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Problem solution · Java

Paint House III

Paint House III: a Java 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
34 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

  • 34 lines of Java from the credited upstream file 1473.java.
  • 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 · JavaJava
Use this to learn the idea, then write your own version.
class Solution {  public int minCost(int[] houses, int[][] cost, int m, int n, int target) {    int[][][] mem = new int[target + 1][m][n + 1];    // Initialize `prevColor` to 0 (the virtual neighbor).    final int c = minCost(houses, cost, m, n, target, 0, 0, mem);    return c == MAX ? -1 : c;  }   private static final int MAX = 1_000_001;   // Returns the minimum cost to paint houses[i..m) into k neighborhoods, where  // there are houses[i - 1] colors = prevColor.  public int minCost(int[] houses, int[][] cost, int m, int n, int k, int i, int prevColor,                     int[][][] mem) {    if (i == m || k < 0)      return k == 0 ? 0 : MAX;    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] ? 0 : 1), i + 1, houses[i],                     mem);     int ans = MAX;     // Try to paint the houses[i] with each color in 1..n.    for (int color = 1; color <= n; ++color)      ans = Math.min(ans, cost[i][color - 1] + minCost(houses, cost, m, n,                                                       k - (prevColor == color ? 0 : 1), i + 1,                                                       color, mem));     return mem[k][i][prevColor] = ans;  }}

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