Problem: Gaussian Image Band Processing

The problem involves processing specified 600x600 bands from binary file AA (found in predefined paths, rows flipped) using Gaussian spatial weighting (centered at midpoint, sigma = max dimension/4) to compute metrics like weighted pixel counts, optimal thresholds, ratios, and accuracy based on pixel value conditions, returning required values for different parameters.


Input/Output: The problem receives integer parameters (band_num, threshold(s) varying by subproblem) and accesses a binary file "AA" from paths test_data/AA, ../test_data/AA, ../../test_data/AA. For each subproblem, it reads the specified 600x600 band (flipping rows vertically), applies Gaussian spatial weighting (center at image midpoint, sigma = 150), computes a metric (weighted count of pixels meeting value conditions, optimal Otsu threshold, weighted ratio, accuracy vs mean, or count of pixels with ≥5 neighbors), and returns an integer (rounded) or double (precise) result corresponding to the subproblem's requirement.

Required dependencies:
#include <vector>
#include <string>
#include <fstream>
#include <iostream>
#include <cmath>
#include <algorithm>
#include <iomanip>
#include <cstdlib>
using namespace std;

Sub-steps:
step_number: 1
step_description_prompt: Please write a C++ function named problem_17_1 that takes two integers band_num and threshold as parameters and returns an integer. This function calculates the weighted count of pixels exceeding the threshold in a specified band of a 600x600 binary image using Gaussian spatial weighting. The function signature is int problem_17_1(int band_num, int threshold). First, find the valid file path from three possible paths: "test_data/AA", "../test_data/AA", "../../test_data/AA" by checking if the file can be opened. If no valid path is found, output "Error: Cannot find data file AA" to stderr and return -1. Then, read the specified band data from the binary file: skip (band_num - 1) * 600 * 600 bytes to reach the target band, read 600 rows of 600 bytes each, and store the data in a 2D vector band (size 600x600) with rows flipped (using rows - 1 - i for the row index). Next, compute the weighted count: the center of the image is (300.0, 300.0), sigma is max(600, 600) / 4.0. For each pixel (i,j), if the pixel value exceeds threshold, calculate the squared distance from the center, compute the weight as exp(-dist_sq / (2.0 * sigma * sigma)), and accumulate the weight into weighted_count. Finally, round weighted_count to the nearest integer (add 0.5 and cast to int) and return it. Note to handle binary file reading, check file paths, skip preceding bands, and flip rows when storing data. Use necessary headers like <fstream>, <vector>, <cmath>, <iostream>, <algorithm>, etc. Ensure functions like exp, max are available.
function_header: int problem_17_1(int band_num, int threshold)
test_cases: // ==================== Main function: Testing ====================
int main() {
    srand(42);
    cout << fixed << setprecision(6);
    cout << "Problem 17.1" << endl;
    
    int correct_count = 0;
    
    // Test 1
    int band1 = 1;
    int threshold1 = 128;

    int result1 = problem_17_1(band1, threshold1);
    if (result1 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        int correct1 = 37;  // Expected value (updated from actual result)
        if (result1 == correct1) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 2
    int band2 = 2;
    int threshold2 = 150;

    int result2 = problem_17_1(band2, threshold2);
    if (result2 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        int correct2 = 0;  // Expected value (updated from actual result)
        if (result2 == correct2) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 3
    int band3 = 3;
    int threshold3 = 100;

    int result3 = problem_17_1(band3, threshold3);
    if (result3 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        int correct3 = 11;  // Expected value (updated from actual result)
        if (result3 == correct3) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }

    
    if (correct_count == 3) {
        cout << "Completely correct!" << endl;
    }
    
    return 0;
}

step_number: 2
step_description_prompt: Please write a C++ function named problem_17_2 that takes three int parameters (band_num, threshold1, threshold2) and returns an int. The function calculates the rounded Gaussian-weighted count of pixels in a specific band of a 600x600 binary image file where pixel values are between threshold1 (exclusive) and threshold2 (inclusive).

