// How do you normalize a vector? Divide each component by its magnitude.
// Normalization means scaling a vector so that its length becomes 1,
// but its direction stays the same.
#include <iostream>
#include <vector>
#include <algorithm> // for std::transform
#include <numeric> // for std::inner_product
#include <cmath> // for std::sqrt
// ------------------------------------------------------------
// Compute the magnitude (Euclidean norm) of a vector.
// This uses std::inner_product to compute the sum of squares:
// v·v = v[0]^2 + v[1]^2 + ... + v[n]^2
// Then takes the square root.
// ------------------------------------------------------------
double magnitude(const std::vector<double>& v) {
return std::sqrt(std::inner_product(v.begin(), v.end(),
v.begin(), 0.0));
}
// ------------------------------------------------------------
// Normalize a vector: scale it so its magnitude becomes 1.
// Formula for each component:
// normalized[i] = v[i] / |v|
// std::transform applies this operation to each element.
// ------------------------------------------------------------
std::vector<double> normalize(const std::vector<double>& v) {
double mag = magnitude(v); // compute vector length
std::vector<double> out(v.size()); // output vector
// Divide each element by the magnitude
std::transform(v.begin(), v.end(), out.begin(),
[mag](double x) { return x / mag; });
return out;
}
int main() {
std::vector<double> v = {3, 4};
// Normalize the vector
auto n = normalize(v);
std::cout << "Normalized vector: ["
<< n[0] << ", " << n[1] << "]\n";
}
/*
run:
Normalized vector: [0.6, 0.8]
*/
