I have a question about MLP Backpropagation - c++

Question

I'm studying MLP reversal while reading this, but there's nothing I'm curious about, so I'm posting questions
In the code above, It used W, V, c, and b as parameters for the train function, but I don't understand why we use random and what it means.
Also, I don't know why I resize and make_pair the value to be handed over to the training function in the training set regarding the vector.
To summarize the questions,
What the parameters of W,V,c,b mean and why rand() is written in the main function
Reasons for using pair, resize, and make_pair in Trainset vectors, which are data for training neural networks
#include <iostream>
#include <vector>
#include <math.h>
#include <time.h>
using namespace std;
#define Train_Set_Size 20
#define PI 3.141592653589793238463
#define N 5
#define epsilon 0.05
#define epoch 50000
double c[N] = {};
double W[N] = {};
double V[N] = {};
double b = 0;
double sigmoid(double x) {
return (1.0f / (1.0f + std::exp(-x)));
}
double f_theta(double x) {
double result = b;
for (int i = 0; i < N; i++) {
result += V[i] * sigmoid(c[i] + W[i] * x);
}
return result;
}
void train(double x, double y) {
for (int i = 0; i < N; i++) {
W[i] = W[i] - epsilon * 2 * (f_theta(x) - y) * V[i] * x *
(1 - sigmoid(c[i] + W[i] * x)) * sigmoid(c[i] + W[i] * x);
}
for (int i = 0; i < N; i++) {
V[i] = V[i] - epsilon * 2 * (f_theta(x) - y) * sigmoid(c[i] + W[i] * x);
}
b = b - epsilon * 2 * (f_theta(x) - y);
for (int i = 0; i < N; i++) {
c[i] = c[i] - epsilon * 2 * (f_theta(x) - y) * V[i] *
(1 - sigmoid(c[i] + W[i] * x)) * sigmoid(c[i] + W[i] * x);
}
}
int main() {
srand(time(NULL));
for (int i = 0; i < N; i++) {
W[i] = 2 * rand() / RAND_MAX -1;
V[i] = 2 * rand() / RAND_MAX -1;
c[i] = 2 * rand() / RAND_MAX -1;
}
vector<pair<double, double>> trainSet;
trainSet.resize(Train_Set_Size);
for (int i = 0; i < Train_Set_Size; i++) {
trainSet[i] = make_pair(i * 2 * PI / Train_Set_Size, sin(i * 2 * PI / Train_Set_Size));
}
for (int j = 0; j < epoch; j++) {
for (int i = 0; i < Train_Set_Size; i++) {
train(trainSet[i].first, trainSet[i].second);
}
std::cout << j << "\r";
}
//Plot the results
vector<float> x;
vector<float> y1, y2;
for (int i = 0; i < 1000; i++) {
x.push_back(i * 2 * PI / 1000);
y1.push_back(sin(i * 2 * PI / 1000));
y2.push_back(f_theta(i * 2 * PI / 1000));
}
FILE * gp = _popen("gnuplot", "w");
fprintf(gp, "set terminal wxt size 600,400 \n");
fprintf(gp, "set grid \n");
fprintf(gp, "set title '%s' \n", "f(x) = sin (x)");
fprintf(gp, "set style line 1 lt 3 pt 7 ps 0.1 lc rgb 'green' lw 1 \n");
fprintf(gp, "set style line 2 lt 3 pt 7 ps 0.1 lc rgb 'red' lw 1 \n");
fprintf(gp, "plot '-' w p ls 1, '-' w p ls 2 \n");
//Exact f(x) = sin(x) -> Green Graph
for (int k = 0; k < x.size(); k++) {
fprintf(gp, "%f %f \n", x[k], y1[k]);
}
fprintf(gp, "e\n");
//Neural Network Approximate f(x) = sin(x) -> Red Graph
for (int k = 0; k < x.size(); k++) {
fprintf(gp, "%f %f \n", x[k], y2[k]);
}
fprintf(gp, "e\n");
fflush(gp);
system("pause");
_pclose(gp);
return 0;
}