demo.cpp

// Implemented by Kritagya Kumra
//  An efficient method to find maximum value of mat[d]
//  - ma[a][b] such that c > a and d > b
#include <iostream>
using namespace std;
#define N 5

// The function returns maximum value A(c,d) - A(a,b)
// over all choices of indexes such that both c > a
// and d > b.
int findMaxValue(int mat[][N])
{
    // stores maximum value
    int maxValue = -18999;

    // maxArr[i][j] stores max of elements in matrix
    // from (i, j) to (N-1, N-1)
    int maxArr[N][N];

    // last element of maxArr will be same's as of
    // the input matrix
    maxArr[N - 1][N - 1] = mat[N - 1][N - 1];

    // preprocess last row
    int maxv = mat[N - 1][N - 1]; // Initialize max
    for (int j = N - 2; j >= 0; j--)
    {
        if (mat[N - 1][j] > maxv)
            maxv = mat[N - 1][j];
        maxArr[N - 1][j] = maxv;
    }

    // preprocess last column
    maxv = mat[N - 1][N - 1]; // Initialize max
    for (int i = N - 2; i >= 0; i--)
    {
        if (mat[i][N - 1] > maxv)
            maxv = mat[i][N - 1];
        maxArr[i][N - 1] = maxv;
    }

    // preprocess rest of the matrix from bottom
    for (int i = N - 2; i >= 0; i--)
    {
        for (int j = N - 2; j >= 0; j--)
        {
            // Update maxValue
            if (maxArr[i + 1][j + 1] - mat[i][j] >
                maxValue)
                maxValue = maxArr[i + 1][j + 1] - mat[i][j];

            // set maxArr (i, j)
            maxArr[i][j] = max(mat[i][j], max(maxArr[i][j + 1], maxArr[i + 1][j]));
        }
    }

    return maxValue;
}

// Driver program to test above function
int main()
{
    int mat[N][N] = {
        {1, 2, -1, -4, -20},
        {-8, -3, 4, 2, 1},
        {3, 8, 6, 1, 3},
        {-4, -1, 1, 7, -6},
        {0, -4, 10, -5, 1}};
    cout << "Maximum Value is " << findMaxValue(mat);

    return 0;
}
// Implemented by Kritagya Kumra