Period 3 2D Arrays Pt 2 - Homework

Problem

Farmer John has a rectangular grass pasture with N rows and M columns for the cows to graze on. Each pasture has a certain tastiness value. However, the gen alpha Bessie has gotten quite picky with what she eats.

Given a 2D array (template below) with size NxM, please write functions for the following:

1. getTotalGrass()
   • Return total sum of all “tastiness values” from the pastures in the 2D array
2. maxSquare()
   • Because Bessie sometimes likes enjoying square grass patches, she wants to find the best one.
   • Returns the maximum sum of tastiness value of a square in the 2D array. (Square could be 1x1, 2x2, 3x3, etc.)
3. maxSubarraySum()
   • Sometimes, Bessie enjoys eating grass in a line.
   • Return the maximum sum of a continuous subarray in this array if it was “flattened” to be a 1D array. In other words, make the 2D array into a 1D array by combining all rows and find the max subarray sum.

For an example case, see below in the code.

Extra Credit Opportunities

Extra Credit 1 (+0.01): What is the time complexity of your maxSquare code? Explain.

Extra Credit 2 (+0.01): This is achieved if you get the optimal complexity for maxPatch.

Extra Credit 3 (+0.01): What is the time complexity of your maxSubarraySum code? Explain.

Extra Credit 4 (+0.01): This is achieved if you get the optimal complexity for maxSubarraySum.

public class GrassPasture {
    
    private int[][] pastures;

    public GrassPasture(int[][] pastures) {
        this.pastures = pastures;
    }

    public int getTotalGrass() {
        int total = 0;
        for (int[] row : pastures) {
            for (int value : row) {
                total += value;
            }
        }
        return total;
    }

    public int maxSquare() {
        int n = pastures.length;
        int m = pastures[0].length;
        int maxSum = Integer.MIN_VALUE;

        int[][] prefixSum = new int[n + 1][m + 1];
        for (int i = 1; i <= n; i++) {
            for (int j = 1; j <= m; j++) {
                prefixSum[i][j] = pastures[i - 1][j - 1] + prefixSum[i - 1][j] + prefixSum[i][j - 1] - prefixSum[i - 1][j - 1];
            }
        }

        for (int size = 1; size <= Math.min(n, m); size++) {
            for (int i = size; i <= n; i++) {
                for (int j = size; j <= m; j++) {
                    int sum = prefixSum[i][j] - prefixSum[i - size][j] - prefixSum[i][j - size] + prefixSum[i - size][j - size];
                    maxSum = Math.max(maxSum, sum);
                }
            }
        }

        return maxSum;
    }

    public int maxSubarraySum() {
        int n = pastures.length;
        int m = pastures[0].length;

        int[] flattened = new int[n * m];
        int index = 0;
        for (int[] row : pastures) {
            for (int value : row) {
                flattened[index++] = value;
            }
        }

        int maxSum = Integer.MIN_VALUE;
        int currentSum = 0;
        for (int value : flattened) {
            currentSum = Math.max(value, currentSum + value);
            maxSum = Math.max(maxSum, currentSum);
        }

        return maxSum;
    }

    public static void main(String[] args) {
        int[][] pastures = {
            {-3, 6, -1},
            {2, -1, 5},
            {-9, 4, -1}
        };

        GrassPasture gp = new GrassPasture(pastures);

        System.out.println("Total Tastiness: " + gp.getTotalGrass());

        System.out.println("Max Square Sum: " + gp.maxSquare());

        System.out.println("Max Subarray Sum: " + gp.maxSubarraySum());
    }
}
GrassPasture.main(null);

Total Tastiness: 2
Max Square Sum: 9
Max Subarray Sum: 11