Function definition: int problem_17_2(int band_num, int threshold1, int threshold2);

Algorithm steps: 1. Check three possible paths ("test_data/AA", "../test_data/AA", "../../test_data/AA") to find the existing binary file. If no path is valid, output "Error: Cannot find data file AA" to cerr and return -1. 2. Read the specified band (band_num) from the binary file into a 600x600 vector<vector<unsigned char>>, reversing rows (store buf[j] into band[599 - i][j] for each row i). 3. For each pixel in the 600x600 matrix: if the value is greater than threshold1 and less than or equal to threshold2, compute Gaussian weight using distance to center (sigma = 150), sum the weights. 4. Return the sum rounded to the nearest integer (add 0.5 before casting to int).

Note: Use binary mode to read the file. Skip (band_num - 1) * 600 * 600 bytes to reach the target band. Gaussian weight formula: exp(-dist_sq / (2 * sigma * sigma)) where dist_sq is (i - 300.0)^2 + (j - 300.0)^2.
function_header: int problem_17_2(int band_num, int threshold1, int threshold2)
test_cases: // ==================== Main function: Testing ====================
int main() {
    srand(42);
    cout << fixed << setprecision(6);
    cout << "Problem 17.2" << endl;
    
    int correct_count = 0;
    
    // Test 1
    int band1 = 1;
    int threshold1_1 = 100, threshold2_1 = 200;

    int result1 = problem_17_2(band1, threshold1_1, threshold2_1);
    if (result1 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        int correct1 = 920;  // Expected value (updated from actual result)
        if (result1 == correct1) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 2
    int band2 = 2;
    int threshold1_2 = 120, threshold2_2 = 180;

    int result2 = problem_17_2(band2, threshold1_2, threshold2_2);
    if (result2 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        int correct2 = 0;  // Expected value (updated from actual result)
        if (result2 == correct2) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 3
    int band3 = 3;
    int threshold1_3 = 80, threshold2_3 = 160;

    int result3 = problem_17_2(band3, threshold1_3, threshold2_3);
    if (result3 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        int correct3 = 125;  // Expected value (updated from actual result)
        if (result3 == correct3) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }

    
    if (correct_count == 3) {
        cout << "Completely correct!" << endl;
    }
    
    return 0;
}

step_number: 3
step_description_prompt: Please write a C++ function named problem_17_3 that takes an int parameter band_num and returns an int. The function computes the optimal Otsu threshold using a spatially weighted histogram for a specified band from a binary file.

Function definition: int problem_17_3(int band_num);

Algorithm flow:
1. Search for the binary file "AA" in the paths {"test_data/AA", "../test_data/AA", "../../test_data/AA"}. If the file is not found, output "Error: Cannot find data file AA" to cerr and return -1.
2. Read the specified band (band_num) from the file: skip (band_num - 1) * 600 * 600 bytes from the start, read 600x600 unsigned char data, and flip the data vertically (store buf[j] in band[rows - 1 - i][j] where rows=600, cols=600).
3. Compute a spatially weighted histogram of 256 bins: for each pixel (i,j), calculate weight as exp(-((i - 300.0)^2 + (j - 300.0)^2) / (2 * 150.0 * 150.0)) (sigma = max(600,600)/4 = 150), accumulate weight into histogram[v] (v is pixel value), and sum all weights as total_weight.
4. Calculate Otsu threshold: iterate t from 1 to 254, compute weighted sums w0, sum0 (for i ≤ t) and w1, sum1 (for i > t) using the histogram. Compute between-class variance as (w0 * w1 * (mean0 - mean1)^2) / (total_weight * total_weight) (mean0 = sum0/w0, mean1 = sum1/w1). Track t with maximum variance as best_threshold.
5. Return best_threshold.

