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Problem solution · Java

Maximum Value Sum by Placing Three Rooks II

Maximum Value Sum by Placing Three Rooks II: a Java solution using sorting and greedy selection. Learn the idea, check the complexity, and read the full code, with credit to walkccc LeetCode Solutions.

Technique
Sorting and greedy selection
Source
walkccc LeetCode Solutions
Length
62 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

Sorting and greedy selection

For Maximum Value Sum by Placing Three Rooks II, the implementation first exposes a useful order, then scans that order while making locally justified choices.

  1. Choose the key that reveals the greedy or grouping structure.
  2. Sort the relevant records by that key.
  3. Scan in order, maintaining the invariant that makes each local choice safe.

Code notes

  • 62 lines of Java from the credited upstream file 3257.java.
  • The implementation visibly relies on sequence storage, hash lookup, ordered lookup.
  • 9 loop blocks detected.

Complexity

Sorting is typically the dominant term unless the subsequent scan uses a more expensive nested operation.

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 codeMaximum Value Sum by Placing Three Rooks II · JavaJava
Use this to learn the idea, then write your own version.
class Solution {  // Same as 3256. Maximum Value Sum by Placing Three Rooks I  public long maximumValueSum(int[][] board) {    final int m = board.length;    final int n = board[0].length;    long ans = Long.MIN_VALUE;    List<int[]>[] rows = new ArrayList[m];    List<int[]>[] cols = new ArrayList[n];    Set<int[]> rowSet = new HashSet<>();    Set<int[]> colSet = new HashSet<>();    Set<int[]> boardSet = new HashSet<>();     for (int i = 0; i < m; ++i)      rows[i] = new ArrayList<>();     for (int j = 0; j < n; ++j)      cols[j] = new ArrayList<>();     for (int i = 0; i < m; ++i)      for (int j = 0; j < n; ++j) {        int[] cell = new int[] {board[i][j], i, j};        rows[i].add(cell);        cols[j].add(cell);      }     Comparator<int[]> comparator = Comparator.comparingInt(a -> - a[0]);     for (List<int[]> row : rows) {      row.sort(comparator);      rowSet.addAll(row.subList(0, Math.min(3, row.size())));    }     for (List<int[]> col : cols) {      col.sort(comparator);      colSet.addAll(col.subList(0, Math.min(3, col.size())));    }     boardSet.addAll(rowSet);    boardSet.retainAll(colSet);     // At least 9 positions are required on the board to place 3 rooks such that    // none can attack another.    List<int[]> topNine = new ArrayList<>(boardSet);    topNine.sort(comparator);    topNine = topNine.subList(0, Math.min(9, topNine.size()));     for (int i = 0; i < topNine.size(); ++i)      for (int j = i + 1; j < topNine.size(); ++j)        for (int k = j + 1; k < topNine.size(); ++k) {          int[] t1 = topNine.get(i);          int[] t2 = topNine.get(j);          int[] t3 = topNine.get(k);          if (t1[1] == t2[1] || t1[1] == t3[1] || t2[1] == t3[1] || //              t1[2] == t2[2] || t1[2] == t3[2] || t2[2] == t3[2])            continue;          ans = Math.max(ans, (long) t1[0] + t2[0] + t3[0]);        }     return ans;  }}

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