largest_product_in_grid.c

/**
 * Largest product in a grid
 * https://projecteuler.net/problem=11
 */

#include <stdio.h>
#include <assert.h>

#define WIDTH 20
#define HEIGHT 20
#define ADJACENT 4

#define MAX(a, b) (a > b ? a : b)

unsigned long long largestProductHorizontallyAndVertically(int grid[WIDTH][HEIGHT])
{
    unsigned long long productHorizontal;
    unsigned long long productVertical;
    unsigned long long largest = 1;

    for (int i = 0; i < WIDTH - ADJACENT; i++) {
        for (int j = 0; j < HEIGHT - ADJACENT; j++) {
            productHorizontal = productVertical = 1;
            for (int k = j; k < j + ADJACENT; k++) {
                if (k < 0 || k >= 20) continue;
                productHorizontal *= grid[i][k];
                productVertical *= grid[k][i];
            }

            largest = MAX(MAX(productHorizontal, largest), productVertical);
        }
    }

    return largest;
}

unsigned long long largestProductDiagonallyUpDown(int grid[WIDTH][HEIGHT])
{
    unsigned long long product;
    unsigned long long largest = 1;

    int x, l;

    for (int z = 0; z < WIDTH + HEIGHT - ADJACENT; z++) {
        for (int y = 0; y < HEIGHT - ADJACENT; y++) {
            x = WIDTH - z + y;

            if (x < 0 || x >= WIDTH) continue;

            product = 1;
            for (int k = y; k < (y + ADJACENT); k++) {
                l = WIDTH - z + k;

                if (l < 0 || l >= WIDTH) continue;
                if (k < 0 || k >= HEIGHT) continue;

                product *= grid[l][k];
            }

            largest = MAX(product, largest);
        }
    }

    return largest;
}

unsigned long long largestProductDiagonallyDownUp(int grid[WIDTH][HEIGHT])
{
    unsigned long long product;
    unsigned long long largest = 1;

    int x, l;

    for (int z = -(WIDTH - 1); z < WIDTH + HEIGHT - ADJACENT; z++) {
        for (int y = 0; y < HEIGHT - ADJACENT; y++) {
            x = WIDTH - z - y;

            if (x < 0 || x >= WIDTH) continue;

            product = 1;
            for (int k = y; k < (y + ADJACENT); k++) {
                l = WIDTH - z - k;

                if (l < 0 || l >= WIDTH) continue;
                if (k < 0 || k >= HEIGHT) continue;

                product *= grid[l][k];
            }

            largest = MAX(product, largest);
        }
    }

    return largest;
}

int main()
{
    int grid[WIDTH][HEIGHT] = {
        {8, 2, 22, 97, 38, 15, 0, 40, 0, 75, 4, 5, 7, 78, 52, 12, 50, 77, 91, 8},
        {49, 49, 99, 40, 17, 81, 18, 57, 60, 87, 17, 40, 98, 43, 69, 48, 04, 56, 62, 0},
        {81, 49, 31, 73, 55, 79, 14, 29, 93, 71, 40, 67, 53, 88, 30, 3, 49, 13, 36, 65},
        {52, 70, 95, 23, 4, 60, 11, 42, 69, 24, 68, 56, 1, 32, 56, 71, 37, 2, 36, 91},
        {22, 31, 16, 71, 51, 67, 63, 89, 41, 92, 36, 54, 22, 40, 40, 28, 66, 33, 13, 80},
        {24, 47, 32, 60, 99, 3, 45, 2, 44, 75, 33, 53, 78, 36, 84, 20, 35, 17, 12, 50},
        {32, 98, 81, 28, 64, 23, 67, 10, 26, 38, 40, 67, 59, 54, 70, 66, 18, 38, 64, 70},
        {67, 26, 20, 68, 2, 62, 12, 20, 95, 63, 94, 39, 63, 8, 40, 91, 66, 49, 94, 21},
        {24, 55, 58, 5, 66, 73, 99, 26, 97, 17, 78, 78, 96, 83, 14, 88, 34, 89, 63, 72},
        {21, 36, 23, 9, 75, 0, 76, 44, 20, 45, 35, 14, 0, 61, 33, 97, 34, 31, 33, 95},
        {78, 17, 53, 28, 22, 75, 31, 67, 15, 94, 3, 80, 4, 62, 16, 14, 9, 53, 56, 92},
        {16, 39, 5, 42, 96, 35, 31, 47, 55, 58, 88, 24, 0, 17, 54, 24, 36, 29, 85, 57},
        {86, 56, 0, 48, 35, 71, 89, 7, 5, 44, 44, 37, 44, 60, 21, 58, 51, 54, 17, 58},
        {19, 80, 81, 68, 5, 94, 47, 69, 28, 73, 92, 13, 86, 52, 17, 77, 4, 89, 55, 40},
        {4, 52, 8, 83, 97, 35, 99, 16, 7, 97, 57, 32, 16, 26, 26, 79, 33, 27, 98, 66},
        {88, 36, 68, 87, 57, 62, 20, 72, 3, 46, 33, 67, 46, 55, 12, 32, 63, 93, 53, 69},
        {4, 42, 16, 73, 38, 25, 39, 11, 24, 94, 72, 18, 8, 46, 29, 32, 40, 62, 76, 36},
        {20, 69, 36, 41, 72, 30, 23, 88, 34, 62, 99, 69, 82, 67, 59, 85, 74, 4, 36, 16},
        {20, 73, 35, 29, 78, 31, 90, 1, 74, 31, 49, 71, 48, 86, 81, 16, 23, 57, 5, 54},
        {1, 70, 54, 71, 83, 51, 54, 69, 16, 92, 33, 48, 61, 43, 52, 1, 89, 19, 67, 48}
    };

    unsigned long long largestProductHorizontalAndVertical = largestProductHorizontallyAndVertically(grid);
    unsigned long long largestProductDiagonalClockwise = largestProductDiagonallyUpDown(grid);
    unsigned long long largestProductDiagonalAntiClockwise = largestProductDiagonallyDownUp(grid);

    unsigned long long largest = MAX(
        MAX(largestProductHorizontalAndVertical, largestProductDiagonalClockwise),
        largestProductDiagonalAntiClockwise
    );

    printf("Largest Product: %llu", largest);

    assert(70600674 == largest);

    return 0;
}