Note: Use ifstream to read the file in binary mode. The image size is fixed at 600x600. Assume used functions (ifstream, vector, cerr, exp) are defined.
function_header: int problem_17_3(int band_num)
test_cases: // ==================== Main function: Testing ====================
int main() {
    srand(42);
    cout << fixed << setprecision(6);
    cout << "Problem 17.3" << endl;
    
    int correct_count = 0;
    
    // Test 1
    int band1 = 1;

    int result1 = problem_17_3(band1);
    if (result1 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        int correct1 = 81;  // Expected value (updated from actual result)
        if (result1 == correct1) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 2
    int band2 = 2;

    int result2 = problem_17_3(band2);
    if (result2 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        int correct2 = 37;  // Expected value (updated from actual result)
        if (result2 == correct2) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 3
    int band3 = 3;

    int result3 = problem_17_3(band3);
    if (result3 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        int correct3 = 45;  // Expected value (updated from actual result)
        if (result3 == correct3) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }

    
    if (correct_count == 3) {
        cout << "Completely correct!" << endl;
    }
    
    return 0;
}

step_number: 4
step_description_prompt: Please write a C++ function named problem_17_4 that calculates the rounded weighted count of pixels where the average of two specific bands from a binary file exceeds a threshold, using Gaussian spatial weighting centered at the image center. The function takes three int parameters (band1, band2, threshold) and returns an int.

Function definition: int problem_17_4(int band1, int band2, int threshold);

Algorithm flow: 1. Check paths "test_data/AA", "../test_data/AA", "../../test_data/AA" to find the existing binary file; if none exist, output "Error: Cannot find data file AA" to cerr and return -1. 2. Read two 600x600 unsigned char bands (band1 and band2) from the file: for each band N, seek to (N-1)*600*600 offset, read each row, and store rows in reverse order (rows-1-i). 3. For each pixel (i,j), compute the average of the two bands; if average > threshold, calculate Gaussian weight (sigma = max(600,600)/4, weight = exp(-((i-300.0)*(i-300.0) + (j-300.0)*(j-300.0))/(2.0*sigma*sigma))) and accumulate weighted_count. 4. Return (int)(weighted_count + 0.5).

Note: The binary file contains sequential 600x600 unsigned char bands. Use ifstream with ios::binary to read the file. Assume necessary headers (e.g., <vector>, <fstream>, <cmath>, <iostream>) and functions (e.g., exp) are available.
function_header: int problem_17_4(int band1, int band2, int threshold)
test_cases: // ==================== Main function: Testing ====================
int main() {
    srand(42);
    cout << fixed << setprecision(6);
    cout << "Problem 17.4" << endl;
    
    int correct_count = 0;
    
    // Test 1
    int band1_1 = 1, band2_1 = 2;
    int threshold1 = 128;

    int result1 = problem_17_4(band1_1, band2_1, threshold1);
    if (result1 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        int correct1 = 0;  // Expected value (updated from actual result)
        if (result1 == correct1) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 2
    int band1_2 = 2, band2_2 = 3;
    int threshold2 = 150;

    int result2 = problem_17_4(band1_2, band2_2, threshold2);
    if (result2 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        int correct2 = 0;  // Expected value (updated from actual result)
        if (result2 == correct2) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 3
    int band1_3 = 3, band2_3 = 4;
    int threshold3 = 100;

    int result3 = problem_17_4(band1_3, band2_3, threshold3);
    if (result3 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        int correct3 = 7;  // Expected value (updated from actual result)
        if (result3 == correct3) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }

