CPMagical CP Library

Problem solution · C++

Paint House III

Paint House III: a C++ solution using direct simulation. Learn the idea, check the complexity, and read the full code, with credit to walkccc LeetCode Solutions.

Technique
Direct simulation
Source
walkccc LeetCode Solutions
Length
39 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

Direct simulation

For Paint House III, the implementation follows the problem’s operations directly while maintaining only the state needed for the next decision.

  1. Translate each rule into one explicit state update.
  2. Maintain the invariant after every processed item.
  3. Return the accumulated state once all relevant input has been handled.

Code notes

  • 39 lines of C++ from the credited upstream file 1473.cpp.
  • The implementation visibly relies on sequence storage.
  • 1 loop block detected.

Complexity

Count the number and nesting of passes over the input, then include the maintained containers in the memory estimate.

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 codePaint House III · C++C++
Use this to learn the idea, then write your own version.
class Solution { public:  int minCost(vector<int>& houses, vector<vector<int>>& cost, int m, int n,              int target) {    vector<vector<vector<int>>> mem(target + 1,                                    vector<vector<int>>(m, vector<int>(n + 1)));    // Initialize `prevColor` to 0 (the virtual neighbor).    const int c = minCost(houses, cost, m, n, target, 0, 0, mem);    return c == kMax ? -1 : c;  }  private:  static constexpr int kMax = 1'000'001;   // Returns the minimum cost to paint houses[i..m) into k neighborhoods, where  // there are houses[i - 1] colors = prevColor.  int minCost(const vector<int>& houses, const vector<vector<int>>& cost,              const int& m, const int& n, int k, int i, int prevColor,              vector<vector<vector<int>>>& mem) {    if (i == m || k < 0)      return k == 0 ? 0 : kMax;    if (mem[k][i][prevColor] > 0)      return mem[k][i][prevColor];    if (houses[i] > 0)  // The house was painted last year.      return minCost(houses, cost, m, n, k - (prevColor != houses[i]), i + 1,                     houses[i], mem);     int res = kMax;     // Try to paint the houses[i] with each color in 1..n.    for (int color = 1; color <= n; ++color)      res = min(res, cost[i][color - 1] + minCost(houses, cost, m, n,                                                  k - (prevColor != color),                                                  i + 1, color, mem));     return mem[k][i][prevColor] = res;  }};

Keep practising

Did this explanation save you time? I'm a Grade 11 student building this free library to make difficult algorithms easier to understand.

Buy me a coffee ↗