From 8933e4b2208e7e51f9d74320e4eabd9d25458649 Mon Sep 17 00:00:00 2001
From: dm1sh <me@dmitriy.icu>
Date: Sat, 30 Oct 2021 13:12:39 +0300
Subject: [PATCH 1/6] Fixed resize function, separated array index convertion
 to convert_pos function, added separated get function

---
 main.c                      | 40 +++++++++++++++++++++++--------------
 polynominal_interpolation.h |  2 ++
 2 files changed, 27 insertions(+), 15 deletions(-)

diff --git a/main.c b/main.c
index e007adf..cd3423f 100644
--- a/main.c
+++ b/main.c
@@ -41,12 +41,12 @@ arr *resize(arr *a, int new_size)
 
     double *new_p = (double *)malloc(sizeof(double) * new_size);
     for (int i = 0; i < min(new_size, a->size); i++)
-        new_p[i] = a->p[i];
+        new_p[i] = get(a, i);
 
     free(a->p);
 
     for (int i = a->size; i < new_size; i++)
-        new_p = 0;
+        new_p[i] = 0;
 
     a->p = new_p;
     a->size = new_size;
@@ -54,19 +54,29 @@ arr *resize(arr *a, int new_size)
     return a;
 }
 
+int convert_pos(int size, int pos)
+{
+    pos = pos % size;
+    if (pos < 0)
+        pos = size + pos;
+
+    return pos;
+}
+
 void insert(arr *a, int pos, double val)
 {
-    pos = pos % a->size;
-    if (pos < 0)
-        pos = a->size + pos;
+    a->p[convert_pos(a->size, pos)] = val;
+}
 
-    a->p[pos] = val;
+double get(arr *a, int pos)
+{
+    return a->p[convert_pos(a->size, pos)];
 }
 
 arr *add(arr *a, arr *b)
 {
     for (int i = 0; i < a->size; i++)
-        insert(a, i, a->p[i] + b->p[i]);
+        insert(a, i, get(a, i) + get(b, i));
 
     return a;
 }
@@ -76,7 +86,7 @@ arr *mult(arr *a, double mul)
     arr *res = init(a->size);
 
     for (int i = 0; i < a->size; i++)
-        insert(res, i, a->p[i] * mul);
+        insert(res, i, get(a, i) * mul);
 
     return res;
 }
@@ -90,7 +100,7 @@ void printa(arr *a)
     printf("\n");
 
     for (int i = 0; i < a->size; i++)
-        printf("%5.2f ", a->p[i]);
+        printf("%5.2f ", get(a, i));
     printf("\n");
 }
 
@@ -101,7 +111,7 @@ arr *arr_without_el(arr *a, int ex_pos)
     {
         if (i == ex_pos)
             continue;
-        insert(res, pos, a->p[i]);
+        insert(res, pos, get(a, i));
         pos++;
     }
 
@@ -112,7 +122,7 @@ arr *reverse(arr *a)
 {
     arr *res = init(a->size);
     for (int i = 0; i < a->size; i++)
-        insert(res, i, a->p[a->size - 1 - i]);
+        insert(res, i, get(a, a->size - 1 - i));
 
     return res;
 }
@@ -161,7 +171,7 @@ int mult_by_index(arr *a, int *coords, int n)
 {
     double res = 1;
     for (int i = 0; i < n; i++)
-        res = res * a->p[coords[i]];
+        res = res * get(a, coords[i]);
 
     return res;
 }
@@ -173,7 +183,7 @@ int sum_of_mult_of_n_combinations(arr *a, int n)
 
     if (a->size == 1)
     {
-        return a->p[0];
+        return get(a, 0);
     }
 
     double acc = 0;
@@ -197,7 +207,7 @@ double compose_denominator(arr *a, int pos)
         if (i == pos)
             continue;
 
