Get Biggest Three Rhombus Sums in a Grid — Algorithm Visualization & Coding Challenge

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Understanding Get Biggest Three Rhombus Sums in a Grid

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Problem Overview

· Get Biggest Three Rhombus Sums in a Grid

Difficulty: Medium | Topics: Matrix, Prefix Sum, Enumeration

You are given an m x n integer matrix grid.

A rhombus sum is the sum of the elements that form the border of a regular rhombus shape in grid. The rhombus must have the shape of a square rotated 45° with each of its corners centered in a grid cell.

Note: A rhombus can have an area of 0, represented by a single cell.

Return the biggest three distinct rhombus sums in the grid in descending order.
If there are fewer than three distinct values, return all of them.

Examples

Example 1

Input:  grid = [[3,4,5,1,3],[3,3,4,2,3],[20,30,200,40,10],[1,5,5,4,1],[4,3,2,2,5]]
Output: [228, 216, 211]

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🔵 Blue: 20 + 3 + 200 + 5 = 228
🔴 Red: 200 + 2 + 10 + 4 = 216
🟢 Green: 5 + 200 + 4 + 2 = 211

Example 2

Input:  grid = [[1,2,3],[4,5,6],[7,8,9]]
Output: [20, 9, 8]

🔵 Blue: 4 + 2 + 6 + 8 = 20
🔴 Red: 9 (area 0 rhombus — bottom right)
🟢 Green: 8 (area 0 rhombus — bottom middle)

Example 3

Input:  grid = [[7,7,7]]
Output: [7]

All three possible rhombus sums are identical — return [7].

Constraints

Parameter	Bound
`m == grid.length`	—
`n == grid[i].length`	—
`m`, `n`	`1 ≤ m, n ≤ 50`
`grid[i][j]`	`1 ≤ value ≤ 10⁵`

Java Solution

java

class Solution {
    public int[] getBiggestThree(int[][] grid) {
        int m = grid.length, n = grid[0].length;
        TreeSet<Integer> set = new TreeSet<>();

        // iterate every center cell (r, c) and every radius k
        for (int r = 0; r < m; r++) {
            for (int c = 0; c < n; c++) {
                // radius 0 — single cell
                addToSet(set, grid[r][c]);

                for (int k = 1; r - k >= 0 && r + k < m
                         && c - k >= 0 && c + k < n; k++) {
                    int sum = 0;
                    // top → right (↘)
                    for (int i = 0; i < k; i++)
                        sum += grid[r - k + i][c + i];
                    // right → bottom (↙)
                    for (int i = 0; i < k; i++)
                        sum += grid[r + i][c + k - i];
                    // bottom → left (↖)
                    for (int i = 0; i < k; i++)
                        sum += grid[r + k - i][c - i];
                    // left → top (↗)
                    for (int i = 0; i < k; i++)
                        sum += grid[r - i][c - k + i];
                    addToSet(set, sum);
                }
            }
        }

        int[] res = new int[set.size()];
        int idx = 0;
        for (int val : set.descendingSet())
            res[idx++] = val;
        return res;
    }

    private void addToSet(TreeSet<Integer> set, int val) {
        set.add(val);
        if (set.size() > 3) set.pollFirst(); // keep only top 3
    }
}

Time Complexity: O(m · n · min(m, n))
Space Complexity: O(1) — TreeSet holds at most 3 elements

— Written by Saurabh Patil • B.Tech CSE • Software Developer

Reference Link

https://leetcode.com/problems/get-biggest-three-rhombus-sums-in-a-grid/editorial/

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