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Problem solution · Java

Tiling a Rectangle with the Fewest Squares

Tiling a Rectangle with the Fewest Squares: a Java solution using hash-based lookup. Learn the idea, check the complexity, and read the full code, with credit to walkccc LeetCode Solutions.

Technique
Hash-based lookup
Source
walkccc LeetCode Solutions
Length
50 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

Hash-based lookup

For Tiling a Rectangle with the Fewest Squares, the implementation stores previously seen values or frequencies in a hash table for direct membership and lookup operations.

  1. Decide the key that represents the information needed later.
  2. Update its count or stored state while scanning the input.
  3. Use constant-time expected lookups to detect matches or assemble the result.

Code notes

  • 50 lines of Java from the credited upstream file 1240.java.
  • The implementation visibly relies on sequence storage, hash lookup, ordered lookup.
  • 5 loop blocks detected.

Complexity

Expected hash operations are constant time, but the surrounding scan and the number of stored keys determine total work and memory.

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 codeTiling a Rectangle with the Fewest Squares · JavaJava
Use this to learn the idea, then write your own version.
class Solution {  public int tilingRectangle(int n, int m) {    return tilingRectangle(n, m, 0, new int[m]);  }   private static final int BASE = 13;  private Map<Long, Integer> dp = new HashMap<>();   private int tilingRectangle(int n, int m, long hashedHeights, int[] heights) {    if (dp.containsKey(hashedHeights))      return dp.get(hashedHeights);     final int minHeight = Arrays.stream(heights).min().getAsInt();    if (minHeight == n) // All filled.      return 0;     int ans = m * n;    int start = -1;     for (int i = 0; i < m; ++i)      if (heights[i] == minHeight) {        start = i;        break;      }     // Try to put square of different size that doesn't exceed the width/height.    for (int sz = 1; sz <= Math.min(m - start, n - minHeight); ++sz) {      // heights[start..start + sz) must has the same height.      if (heights[start + sz - 1] != minHeight)        break;      // Put a square of size `sz` to cover heights[start..start + sz).      for (int i = start; i < start + sz; ++i)        heights[i] += sz;      ans = Math.min(ans, tilingRectangle(n, m, hash(heights), heights));      for (int i = start; i < start + sz; ++i)        heights[i] -= sz;    }     dp.put(hashedHeights, 1 + ans);    return 1 + ans;  }   private long hash(int[] heights) {    long hashed = 0;    for (int i = heights.length - 1; i >= 0; --i)      hashed = hashed * BASE + heights[i];    return hashed;  }}

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