-        res = res * (a->p[pos] - a->p[i]);
+        res = res * (get(a, pos) - get(a, i));
     }
     return res;
 }
@@ -211,7 +221,7 @@ arr *compose_interpolation_polynomial(arr *xes, arr *ys)
     {
         int minus = !(xes->size % 2);
         double denominator = compose_denominator(xes, j);
-        double multiplicator = ys->p[j];
+        double multiplicator = get(ys, j);
 
         arr *xis = arr_without_el(xes, j);
 
diff --git a/polynominal_interpolation.h b/polynominal_interpolation.h
index 983cf2f..f702dcf 100644
--- a/polynominal_interpolation.h
+++ b/polynominal_interpolation.h
@@ -20,7 +20,9 @@ typedef struct
 
 arr *init(int n);
 arr *resize(arr *a, int new_size);
+int convert_pos(int size, int pos);
 void insert(arr *a, int pos, double val);
+double get(arr *a, int pos);
 arr *add(arr *a, arr *b);
 arr *mult(arr *a, double mul);
 void printa(arr *a);

From 44281e14b31640e5ce8efe2503fdb0ec8b835af3 Mon Sep 17 00:00:00 2001
From: dm1sh <me@dmitriy.icu>
Date: Sat, 30 Oct 2021 13:15:40 +0300
Subject: [PATCH 2/6] Updated readme

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 973dcb6..d78d042 100644
--- a/README.md
+++ b/README.md
@@ -1,3 +1,3 @@
 # Polynomial Interpolation
 
-ANSI C program which composes polynomial of n - 1 degree for n dots.
+ANSI C program which composes polynomial of n - 1 degree that passes through n dots.

From 49619c27e0b5d43f91d877f2e4dc5e109d6ae6f9 Mon Sep 17 00:00:00 2001
From: dm1sh <me@dmitriy.icu>
Date: Sat, 30 Oct 2021 15:35:40 +0300
Subject: [PATCH 3/6] First Newton interpolation polynomial implementation. No
 dots input, no polynomial simplification

---
 main.c                      | 295 ++++--------------------------------
 polynominal_interpolation.h |  36 +----
 2 files changed, 33 insertions(+), 298 deletions(-)

diff --git a/main.c b/main.c
index cd3423f..5634325 100644
--- a/main.c
+++ b/main.c
@@ -1,281 +1,46 @@
-#include <stdio.h>
-#include <stdlib.h>
-
 #include "./polynominal_interpolation.h"
 
-/*
- Utils
-*/
-
-int min(int a, int b)
+/* Divided difference is evaluated for:
+   array y stands for f(x)
+   array x stands for x
+   number i stands for index of evaluated difference (from 0)
+   number d stands for order of difference (from 0)
+   example: https://shorturl.at/tBCPS */
+double div_diff(double *y, double *x, int i, int d)
 {
-    return (a + b - abs(a - b)) / 2;
+  return (y[i] - y[i - 1]) / (x[i] - x[i - d]);
 }
 
-int max(int a, int b)
+/* Evaluates divided differences of n values - array of some kind of derivatives with big enough dx
+   Example: https://shorturl.at/tBCPS
+   Warning: result is evaluated in `double *y` array */
+double *div_diff_es(double *x, double *y, int n)
 {
-    return (a + b + abs(a - b)) / 2;
+  for (int i = 1; i < n; i++)        // first element remains unchanged
+    for (int j = n - 1; j >= i; j--) // evaluate from the end of array, decreacing number of step every repeation
+      y[j] = div_diff(y, x, j, i);
+
+  return y;
 }
 
-/*
- Array utils
-*/
-
-arr *init(int n)
+/* Prints interpolation polynomial in Newton notation */
+void print_newton_poly(double *f, double *x, int n)
 {
-    arr *a = (arr *)malloc(sizeof(arr));
+  for (int i = 0; i < n; i++)
+  {
+    printf("(%lf)", f[i]);
+    for (int j = 0; j < i; j++)
+      printf("*(x-(%lf))", x[j]);
 
