1. Inserting and removing elements

A. Write a function
void insert_element(vector<int>, int)
that inserts an element in a vector of integers. Suppose that the elements are sorted in increasing order and the new element must be inserted in such a way that the vector be sorted again. Test the function with a vector, whose elements are stored in a file (using input redirection).

To insert an element in the middle of a vector, you must add a new element at the end of the vector and move all elements above the insertion location up by one slot.

void insert(vector<string>& v, int pos, string s)
{ int last = v.size()-1;
for (int i = last; i > pos; i--) v[i] = v[i-1];
v[pos] = s;

To link a file to the input of a program words, you type

words < article.txt
on a command line. The input instructions no longer expect input from the keyboard but from the file article.txt.

B. Write a function
void erase_first(vector<int>)
that removes the fist element of an integer vector, not changing the order of the remaining elements.
You must move all elements down by one slot, then shrink the size of the vector.
void erase(vector<string>& v, int pos)
{ for (int i = pos; i < v.size()-1; i++) v[i] = v[i+1];
Read a vector from a file, remove the first element, and save the elements to another file.

2. Parallel vectors

  Look at the program and explain its purpose. Write down the code, compile and start the program.
using namespace std;

#include "ccc_win.h"

class Cloud {
   void add_point(Point p);
   void plot() const;
   vector<Point> dots;

void rand_seed()
{  int seed = static_cast<int>(time(0));

double rand_double(double a, double b)
{  return a + (b - a) * rand() * (1.0 / RAND_MAX); }


void Cloud::add_point(Point p)
{  dots.push_back(p); }

void Cloud::plot() const
{  int i;
   for (i = 0; i < dots.size(); i++) cwin << dots[i];

int main()
{  rand_seed();
   Cloud random_cloud;
   int i;
   for (i = 1; i <= 100; i++)
random_cloud.add_point(Point(rand_double(-4, 4),
           rand_double(-4, 4)));
   return 0;

3. Character arrays

Write a program, that reads an natural number as a string, then convert it to a floating point number and output it's square root. Use the member-function c_str() and atoi(const char []) function.

4. Two-dimensional arrays

Syntax 9.4 : Two-Dimensional Array Definition
type_name variable_name[size1][size2];
double monthly_sales[NREGIONS][12];
Purpose: Define a new variable that is a two-dimensional array.

Write a program, that produces a table of account balances, when varying interest rates over multiple years.
void print_table(const double table[][BALANCES_COLS], int table_rows)
{  const int WIDTH = 10;
   cout << setiosflags(ios::fixed) << setprecision(2);
   for (int i = 0; i < table_rows; i++)
   {  for (int j = 0; j < BALANCES_COLS; j++)
         cout << setw(WIDTH) << table[i][j];
      cout << "\n";
double future_value(double initial_balance, double p, int n)
{  double b = initial_balance * pow(1 + p / 100, n);
   return b