeToLcms,                                     long m) {    long res = 0;    for (int sz = 1; sz < sizeToLcms.size(); ++sz)      for (const long lcm : sizeToLcms[sz])        // Principle of Inclusion-Exclusion (PIE)        res += m / lcm * pow(-1, sz + 1);    return res;  };   // Returns the LCMs for each number of combination of coins.  vector<vector<long>> getSizeToLcms(const vector<int>& coins) {    const int n = coins.size();    const int maxMask = 1 << n;    vector<vector<long>> sizeToLcms(n + 1);     for (unsigned mask = 1; mask < maxMask; ++mask) {      long lcmOfSelectedCoins = 1;      for (int i = 0; i < n; ++i)        if (mask >> i & 1)          lcmOfSelectedCoins = lcm(lcmOfSelectedCoins, coins[i]);      sizeToLcms[popcount(mask)].push_back(lcmOfSelectedCoins);    }     return sizeToLcms;  }};

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