-    a->size = n;
-
-    a->p = (double *)malloc(sizeof(double) * n);
-    for (int i = 0; i < n; i++)
-        insert(a, i, 0);
-
-    return a;
-}
-
-arr *resize(arr *a, int new_size)
-{
-    if (a->size == new_size)
-        return a;
-
-    double *new_p = (double *)malloc(sizeof(double) * new_size);
-    for (int i = 0; i < min(new_size, a->size); i++)
-        new_p[i] = get(a, i);
-
-    free(a->p);
-
-    for (int i = a->size; i < new_size; i++)
-        new_p[i] = 0;
-
-    a->p = new_p;
-    a->size = new_size;
-
-    return a;
-}
-
-int convert_pos(int size, int pos)
-{
-    pos = pos % size;
-    if (pos < 0)
-        pos = size + pos;
-
-    return pos;
-}
-
-void insert(arr *a, int pos, double val)
-{
-    a->p[convert_pos(a->size, pos)] = val;
-}
-
-double get(arr *a, int pos)
-{
-    return a->p[convert_pos(a->size, pos)];
-}
-
-arr *add(arr *a, arr *b)
-{
-    for (int i = 0; i < a->size; i++)
-        insert(a, i, get(a, i) + get(b, i));
-
-    return a;
-}
-
-arr *mult(arr *a, double mul)
-{
-    arr *res = init(a->size);
-
-    for (int i = 0; i < a->size; i++)
-        insert(res, i, get(a, i) * mul);
-
-    return res;
-}
-
-void printa(arr *a)
-{
-    printf("Array of size %d:\n", a->size);
-
-    for (int i = 0; i < a->size; i++)
-        printf("%5d ", i + 1);
-    printf("\n");
-
-    for (int i = 0; i < a->size; i++)
-        printf("%5.2f ", get(a, i));
-    printf("\n");
-}
-
-arr *arr_without_el(arr *a, int ex_pos)
-{
-    arr *res = init(a->size - 1);
-    for (int i = 0, pos = 0; i < a->size; i++)
-    {
-        if (i == ex_pos)
-            continue;
-        insert(res, pos, get(a, i));
-        pos++;
-    }
-
-    return res;
-}
-
-arr *reverse(arr *a)
-{
-    arr *res = init(a->size);
-    for (int i = 0; i < a->size; i++)
-        insert(res, i, get(a, a->size - 1 - i));
-
-    return res;
-}
-
-void free_arr(arr *a)
-{
-    free(a->p);
-    free(a);
-}
-
-/*
- Business logic
-*/
-
-int has_comb(int *arr, int n, int k)
-{
-    if (n == k)
-        return 0;
-
-    int pos = k - 1;
-
-    if (arr[pos] == n - 1)
-    {
-        if (k == 1)
-            return 0;
-
-        while ((pos > 0) && arr[pos] == n - 1)
-        {
-            pos--;
-            arr[pos]++;
-        }
-
-        for (int i = pos + 1; i < k; i++)
-            arr[i] = arr[i - 1] + 1;
-
-        if (arr[0] > n - k)
-            return 0;
-    }
-    else
-        arr[pos]++;
-
-    return 1;
-}
-
-int mult_by_index(arr *a, int *coords, int n)
-{
-    double res = 1;
-    for (int i = 0; i < n; i++)
-        res = res * get(a, coords[i]);
-
-    return res;
-}
-
-int sum_of_mult_of_n_combinations(arr *a, int n)
-{
-    if (n == 0)
-        return 1;
-
-    if (a->size == 1)
-    {
-        return get(a, 0);
-    }
-
-    double acc = 0;
-
-    int coords[n];
-    for (int i = 0; i < n; i++)
-        coords[i] = i;
-
-    acc += mult_by_index(a, coords, n);
-    while (has_comb(coords, a->size, n))
-        acc += mult_by_index(a, coords, n);
-
-    return acc;
-}
-
-double compose_denominator(arr *a, int pos)
-{
-    double res = 1;
-    for (int i = 0; i < a->size; i++)
-    {
-        if (i == pos)
-            continue;
-
-        res = res * (get(a, pos) - get(a, i));
-    }
-    return res;
-}
-
-arr *compose_interpolation_polynomial(arr *xes, arr *ys)
-{
-    arr *res = init(xes->size);
-
-    arr *jcoef = init(xes->size);
-    for (int j = 0; j < xes->size; j++)
-    {
-        int minus = !(xes->size % 2);
-        double denominator = compose_denominator(xes, j);
-        double multiplicator = get(ys, j);
-
-        arr *xis = arr_without_el(xes, j);
-
-        for (int i = 0; i < xes->size; i++)
-        {
-            double k_sum = sum_of_mult_of_n_combinations(xis, xes->size - 1 - i);
-            insert(jcoef, i, (minus ? -1 : 1) * (multiplicator * k_sum) / denominator);
-            minus = !minus;
-        }
-
-        res = add(res, jcoef);
-
-        free_arr(xis);
-    }
-
-    free_arr(jcoef);
-
-    return res;
+    if (i != n - 1)
+      printf("+");
+  }
 }
 
