Task 1 was done!

2025.04.18/01Ex/solve.c

@@ -0,0 +1,43 @@
+#include "solve.h"
+
+#include <float.h>
+#include <math.h>
+
+// the Lagrange interpolation polynomial
+double t1_solve (const double x_0, const int n, const double * restrict X, const double * restrict Y)
+{
+	double value = 0;
+
+	for (int i = 0; i < n; ++i)
+	{
+		double x_i = X[i];
+		double y_i = Y[i];
+		
+		double numerator = y_i;
+		double denominator = 1;
+
+		if (fabs(x_0 - x_i) < DBL_EPSILON)
+			return y_i;
+
+		for (int j = 0; j < i; ++j)
+		{
+			double x_j = X[j];
+			numerator *= (x_0 - x_j);
+			denominator *= (x_i - x_j);
+		}
+
+		for (int j = i+1; j < n; ++j)
+		{
+			double x_j = X[j];
+			numerator *= (x_0 - x_j);
+			denominator *= (x_i - x_j);
+		}
+
+		if (fabs(denominator) < DBL_EPSILON)
+			return DBL_MAX;
+		
+		value += numerator / denominator;
+	}
+
+	return value;
+}