    
    if (correct_count == 3) {
        cout << "Completely correct!" << endl;
    }
    
    return 0;
}

step_number: 5
step_description_prompt: Please write a C++ function named problem_17_5 that calculates a weighted classification ratio of pixels above a threshold from a specific band of a binary image file using Gaussian spatial weighting. The function takes two integers (band_num for the target band index, threshold for pixel value threshold) and returns a double.
double problem_17_5(int band_num, int threshold);
1. Attempt to open the binary data file "AA" from paths {"test_data/AA", "../test_data/AA", "../../test_data/AA"}. If no path works, output "Error: Cannot find data file AA" to cerr and return -1.0.
2. Read the specified band (band_num) from the file: skip (band_num - 1) * 600 * 600 bytes from the start, read 600 rows × 600 cols of unsigned char data, invert the row order (store in band[rows - 1 - i][j] when reading the i-th row from the file).
3. For each pixel (i,j) in the 600x600 band: calculate Gaussian weight using center (300.0, 300.0) and sigma = 150.0 (max(600,600)/4), sum weights of pixels with value > threshold (weighted_count) and total weights (weight_sum).
4. Return weighted_count / weight_sum if weight_sum > 1e-10, else 0.0.
Note: The file is binary, image size is fixed at 600x600. Use ifstream with ios::binary mode, seekg for skipping bytes, read to a buffer, and invert rows when storing band data.
function_header: double problem_17_5(int band_num, int threshold)
test_cases: // ==================== Main function: Testing ====================
int main() {
    srand(42);
    cout << fixed << setprecision(6);
    cout << "Problem 17.5" << endl;
    
    int correct_count = 0;
    const double tolerance = 1e-5;
    
    // Test 1
    int band1 = 1;
    int threshold1 = 128;

    double result1 = problem_17_5(band1, threshold1);
    if (result1 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct1 = 0.000284;  // Expected value (updated from actual result)
        if (abs(result1 - correct1) < tolerance) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 2
    int band2 = 2;
    int threshold2 = 150;

    double result2 = problem_17_5(band2, threshold2);
    if (result2 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct2 = 0.000000;  // Expected value (updated from actual result)
        if (abs(result2 - correct2) < tolerance) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 3
    int band3 = 3;
    int threshold3 = 100;

    double result3 = problem_17_5(band3, threshold3);
    if (result3 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct3 = 0.000084;  // Expected value (updated from actual result)
        if (abs(result3 - correct3) < tolerance) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }

    
    if (correct_count == 3) {
        cout << "Completely correct!" << endl;
    }
    
    return 0;
}

step_number: 6
step_description_prompt: Please write a C++ function named problem_17_6 that calculates a weighted count of pixels in a specific band from a binary data file, where pixels meet two threshold ranges and are weighted by a Gaussian spatial weight centered at the image center. The function takes four integers (band_num, threshold1, threshold2, threshold3) and returns an integer.

The function definition is: int problem_17_6(int band_num, int threshold1, int threshold2, int threshold3);

Algorithm steps: 1. Try to open the binary file "AA" from paths {"test_data/AA", "../test_data/AA", "../../test_data/AA"} in order; if none exist, output "Error: Cannot find data file AA" to cerr and return -1. 2. Read the specified band (band_num) from the file: skip (band_num - 1) * 600 * 600 bytes from the start, then read 600 rows (each 600 bytes), storing each row in reverse order (rows-1-i) into a 600x600 2D vector of unsigned char. 3. Compute Gaussian weight parameters: center at (300.0, 300.0), sigma = 600 / 4.0. 4. Iterate over all pixels: if the pixel value is greater than threshold1 and ≤ threshold2, or greater than threshold2 and ≤ threshold3, calculate the weight as exp(-(distance from center squared)/(2*sigma²)), sum these weights. 5. Return the sum rounded to the nearest integer (add 0.5 before casting to int).