 int main()
 {
-    printf("Insert number of dots: ");
-    int n = 0;
-    scanf("%d", &n);
+  double x[] = {0, 1, 2, 3},
+         y[] = {-2, -5, 0, -4};
 
-    printf("Insert dots coordinates in the following format:\n<x> (space) <y>\nEach dot on new line\n");
-
-    arr *xes = init(n);
-    arr *ys = init(n);
-
-    for (int i = 0; i < n; i++)
-    {
-        double x, y;
-        scanf("%lf %lf", &x, &y);
-
-        insert(xes, i, x);
-        insert(ys, i, y);
-    }
-
-    printf("Inserted the following doths:\n");
-    printa(xes);
-    printa(ys);
-
-    arr *res = compose_interpolation_polynomial(xes, ys);
-
-    printf("Resulting polynomial will have such coeficients:\n");
-    arr *reversed = reverse(res);
-    printa(reversed);
-
-    free_arr(reversed);
-    free_arr(res);
-    free_arr(xes);
-    free_arr(ys);
-
-    return 0;
+  print_newton_poly(div_diff_es(x, y, 4), x, 4);
 }
\ No newline at end of file
diff --git a/polynominal_interpolation.h b/polynominal_interpolation.h
index f702dcf..729d043 100644
--- a/polynominal_interpolation.h
+++ b/polynominal_interpolation.h
@@ -1,42 +1,12 @@
 #ifndef POLYNOMIAL_INTERPOLATION_H
 #define POLYNOMIAL_INTERPOLATION_H
 
-/*
- Utils
-*/
-
-int min(int a, int b);
-int max(int a, int b);
-
-/*
- Array utils
-*/
-
-typedef struct
-{
-    int size;
-    double *p;
-} arr;
-
-arr *init(int n);
-arr *resize(arr *a, int new_size);
-int convert_pos(int size, int pos);
-void insert(arr *a, int pos, double val);
-double get(arr *a, int pos);
-arr *add(arr *a, arr *b);
-arr *mult(arr *a, double mul);
-void printa(arr *a);
-arr *arr_without_el(arr *a, int ex_pos);
-arr *reverse(arr *a);
-
 /*
  Business logic
 */
 
-int has_comb(int *arr, int n, int k);
-int mult_by_index(arr *a, int *coords, int n);
-int sum_of_mult_of_n_combinations(arr *a, int n);
-double compose_denominator(arr *a, int pos);
-arr *compose_interpolation_polynomial(arr *xes, arr *ys);
+double div_diff(double *y, double *x, int i, int d);
+double *div_diff_es(double *x, double *y, int n);
+void print_newton_poly(double *f, double *x, int n);
 
 #endif
\ No newline at end of file

From c83cc2894c09a8bda139032de16d37b0820aad2a Mon Sep 17 00:00:00 2001
From: dm1sh <me@dmitriy.icu>
Date: Sat, 30 Oct 2021 16:16:56 +0300
Subject: [PATCH 4/6] Added polynomial input interface

---
 main.c                      | 33 ++++++++++++++++++++++++++++++---
 polynominal_interpolation.h | 10 ++++++++++
 2 files changed, 40 insertions(+), 3 deletions(-)

diff --git a/main.c b/main.c
index 5634325..d92ea80 100644
--- a/main.c
+++ b/main.c
@@ -37,10 +37,37 @@ void print_newton_poly(double *f, double *x, int n)
   }
 }
 
