#include <stdio.h>
#include <stdlib.h>

#define MAX_DEGREE 100

typedef struct Polynomial* polynomial;
struct Polynomial
{
    int coeff_array[MAX_DEGREE + 1];
    int high_power;
};

int max(int x, int y)
{
    return x > y ? x : y;
}

void zero_polynomial(polynomial poly)
{
    int i;

    for(i = 0; i <= MAX_DEGREE; i++)
        poly->coeff_array[i] = 0;
    poly->high_power == 0;
}

void add_polynomial(const polynomial poly1, const polynomial poly2,
        polynomial poly_sum)
{
    int i;
    
    poly_sum->high_power = max(poly1->high_power, poly2->high_power);

    for(i = 0; i <= poly_sum->high_power; i++) {
        poly_sum->coeff_array[i] = poly1->coeff_array[i]
            + poly2->coeff_array[i];
    }
}

void mult_polynomial(const polynomial poly1, const polynomial poly2,
        polynomial poly_prod)
{
    int i, j;

    poly_prod->high_power = poly1->high_power + poly2->high_power;

    for(i = 0; i <= poly1->high_power; i++) {
        for(j = 0; j<= poly2->high_power; j++)
            /* += used here */
            poly_prod->coeff_array[i + j] += poly1->coeff_array[i]
                * poly2->coeff_array[j];
    }
}

void print_poly(const polynomial poly)
{
    int i;
    
    for(i = 0; i <= poly->high_power; i++)
        if(poly->coeff_array[i] != 0)
            printf("%dx^%d + ", poly->coeff_array[i], i);

    printf("\n");
}

void test()
{
    int i;

    polynomial poly1, poly2, poly_sum, poly_prod;
    poly1 = malloc(sizeof(struct Polynomial));
    poly2 = malloc(sizeof(struct Polynomial));
    poly_sum = malloc(sizeof(struct Polynomial));
    poly_prod = malloc(sizeof(struct Polynomial));

    for(i = 0; i <= 20; i++) {
        if(i % 2 == 0) {
            poly1->coeff_array[i] = i;
            poly1->high_power = i;
        } else {
            poly2->coeff_array[i] = i;
            poly2->high_power = i;
        }
    }

    print_poly(poly1);
    print_poly(poly2);

    /* test sum */
    add_polynomial(poly1, poly2, poly_sum);
    print_poly(poly_sum);

    /* test mult foo */
    mult_polynomial(poly1, poly2, poly_prod);
    print_poly(poly_prod);
}

int main()
{
    test();
    
    return 0;
}