This code is a C program that calculates a "special...

August 26, 2025 at 08:44 AM

#include <stdio.h>
#define NMAX 30

int input(int *array, int *n);
double mean(int *array, int n);
double standard_deviation(int *array, int n, double mean_v);
int find_special_number(int *array, int n, double mean_v, double std_dev);

int main() {
    int n, data[NMAX];

    if (input(data, &n) != 1) {
        printf("n/a\n");
        return 0;
    }

    double mean_v = mean(data, n);
    double std_dev = standard_deviation(data, n, mean_v);

    int result = find_special_number(data, n, mean_v, std_dev);

    printf("%d\n", result);

    return 0;
}

int input(int *array, int *n) {
    if (scanf("%d", n) != 1 || *n <= 0 || *n > NMAX) {
        return 0;
    }
    for (int i = 0; i < *n; i++) {
        if (scanf("%d", &array[i]) != 1) {
            return 0;
        }
    }
    return 1;
}

double mean(int *array, int n) {
    double sum = 0.0;
    for (int i = 0; i < n; i++) {
        sum += array[i];
    }
    return sum / n;
}

double standard_deviation(int *array, int n, double mean_v) {
    double sum = 0.0;
    for (int i = 0; i < n; i++) {
        sum += (array[i] - mean_v) * (array[i] - mean_v);
    }
    return sqrt(sum / n);
}

int find_special_number(int *array, int n, double mean_v, double std_dev) {
    double lower_bound = mean_v - 3 * std_dev;
    double upper_bound = mean_v + 3 * std_dev;

    for (int i = 0; i < n; i++) {
        if (array[i] >= mean_v && array[i] % 2 == 0 && array[i] != 0 &&
            array[i] >= lower_bound && array[i] <= upper_bound) {
            return array[i];
        }
    }

    return 0; // В случае если нет нужного число
}

This code is a C program that calculates a "special number" from an array of integers. Here's a step-by-step explanation of its function:

Overview of Functionality

Input Reading:
- The program reads a number n (size of the array) and then n integers into an array.
- The input size n must be between 1 and NMAX (maximum size of 30). Any invalid input returns n/a and terminates the program.
Mean Calculation:
- The program calculates the arithmetic mean (average) of the elements in the array.
Standard Deviation Calculation:
- Using the calculated mean, it computes the standard deviation of the array elements.
Finding the "Special Number":
- The program goes through the array and finds the first number that satisfies all these conditions:
  - Greater than or equal to the mean.
  - Even (divisible by 2).
  - Non-zero.
  - Within the range defined by mean - 3 * std_dev and mean + 3 * std_dev.
- If no number satisfies these conditions, it returns 0.
Output:
- The result (either the special number or 0 if no such number exists) is printed to the standard output.

Detailed Breakdown of the Code:

input Function:
- Reads inputs into the array array and size n.
- Validates that n is positive and does not exceed NMAX.
- If any input is invalid (e.g., non-integer or out-of-range values), the function returns 0.
mean Function:
- Computes the arithmetic mean of the elements in the array: [ \text{mean} = \frac{\text{Sum of all elements in the array}}{n} ]
standard_deviation Function:
- Computes the standard deviation of the array using the formula: [ \text{standard_deviation} = \sqrt{\frac{1}{n} \sum_{i=0}^{n-1} (\text{array}[i] - \text{mean})^2} ]
find_special_number Function:
- Constructs a valid range:
  - Lower bound: mean - 3 * standard deviation.
  - Upper bound: mean + 3 * standard deviation.
- Iterates through the array and returns the first number that:
  - Is greater than or equal to the mean (array[i] >= mean_v).
  - Is even (array[i] % 2 == 0).
  - Is non-zero (array[i] != 0).
  - Lies within the bounds (lower_bound <= array[i] <= upper_bound).
- If no such number exists, returns 0.
main Function:
- Runs all the above steps. If the input is invalid, terminates with output n/a.
- Otherwise, calculates the mean and standard deviation to find and print the "special number."

Example Execution:

Consider the following input:

5
1 2 3 4 5

Steps:

The input size is n = 5. The array is [1, 2, 3, 4, 5].
Mean Calculation:
- Mean = ( \frac{1 + 2 + 3 + 4 + 5}{5} = 3.0 ).
Standard Deviation Calculation:
- Variance = ( \frac{(1-3)^2 + (2-3)^2 + (3-3)^2 + (4-3)^2 + (5-3)^2}{5} = 2.0 ).
- Standard Deviation = ( \sqrt{2.0} \approx 1.414 ).
Range:
- Lower bound = ( 3.0 - 3 \cdot 1.414 = -1.242 ).
- Upper bound = ( 3.0 + 3 \cdot 1.414 = 7.242 ).
Find Special Number:
- The first even number in the array, greater than or equal to the mean, and within the bounds is 4.
Output:
- The program prints: 4.

Edge Cases:

No Valid Inputs: If no number in the array satisfies the conditions:
- Example: Input array [-1, 1, 3, 7].
- The program will return 0.
Invalid Input:
- Example: Input n = -5 or non-integer values.
- The program will print n/a.
All Numbers Are Zero:
- If the array is [0, 0, 0], the program will print 0, as none of the numbers are non-zero.

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