+unsigned int insert_n()
+{
+  printf("Insert number of dots: ");
+  unsigned int n = 0;
+  scanf("%u", &n);
+
+  return n;
+}
+
+void insert_coords(double *xes, double *yes, unsigned int n)
+{
+  printf("Insert dots coordinates in the following format:\n<x> (space) <y>\nEach dot on new line\n");
+
+  for (int i = 0; i < n; i++)
+  {
+    double x, y;
+    scanf("%lf %lf", &x, &y);
+
+    xes[i] = x;
+    yes[i] = y;
+  }
+}
+
 int main()
 {
-  double x[] = {0, 1, 2, 3},
-         y[] = {-2, -5, 0, -4};
+  unsigned n = insert_n();
 
-  print_newton_poly(div_diff_es(x, y, 4), x, 4);
+  double *x = (double *)malloc(sizeof(double) * n),
+         *y = (double *)malloc(sizeof(double) * n);
+
+  insert_coords(x, y, n);
+
+  print_newton_poly(div_diff_es(x, y, n), x, n);
 }
\ No newline at end of file
diff --git a/polynominal_interpolation.h b/polynominal_interpolation.h
index 729d043..4ec01bd 100644
--- a/polynominal_interpolation.h
+++ b/polynominal_interpolation.h
@@ -1,12 +1,22 @@
 #ifndef POLYNOMIAL_INTERPOLATION_H
 #define POLYNOMIAL_INTERPOLATION_H
 
+#include <stdio.h>
+#include <stdlib.h>
+
 /*
  Business logic
 */
 
 double div_diff(double *y, double *x, int i, int d);
 double *div_diff_es(double *x, double *y, int n);
+
+/*
+ User interface
+*/
+
+unsigned int insert_n();
 void print_newton_poly(double *f, double *x, int n);
+void insert_coords(double *x, double *y, unsigned int n);
 
 #endif
\ No newline at end of file

From 95a1c4cb8194e92e0c5105ce7e641ce354a031b3 Mon Sep 17 00:00:00 2001
From: dm1sh <me@dmitriy.icu>
Date: Sun, 31 Oct 2021 02:06:56 +0300
Subject: [PATCH 5/6] Added simpified polynomial coefficients computation

---
 main.c                      | 104 ++++++++++++++++++++++++++++++++++--
 polynominal_interpolation.h |  15 ++++--
 2 files changed, 112 insertions(+), 7 deletions(-)

diff --git a/main.c b/main.c
index d92ea80..0ea1d65 100644
--- a/main.c
+++ b/main.c
@@ -1,12 +1,16 @@
 #include "./polynominal_interpolation.h"
 
+/*
+ Newton interpolation polynomial
+*/
+
 /* Divided difference is evaluated for:
    array y stands for f(x)
    array x stands for x
    number i stands for index of evaluated difference (from 0)
    number d stands for order of difference (from 0)
    example: https://shorturl.at/tBCPS */
-double div_diff(double *y, double *x, int i, int d)
+double div_diff(double *y, double *x, unsigned int i, unsigned int d)
 {
   return (y[i] - y[i - 1]) / (x[i] - x[i - d]);
 }
@@ -14,7 +18,7 @@ double div_diff(double *y, double *x, int i, int d)
 /* Evaluates divided differences of n values - array of some kind of derivatives with big enough dx
    Example: https://shorturl.at/tBCPS
    Warning: result is evaluated in `double *y` array */
-double *div_diff_es(double *x, double *y, int n)
+double *div_diff_es(double *x, double *y, unsigned int n)
 {
   for (int i = 1; i < n; i++)        // first element remains unchanged
     for (int j = n - 1; j >= i; j--) // evaluate from the end of array, decreacing number of step every repeation
@@ -23,8 +27,78 @@ double *div_diff_es(double *x, double *y, int n)
   return y;
 }
 
