###### tags: `code`
# c14086028-homework-6-1

#include<stdio.h>
#include<stdlib.h>
#define N 100
#define n 2
int valuefind(int ,int*, int*, int*);
int main(){
	/* use the array to display the polynomial*/
	int a[N] = {0};
	int b[n] = {0};
	int c[N] = {0};
	int  d=0;
	char e = 'x';
	int f = 0;
	printf("input max power of f(x) ( max < %d \n",N);
	scanf_s("%d", &d);
	if (d <= N) {
		for (int i = 0; i < N; i++) {
			if (i < d) {
				printf("innput the coefficient of x^ %d of f(x)\n", i);
				scanf_s("%d", &a[i]);
				continue;
			}
			if (i == d) {
				f = i;
				printf("innput the coefficient of x^ %d of f(x)\n", i);
				scanf_s("%d", &a[i]);
				break;
			}
		}
	}
    else {
		printf("it is not valid number\n");
	}
	printf("innput the coefficient of x^0 of g(x)\n");
	b[1] = 1;
	scanf_s("%d", &b[0]);
	valuefind(f,a, b, c);
	/*print resual*/
	printf("the resual is\n");
	printf("f(x)=");
	for (int i = f ; i >= 0; i--) {
		printf("(%d)%c^%d", a[i], e, i);
		if (i != 0) {
			printf("+");
		}
	}
	printf("\n");

	printf("=");
	printf("(\t");
	for (int i = f ; i > 0; i--) {
		printf("(%d)%c^%d", c[i], e, i - 1);
		if (i != 1) {
			printf("+");
		}
	}
	printf("\t)");

	printf("(\t");
	for (int i = n - 1; i >= 0; i--) {
		printf("(%d)%c^%d", b[i], e, i);
		if (i != 0) {
			printf("+");
		}
	}
	printf("\t)");

	printf("+");
	printf("%d", c[0]);
	system("pause\n");
	return 0;
}
int valuefind(int f,int a[], int b[], int c[]) {
	c[f] = a[f];
	for (int i = f; i > 0; i--) {
		c[i - 1] = a[i-1] + c[i] * -b[0];
	}
	return 0;
}