Note: Use binary mode to open the file, and assume vector, ifstream, ios, exp, max are available.
function_header: int problem_17_6(int band_num, int threshold1, int threshold2, int threshold3)
test_cases: // ==================== Main function: Testing ====================
int main() {
    srand(42);
    cout << fixed << setprecision(6);
    cout << "Problem 17.6" << endl;
    
    int correct_count = 0;
    
    // Test 1
    int band1 = 1;
    int threshold1_1 = 80, threshold2_1 = 150, threshold3_1 = 200;

    int result1 = problem_17_6(band1, threshold1_1, threshold2_1, threshold3_1);
    if (result1 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        int correct1 = 73208;  // Expected value (updated from actual result)
        if (result1 == correct1) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 2
    int band2 = 2;
    int threshold1_2 = 100, threshold2_2 = 160, threshold3_2 = 220;

    int result2 = problem_17_6(band2, threshold1_2, threshold2_2, threshold3_2);
    if (result2 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        int correct2 = 0;  // Expected value (updated from actual result)
        if (result2 == correct2) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 3
    int band3 = 3;
    int threshold1_3 = 60, threshold2_3 = 140, threshold3_3 = 180;

    int result3 = problem_17_6(band3, threshold1_3, threshold2_3, threshold3_3);
    if (result3 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        int correct3 = 4764;  // Expected value (updated from actual result)
        if (result3 == correct3) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }

    
    if (correct_count == 3) {
        cout << "Completely correct!" << endl;
    }
    
    return 0;
}

step_number: 7
step_description_prompt: Please write a C++ function named problem_17_7 that takes two integers (band_num, threshold) as inputs and returns a double value. The function calculates the weighted accuracy of a predicted binary classification (based on threshold) against the actual binary classification (based on weighted mean) for a specific band of a 600x600 image, using Gaussian spatial weighting.
Function definition: double problem_17_7(int band_num, int threshold);
Algorithm steps: 1. Find the data file path by checking "test_data/AA", "../test_data/AA", "../../test_data/AA" in order. If no file is found, output "Error: Cannot find data file AA" and return -1.0. 2. Read the 600x600 band data: skip (band_num-1)*600*600 bytes from the file start, read each row, and store rows in reverse order (band[600-1-i][j] = buffer[j] for row i). 3. Compute weighted mean using Gaussian weights: center at (300.0, 300.0), sigma = max(600,600)/4.0, weight = exp(-( (i-300.0)^2 + (j-300.0)^2 )/(2*sigma*sigma)). 4. For each pixel, predict if value > threshold, actual if value > weighted mean. Calculate weighted accuracy as (sum of weights where prediction == actual) divided by total weights (same Gaussian weighting as step 3).
Note: Use binary mode to read the file, skip the specified bytes for the target band, and reverse row order when storing data. Assume necessary components (like ifstream, vector, exp) are available.
function_header: double problem_17_7(int band_num, int threshold)
test_cases: // ==================== Main function: Testing ====================
int main() {
    srand(42);
    cout << fixed << setprecision(6);
    cout << "Problem 17.7" << endl;
    
    int correct_count = 0;
    const double tolerance = 1e-5;
    
    // Test 1
    int band1 = 1;
    int threshold1 = 128;

    double result1 = problem_17_7(band1, threshold1);
    if (result1 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct1 = 0.497786;  // Expected value (updated from actual result)
        if (abs(result1 - correct1) < tolerance) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 2
    int band2 = 2;
    int threshold2 = 150;

    double result2 = problem_17_7(band2, threshold2);
    if (result2 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct2 = 0.525691;  // Expected value (updated from actual result)
        if (abs(result2 - correct2) < tolerance) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 3
    int band3 = 3;
    int threshold3 = 100;

    double result3 = problem_17_7(band3, threshold3);
    if (result3 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct3 = 0.541252;  // Expected value (updated from actual result)
        if (abs(result3 - correct3) < tolerance) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }

    
    if (correct_count == 3) {
        cout << "Completely correct!" << endl;
    }
    
    return 0;
}

step_number: 8
step_description_prompt: Please write a C++ function named problem_17_8 that takes two integers band_num and threshold as parameters and returns an integer. The function loads a specific band from a binary data file, classifies pixels based on the threshold, computes a Gaussian-spatial-weighted count of pixels with at least 5 neighbors in their 3x3 neighborhood, and returns the rounded weighted count.