+/*
+ Coeficients of simplified polynomial computation
+*/
+
+void simplify_polynomial(double *res, double *rev_el_coef, double *x, unsigned int n)
+{
+  for (int i = 0; i < n; i++)
+    if (rev_el_coef[i])
+      for (int j = 0; j <= i; j++)
+        res[i - j] += (j % 2 ? -1 : 1) * rev_el_coef[i] * compute_sum_of_multiplications_of_k(x, j, i);
+}
+
+double compute_sum_of_multiplications_of_k(double *arr, unsigned int k, unsigned int n)
+{
+  if (k == 0)
+    return 1;
+
+  if (k == 1 && n == 1)
+    return arr[0];
+
+  unsigned int *selected = (unsigned int *)malloc(sizeof(unsigned int) * k); // Indexes of selected for multiplication elements
+
+  int i = 0, // index of `arr` array
+      j = 0; // index of `selected` array
+
+  double sum = 0;
+
+  while (j >= 0)
+  {
+    if (i <= (n + (j - k)))
+    {
+      selected[j] = i;
+
+      if (j == k - 1)
+      {
+        sum += mult_by_indexes(arr, selected, k);
+        i++;
+      }
+      else
+      {
+        i = selected[j] + 1;
+        j++;
+      }
+    }
+    else
+    {
+      j--;
+      if (j >= 0)
+        i = selected[j] + 1;
+    }
+  }
+
+  free(selected);
+
+  return sum;
+}
+
+double mult_by_indexes(double *arr, unsigned int *indexes, unsigned int size)
+{
+  double res = 1;
+  for (int i = 0; i < size; i++)
+    res *= arr[indexes[i]];
+
+  return res;
+}
+
+/*
+ User Interface 
+*/
+
 /* Prints interpolation polynomial in Newton notation */
-void print_newton_poly(double *f, double *x, int n)
+void print_newton_poly(double *f, double *x, unsigned int n)
 {
   for (int i = 0; i < n; i++)
   {
@@ -60,6 +134,18 @@ void insert_coords(double *xes, double *yes, unsigned int n)
   }
 }
 
+void print_array(double *arr, unsigned int n)
+{
+  for (int i = 0; i < n; i++)
+    printf("%lf ", arr[i]);
+
+  printf("\n");
+}
+
+/* 
+ Main
+*/
+
 int main()
 {
   unsigned n = insert_n();
@@ -69,5 +155,15 @@ int main()
 
   insert_coords(x, y, n);
 
-  print_newton_poly(div_diff_es(x, y, n), x, n);
+  double *f = div_diff_es(x, y, n);
+
+  print_newton_poly(f, x, n);
+
+  double *coeficients = (double *)malloc(sizeof(double) * n);
+
+  simplify_polynomial(coeficients, f, x, n);
+
+  print_array(coeficients, n);
+
+  return 0;
 }
\ No newline at end of file
diff --git a/polynominal_interpolation.h b/polynominal_interpolation.h
index 4ec01bd..2815c53 100644
--- a/polynominal_interpolation.h
+++ b/polynominal_interpolation.h
@@ -8,15 +8,24 @@
  Business logic
 */
 
-double div_diff(double *y, double *x, int i, int d);
-double *div_diff_es(double *x, double *y, int n);
+double div_diff(double *y, double *x, unsigned int i, unsigned int d);
+double *div_diff_es(double *x, double *y, unsigned int n);
 
 /*
  User interface
 */
 
 unsigned int insert_n();
-void print_newton_poly(double *f, double *x, int n);
+void print_newton_poly(double *f, double *x, unsigned int n);
 void insert_coords(double *x, double *y, unsigned int n);
+void print_array(double *arr, unsigned int n);
+
+/*
+ Coeficients of simplified polynomial computation
+*/
+
+void simplify_polynomial(double *res, double *rev_el_coef, double *x, unsigned int n);
+double compute_sum_of_multiplications_of_k(double *x, unsigned int k, unsigned int n);
+double mult_by_indexes(double *arr, unsigned int *indexes, unsigned int size);
 
 #endif
\ No newline at end of file

From 9155c87b65b58712b45c75a82ed832aec318f4e1 Mon Sep 17 00:00:00 2001
From: dm1sh <me@dmitriy.icu>
Date: Sun, 31 Oct 2021 03:28:40 +0300
Subject: [PATCH 6/6] Updated (shortened) Newton polynomial printing, added
 simplified polynomial printing

