Initial release

.gitignore

@@ -0,0 +1,3 @@
+a.out
+main
+.vscode

main.c

@@ -0,0 +1,261 @@
+#include <stdio.h>
+#include <stdlib.h>
+
+/*
+ Utils
+*/
+
+int min(int a, int b)
+{
+    return (a + b - abs(a - b)) / 2;
+}
+
+int max(int a, int b)
+{
+    return (a + b + abs(a - b)) / 2;
+}
+
+/*
+ Array utils
+*/
+
+typedef struct
+{
+    int size;
+    float *p;
+} arr;
+
+arr *init(int n)
+{
+    arr *a = (arr *)malloc(sizeof(arr));
+
+    a->size = n;
+
+    a->p = (float *)malloc(sizeof(float) * n);
+    for (int i = 0; i < n; i++)
+        a->p[i] = 0;
+
+    return a;
+}
+
+arr *resize(arr *a, int new_size)
+{
+    if (a->size == new_size)
+        return a;
+
+    float *new_p = (float *)malloc(sizeof(float) * new_size);
+    for (int i = 0; i < min(new_size, a->size); i++)
+        new_p[i] = a->p[i];
+
+    free(a->p);
+
+    for (int i = a->size; i < new_size; i++)
+        new_p = 0;
+
+    a->p = new_p;
+    a->size = new_size;
+
+    return a;
+}
+
+void insert(arr *a, int pos, float val)
+{
+    pos = pos % a->size;
+    if (pos < 0)
+        pos = a->size + pos;
+
+    a->p[pos] = val;
+}
+
+arr *add(arr *a, arr *b)
+{
+    for (int i = 0; i < a->size; i++)
+        a->p[i] = a->p[i] + b->p[i];
+
+    return a;
+}
+
+arr *mult(arr *a, float mul)
+{
+    arr *res = init(a->size);
+
+    for (int i = 0; i < a->size; i++)
+        res->p[i] = a->p[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 ", a->p[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;
+        res->p[pos] = a->p[i];
+        pos++;
+    }
+
+    return res;
+}
+
+arr *reverse(arr *a)
+{
+    arr *res = init(a->size);
+    for (int i = 0; i < a->size; i++)
+        res->p[i] = a->p[a->size - 1 - i];
+
+    return res;
+}
+
+/*
+ Buisness 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)
+{
+    float res = 1;
+    for (int i = 0; i < n; i++)
+        res = res * a->p[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 a->p[0];
+    }
+
+    float 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;
+}
+
+int compose_denominator(arr *a, int pos)
+{
+    float res = 1;
+    for (int i = 0; i < a->size; i++)
+    {
+        if (i == pos)
+            continue;
+
+        res = res * (a->p[pos] - a->p[i]);
+    }
+    return res;
+}
+
+arr *compose_interpolation_polynomial(arr *xes, arr *ys)
+{
+    arr *res = init(xes->size);
+
+    arr *jcoef = init(xes->size - 1);
+    for (int j = 0; j < xes->size; j++)
+    {
+        int minus = !(xes->size % 2);
+        float denominator = compose_denominator(xes, j);
+        float multiplicator = ys->p[j];
+
+        arr *xis = arr_without_el(xes, j);
+
+        for (int i = 0; i < xes->size; i++)
+        {
+            float k_sum = sum_of_mult_of_n_combinations(xis, xes->size - 1 - i);
+            jcoef->p[i] = (minus ? -1 : 1) * (multiplicator * k_sum) / denominator;
+            minus = !minus;
+        }
+
+        res = add(res, jcoef);
+    }
+
+    free(jcoef);
+
+    return res;
+}
+
+int main()
+{
+    printf("Insert number of dots: ");
+    int n = 0;
+    scanf("%d", &n);
+
+    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++)
+    {
+        int x, y;
+        scanf("%d %d", &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");
+    printa(reverse(res));
+
+    return 0;
+}