diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..f94dd38 --- /dev/null +++ b/.gitignore @@ -0,0 +1,3 @@ +a.out +main +.vscode \ No newline at end of file diff --git a/main.c b/main.c new file mode 100644 index 0000000..cbd50fa --- /dev/null +++ b/main.c @@ -0,0 +1,261 @@ +#include +#include + +/* + 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 (space) \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; +} \ No newline at end of file