---
 main.c                      | 82 +++++++++++++++++++++++++++++++++----
 polynominal_interpolation.h |  6 +++
 2 files changed, 80 insertions(+), 8 deletions(-)

diff --git a/main.c b/main.c
index 0ea1d65..0f13dc1 100644
--- a/main.c
+++ b/main.c
@@ -1,5 +1,12 @@
 #include "./polynominal_interpolation.h"
 
+/* Utils */
+
+double fabs(double x)
+{
+  return x > 0 ? x : -x;
+}
+
 /*
  Newton interpolation polynomial
 */
@@ -100,15 +107,42 @@ double mult_by_indexes(double *arr, unsigned int *indexes, unsigned int size)
 /* Prints interpolation polynomial in Newton notation */
 void print_newton_poly(double *f, double *x, unsigned int n)
 {
+  printf("Newton polynomial form:\n");
   for (int i = 0; i < n; i++)
   {
-    printf("(%lf)", f[i]);
-    for (int j = 0; j < i; j++)
-      printf("*(x-(%lf))", x[j]);
+    if (f[i]) // If coefficient != 0
+    {
+      /* Coefficient sign and sum symbol */
+      if (i > 0 && f[i - 1]) // If it's not the first summond
+      {
+        if (f[i] > 0)
+          printf("+ ");
+        else
+          printf("- ");
+      }
+      else if (f[i] < 0) // If it is the first summond and coefficient is below zero
+        printf("-");
 
-    if (i != n - 1)
-      printf("+");
+      printf("%lf", fabs(f[i])); // Print coefficient without sign
+
+      for (int j = 0; j < i; j++) // For each (x-xi) bracket
+      {
+        if (x[j]) // If summond is not zero, print it
+        {
+          if (x[j] > 0)
+            printf("*(x-%lf)", x[j]);
+          else
+            printf("*(x+%lf)", -x[j]);
+        }
+        else
+          printf("*x");
+      }
+
+      printf(" ");
+    }
   }
+
+  printf("\n");
 }
 
 unsigned int insert_n()
@@ -136,12 +170,42 @@ void insert_coords(double *xes, double *yes, unsigned int n)
 
 void print_array(double *arr, unsigned int n)
 {
+  printf("Simplified coefficients array (starting from 0 upto n-1 power):\n");
+
   for (int i = 0; i < n; i++)
     printf("%lf ", arr[i]);
 
   printf("\n");
 }
 
+void print_poly(double *coef, unsigned int n)
+{
+  printf("Simplified polynom:\n");
+
+  for (int i = 0; i < n; i++)
+  {
+    if (coef[i])
+    {
+      if (i > 0 && coef[i - 1])
+        if (coef[i] > 0)
+          printf("+ ");
+        else
+          printf("- ");
+      else
+        printf("-");
+
+      printf("%lf", fabs(coef[i]));
+      if (i > 0)
+        printf("*x");
+      if (i > 1)
+        printf("^%d ", i);
+      else printf(" ");
+    }
+  }
+
+  printf("\n");
+}
+
 /* 
  Main
 */
@@ -159,11 +223,13 @@ int main()
 
   print_newton_poly(f, x, n);
 
-  double *coeficients = (double *)malloc(sizeof(double) * n);
+  double *coefficients = (double *)malloc(sizeof(double) * n);
 
-  simplify_polynomial(coeficients, f, x, n);
+  simplify_polynomial(coefficients, f, x, n);
 
-  print_array(coeficients, n);
+  print_array(coefficients, n);
+
+  print_poly(coefficients, n);
 
   return 0;
 }
\ No newline at end of file
diff --git a/polynominal_interpolation.h b/polynominal_interpolation.h
index 2815c53..1cca3ec 100644
--- a/polynominal_interpolation.h
+++ b/polynominal_interpolation.h
@@ -4,6 +4,11 @@
 #include <stdio.h>
 #include <stdlib.h>
 
+/*
+ Utils
+*/
+double fabs(double x);
+
 /*
  Business logic
 */
@@ -19,6 +24,7 @@ unsigned int insert_n();
 void print_newton_poly(double *f, double *x, unsigned int n);
 void insert_coords(double *x, double *y, unsigned int n);
 void print_array(double *arr, unsigned int n);
+void print_poly(double *coef, unsigned int n);
 
 /*
  Coeficients of simplified polynomial computation