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Problem solution · C++

Balanced K Factor Decomposition

Balanced K Factor Decomposition: a C++ solution using depth-first search. Learn the idea, check the complexity, and read the full code, with credit to Kamyu LeetCode Solutions.

Technique
Depth-first search
Source
Kamyu LeetCode Solutions
Length
129 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

Depth-first search

For Balanced K Factor Decomposition, the implementation follows one branch at a time, making it suitable for components, trees, backtracking, or dependency exploration.

  1. Define the state carried into one recursive or stack frame.
  2. Mark or choose the current state before exploring children.
  3. Combine child results or undo the choice when the branch finishes.

Code notes

  • 129 lines of C++ from the credited upstream file balanced-k-factor-decomposition.cpp.
  • The implementation visibly relies on sequence storage.
  • 5 loop blocks detected.

Complexity

Count unique states for graph traversal; for backtracking, count the branching factor and maximum depth.

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 codeBalanced K Factor Decomposition · C++C++
Use this to learn the idea, then write your own version.
// Time:  precompute: O(rlogr)//        runtime:    O(k * (logn)^(k - 1))// Space: O(rlogr) // backtracking, number theoryconst auto& factors = [](int n) {    vector<vector<int>> result(n + 1);    for (int i = 1; i <= n; ++i) {        for (int j = i; j <= n; j += i) {            result[j].emplace_back(i);        }    }    return result;}; const int MAX_N = 1e5;const auto& FACTORS = factors(MAX_N);class Solution {public:    vector<int> minDifference(int n, int k) {        vector<int> result, curr;        function<void (int)> backtracking = [&](int remain) {            const int start = !empty(curr) ? curr.back() : 1;            if (size(curr) == k - 1) {                if (remain >= start) {                    curr.emplace_back(remain);                    if (empty(result) || result.back() - result[0] > curr.back() - curr[0]) {                        result = curr;                    }                    curr.pop_back();                }                return;            }            const auto& factors = FACTORS[remain];            for (auto it = lower_bound(cbegin(factors), cend(factors), start); it != cend(factors); ++it) {                curr.emplace_back(*it);                backtracking(remain / *it);                curr.pop_back();            }        };         backtracking(n);        return result;    }}; // Time:  O(k * (n^(1/2) * n^(1/4) * n^(1/8) * n^(1/6) + n^(1/2) * n^(1/4) * n^(1/8) + n^(1/2) * n^(1/4) + n^(1/2))) <= O(k^2 * n)// Space: O(k)// backtracking, number theoryclass Solution2 {public:    vector<int> minDifference(int n, int k) {        vector<int> result, curr;        function<void (int)> backtracking = [&](int remain) {            const int start = !empty(curr) ? curr.back() : 1;            if (size(curr) == k - 1) {                if (remain >= start) {                    curr.emplace_back(remain);                    if (empty(result) || result.back() - result[0] > curr.back() - curr[0]) {                        result = curr;                    }                    curr.pop_back();                }                return;            }            for (int i = 1; i * i <= remain; ++i) {                if (remain % i) {                    continue;                }                const int j = remain / i;                if (i >= start) {                    curr.emplace_back(i);                    backtracking(j);                    curr.pop_back();                }                if (j == i) {                    continue;                }                if (j >= start) {                    curr.emplace_back(j);                    backtracking(i);                    curr.pop_back();                }            }        };         backtracking(n);        return result;    }}; // Time:  O(2^(k-1) * k * n)// Space: O(k)// backtracking, number theoryclass Solution3 {public:    vector<int> minDifference(int n, int k) {        vector<int> result, curr;        function<void (int)> backtracking = [&](int remain) {            if (size(curr) == k - 1) {                curr.emplace_back(remain);                if (empty(result) || ranges::max(result) - ranges::min(result) > ranges::max(curr) - ranges::min(curr)) {                    result = curr;                }                curr.pop_back();                return;            }            for (int i = 1; i * i <= remain; ++i) {                if (remain % i) {                    continue;                }                const int j = remain / i;                curr.emplace_back(i);                backtracking(j);                curr.pop_back();                if (j == i) {                    continue;                }                curr.emplace_back(j);                backtracking(i);                curr.pop_back();            }        };         backtracking(n);        return result;    }};

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