Question

In this assignment you’re going to write a complete C program that opens a file “digits.txt”, inputs the values, and analyzes these values to see if they follow Benford’s law. In particular, your program analyzes the first digit of each input value, and outputs: 1. The total # of input values N 2. The counts for each digit: # of values that start with 1, # of values that start with 2, etc. 3. A histogram of the counts for digits 1..9 4. Whether the input data follows Benford’s law (Yes or No) Here’s an example screenshot of your program output for the input shown earlier, assumed to be in the file digits.txt:

Number of inputs: 12 Counts: 3,2,2,1,1,0,1,1,1 1. 2. 3. 4. 5. 6: 7. 8. 9: Benford's law? No 25.00% 16.67% 16.67% 8.33% 8.33% 0.00% 8.33% 8.33% 8.33%

The input file will contain at most 10,000 positive integers, one per line. For the histogram output of *’s, note that the # of *’s is the floor of the percentage; e.g. the percentage 16.6667% yields 16 *’s.

For the purposes of this assignment, assume that a set of values adheres to Benford’s law if all of the following are true:

a. The % of 1’s falls in the range 28.0 .. 38.0, inclusive

b. The % of 2’s falls in the range 15.0 .. 21.0, inclusive

c. The % of 3’s falls in the range 10.0 .. 13.0, inclusive

d. The % of 4’s is strictly less than the % of 3’s

e. The % of 5’s is strictly less than the % of 4’s

f. The % of 6’s is strictly less than the % of 5’s

g. The % of 7’s is strictly less than the % of 6’s

h. The % of 8’s is strictly less than the % of 7’s

i. The % of 9’s is strictly less than the % of 8’s

Benford’s law is based on the first digit of each value. The easiest way to obtain the first digit is input the value as a string, and use [0] to obtain the first digit. This implies the digit will be a character, e.g. ‘2’, and not an integer 2.

Answer 1

If you have any doubts, please give me comment...

#include <iostream>

#include <cstdlib>

#include <string>

#include <fstream>

#include <cmath>

using namespace std;

int main()

{

string numbers[10000];

int n = 0, i, j;

string filename;

cout << "Enter filename: ";

cin >> filename;

ifstream in(filename.c_str());

if (in.fail())

{

cout << "Unable to open file!" << endl;

exit(0);

}

int count[10] = {0};

while (!in.eof())

{

in >> numbers[n];

int first_dig = numbers[n][0] - '0';

count[first_dig]++;

n++;

}

i = 0;

cout << "N: " << n << endl;

cout << "Counts: ";

while (i < 10)

{

cout << count[i];

if (i != 9)

cout << ",";

i++;

}

cout << endl;

i = 1;

bool law = true;

double prev_perc = 0;

while (i < 10)

{

cout << i << ": ";

j = 0;

double perc = ((double)count[i] / n) * 100;

while (j < (int)floor(perc))

{

cout << "*";

j++;

}

if (i == 0 && (perc < 28.0 || perc > 38.0))

law = false;

else if (i == 2 && (perc < 15.0 || perc > 21.0))

law = false;

else if (i == 3 && (perc < 10.0 || perc > 13.0))

{

law = false;

}

else if (prev_perc < perc)

{

law = false;

}

prev_perc = perc;

cout << "(" << perc << "%)" << endl;

i++;

}

cout << "Benfords's law? " << (law ? "Yes" : "No") << endl;

return 0;

}