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

#define NVAR 5
#define MAX_TERM 1000

typedef struct {
   int nterm;
   int term[MAX_TERM][1+NVAR];
} mvpoly;

void polyprint ( mvpoly f )
{
   int i, k;

   for (i=0; i<f.nterm; ++i) if (f.term[i][0]) {
      if ((i)&&(f.term[i][0]>=0)) printf("+");
      if (f.term[i][0] != 1) printf("%d", f.term[i][0]);
      for (k=1; k<=NVAR; ++k) {
         if (f.term[i][k]) printf("%c",'a'+(char)(k-1));
         if (f.term[i][k]>1) printf("^%d", f.term[i][k]);
      }
   }
}

mvpoly polyprod ( mvpoly f, mvpoly g )
{
   int i, j, k, l;
   mvpoly h;        /* The output is computed here */
   int deg[1+NVAR]; /* Temporary storage of degrees of product monomials */
   int found;       /* A flag to locate monomials already added to h */

   h.nterm = 0;
   for (i=0; i<f.nterm; ++i) {
      for (j=0; j<g.nterm; ++j) {
         /* First compute the product monomial */
         for (k=1; k<=NVAR; ++k) deg[k] = f.term[i][k] + g.term[j][k];

         /* Check whether the product monomial already exists */
         found = 0;
         for (l=0; l<h.nterm; ++l) {
            found = 1;
            for (k=1; k<=NVAR; ++k) {
               if (h.term[l][k] != deg[k]) {
                  found = 0; break;
               }
            }
            if (found) break;
         }

         if (found) { /* Adjust the coefficient */
            h.term[l][0] += f.term[i][0] * g.term[j][0];
         } else {     /* Create a new term */
            h.term[h.nterm][0] = f.term[i][0] * g.term[j][0];
            for (k=1; k<=NVAR; ++k) h.term[h.nterm][k] = deg[k];
            ++h.nterm;
         }
      }
   }

   /* This function does not remove zero terms produced as in the example
      (a+b)(a-b) = a^2-ab+ab-b^2. A good product function sould take care
      of this. However, the assignment does not require this, since no
      coefficient generated as above can be zero. */

   return h;
}

mvpoly setpoly ()
{
   mvpoly h;
   int i, k;

   h.nterm = NVAR;
   for (i=0; i<NVAR; ++i) {
      h.term[i][0] = 1;       /* Set the coefficient to 1 */
      for (k=1; k<=NVAR; ++k) /* Only the kth variable has power 1 */
         h.term[i][k] = (k == (i+1)) ? 1 : 0;
   }
   return h;
}

int main ()
{
   mvpoly f, g;
   int i;

   f = g = setpoly();
   printf("("); polyprint(f); printf(")^1 = "); polyprint(g); printf("\n\n");
   for (i=2; i<=NVAR; ++i) {
      g = polyprod(g,f);
      printf("("); polyprint(f); printf(")^%d = ", i); polyprint(g); printf("\n\n");
   }
   exit(0);
}

(a+b+c+d+e)^1 = a+b+c+d+e

(a+b+c+d+e)^2 = a^2+2ab+2ac+2ad+2ae+b^2+2bc+2bd+2be+c^2+2cd+2ce+d^2+2de+e^2

(a+b+c+d+e)^3 = a^3+3a^2b+3a^2c+3a^2d+3a^2e+3ab^2+6abc+6abd+6abe+3ac^2+6acd+6ace+3ad^2+6ade+3ae^2+b^3+3b^2c+3b^2d+3b^2e+3bc^2+6bcd+6bce+3bd^2+6bde+3be^2+c^3+3c^2d+3c^2e+3cd^2+6cde+3ce^2+d^3+3d^2e+3de^2+e^3

(a+b+c+d+e)^4 = a^4+4a^3b+4a^3c+4a^3d+4a^3e+6a^2b^2+12a^2bc+12a^2bd+12a^2be+6a^2c^2+12a^2cd+12a^2ce+6a^2d^2+12a^2de+6a^2e^2+4ab^3+12ab^2c+12ab^2d+12ab^2e+12abc^2+24abcd+24abce+12abd^2+24abde+12abe^2+4ac^3+12ac^2d+12ac^2e+12acd^2+24acde+12ace^2+4ad^3+12ad^2e+12ade^2+4ae^3+b^4+4b^3c+4b^3d+4b^3e+6b^2c^2+12b^2cd+12b^2ce+6b^2d^2+12b^2de+6b^2e^2+4bc^3+12bc^2d+12bc^2e+12bcd^2+24bcde+12bce^2+4bd^3+12bd^2e+12bde^2+4be^3+c^4+4c^3d+4c^3e+6c^2d^2+12c^2de+6c^2e^2+4cd^3+12cd^2e+12cde^2+4ce^3+d^4+4d^3e+6d^2e^2+4de^3+e^4

(a+b+c+d+e)^5 = a^5+5a^4b+5a^4c+5a^4d+5a^4e+10a^3b^2+20a^3bc+20a^3bd+20a^3be+10a^3c^2+20a^3cd+20a^3ce+10a^3d^2+20a^3de+10a^3e^2+10a^2b^3+30a^2b^2c+30a^2b^2d+30a^2b^2e+30a^2bc^2+60a^2bcd+60a^2bce+30a^2bd^2+60a^2bde+30a^2be^2+10a^2c^3+30a^2c^2d+30a^2c^2e+30a^2cd^2+60a^2cde+30a^2ce^2+10a^2d^3+30a^2d^2e+30a^2de^2+10a^2e^3+5ab^4+20ab^3c+20ab^3d+20ab^3e+30ab^2c^2+60ab^2cd+60ab^2ce+30ab^2d^2+60ab^2de+30ab^2e^2+20abc^3+60abc^2d+60abc^2e+60abcd^2+120abcde+60abce^2+20abd^3+60abd^2e+60abde^2+20abe^3+5ac^4+20ac^3d+20ac^3e+30ac^2d^2+60ac^2de+30ac^2e^2+20acd^3+60acd^2e+60acde^2+20ace^3+5ad^4+20ad^3e+30ad^2e^2+20ade^3+5ae^4+b^5+5b^4c+5b^4d+5b^4e+10b^3c^2+20b^3cd+20b^3ce+10b^3d^2+20b^3de+10b^3e^2+10b^2c^3+30b^2c^2d+30b^2c^2e+30b^2cd^2+60b^2cde+30b^2ce^2+10b^2d^3+30b^2d^2e+30b^2de^2+10b^2e^3+5bc^4+20bc^3d+20bc^3e+30bc^2d^2+60bc^2de+30bc^2e^2+20bcd^3+60bcd^2e+60bcde^2+20bce^3+5bd^4+20bd^3e+30bd^2e^2+20bde^3+5be^4+c^5+5c^4d+5c^4e+10c^3d^2+20c^3de+10c^3e^2+10c^2d^3+30c^2d^2e+30c^2de^2+10c^2e^3+5cd^4+20cd^3e+30cd^2e^2+20cde^3+5ce^4+d^5+5d^4e+10d^3e^2+10d^2e^3+5de^4+e^5