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

void count_root(int arrR[], int arrL[], int ans[], int countF, int countL, int *len_ans) {
    int i, j, k = 0;
    for (i = 0; i < countF; i++) {
        for (j = 0; j < countL; j++) {
            if (arrL[j] != 0 && arrR[i] != 0 && arrL[j] % arrR[i] == 0) {
                ans[k++] = arrL[j] / arrR[i];
            }
        }
    }
    *len_ans = k;
}

void plus_root_negative(int arr[], int *len) {
    int i, new_len = *len * 2;
    for (i = 0; i < *len; i++) {
        arr[*len + i] = -arr[i];
    }
    *len = new_len;
}

void find_factor(int num, int fac[], int *count) {
    int i, j = 0;
    for (i = 1; i <= sqrt(abs(num)); i++) {
        if (num % i == 0) {
            fac[j++] = i;
            if (i != num / i) {
                fac[j++] = num / i;
            }
        }
    }
    *count = j;
}

double evaluate_polynomial(int A[], int len, double x) {
    double result = 0;
    int i;
    for (i = 0; i < len; i += 2) {
        result += A[i] * pow(x, A[i+1]);
    }
    return result;
}

void Substitute(int len_root, int arr[], int ans[], int A[], int len_A, int *len_ans) {
    int i, j = 0;
    double result;
    for (i = 0; i < len_root; i++) {
        result = evaluate_polynomial(A, len_A, arr[i]);
        if (fabs(result) < 1e-10) {  // 使用小的閾值來處理浮點誤差
            ans[j++] = arr[i];
        }
    }
    *len_ans = j;
}

int main() {
    int i, len, countF, countL, len_root = 0, len_ans = 0;
    int A[] = { 2, 2, 1, 0, -100};  // x^3 - 2x^2 - x + 2 
    int facF[100], facL[100], root[200], ans[100];
    len = sizeof(A) / sizeof(A[0]);
    
    find_factor(abs(A[0]), facF, &countF);
    find_factor(abs(A[len-2]), facL, &countL);
    
    printf("最高次方項因數為: ");
    for (i = 0; i < countF; i++) {
        printf("%d ", facF[i]);
    }
    printf("\n常數項因數為: ");
    for (i = 0; i < countL; i++) {
        printf("%d ", facL[i]);
    }
    printf("\n");
    
    count_root(facF, facL, root, countF, countL, &len_root);
    plus_root_negative(root, &len_root);
    
    printf("可能的根：\n");
    for (i = 0; i < len_root; i++) {
        printf("root[%d] = %d\n", i, root[i]);
    }
    
    Substitute(len_root, root, ans, A, len, &len_ans);
    
    printf("多項式的根：\n");
    for (i = 0; i < len_ans; i++) {
        printf("x = %d\n", ans[i]);
    }
    
    return 0;
}