Function definition: int problem_17_8(int band_num, int threshold);

Algorithm flow:
1. Check paths {"test_data/AA", "../test_data/AA", "../../test_data/AA"} to find the existing binary file. If not found, output "Error: Cannot find data file AA" to cerr and return -1.
2. Load a 600x600 band: skip (band_num-1)*600*600 bytes from the file start, read each row into a buffer, and store rows in reverse order (band[rows-1-i][j] = buf[j]).
3. Create a 600x600 bool vector classified where classified[i][j] = (band[i][j] > threshold).
4. Calculate weighted_count: set center to (300.0, 300.0) and sigma to 150.0. For each non-border pixel (1≤i<599, 1≤j<599), count 3x3 neighbors in classified. If neighbors ≥5, compute Gaussian weight (exp(-( (i-300.0)^2 + (j-300.0)^2 ) / (2*150.0*150.0))) and add to weighted_count.
5. Return (int)(weighted_count + 0.5).
function_header: int problem_17_8(int band_num, int threshold)
test_cases: // ==================== Main function: Testing ====================
int main() {
    srand(42);
    cout << fixed << setprecision(6);
    cout << "Problem 17.8" << endl;
    
    int correct_count = 0;
    
    // Test 1
    int band1 = 1;
    int threshold1 = 128;

    int result1 = problem_17_8(band1, threshold1);
    if (result1 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        int correct1 = 12;  // Expected value (updated from actual result)
        if (result1 == correct1) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 2
    int band2 = 2;
    int threshold2 = 150;

    int result2 = problem_17_8(band2, threshold2);
    if (result2 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        int correct2 = 0;  // Expected value (updated from actual result)
        if (result2 == correct2) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 3
    int band3 = 3;
    int threshold3 = 100;

    int result3 = problem_17_8(band3, threshold3);
    if (result3 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        int correct3 = 2;  // Expected value (updated from actual result)
        if (result3 == correct3) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }

    
    if (correct_count == 3) {
        cout << "Completely correct!" << endl;
    }
    
    return 0;
}

step_number: 9
step_description_prompt: Please write a C++ function named problem_17_9 that takes an integer band_num as input and returns a double. This function computes the absolute difference between two weighted ratios derived from enhanced weighted thresholding (Otsu and fixed 128) on a specified band of a 600x600 binary image.

Function definition: double problem_17_9(int band_num);

Algorithm flow:
1. Check three paths ("test_data/AA", "../test_data/AA", "../../test_data/AA") to find the valid binary file path for "AA". If no path is valid, output "Error: Cannot find data file AA" to stderr and return -1.0.
2. Read the specified band (band_num) from the binary file: skip (band_num - 1) * 600 * 600 bytes from the start, read 600 rows × 600 columns of unsigned char, and store each row i as rows-1-i (flip rows vertically).
3. Compute a 256-bin weighted histogram using Gaussian weight: weight = exp(-((i-300)^2 + (j-300)^2)/(2*150^2)), where (300,300) is the center and sigma = 150 (max(600,600)/4).
4. Calculate Otsu threshold by iterating t from 1 to 254, maximizing weighted between-class variance (w0*w1*(mean0-mean1)^2/(total_weight^2)) from the histogram.
5. Compute the weighted ratio of pixels above Otsu threshold using the same Gaussian weight.
6. Compute the weighted ratio of pixels above fixed threshold 128 using the same Gaussian weight.
7. Return the absolute difference between the two ratios.

Note: Use binary read for the file, skip the correct number of bytes for the specified band, and flip rows when storing the band data. Ensure all required headers (e.g., <vector>, <fstream>, <cmath>, <cerr>) are included.
function_header: double problem_17_9(int band_num)
test_cases: // ==================== Main function: Testing ====================
int main() {
    srand(42);
    cout << fixed << setprecision(6);
    cout << "Problem 17.9" << endl;
    
    int correct_count = 0;
    const double tolerance = 1e-5;
    
    // Test 1
    int band1 = 1;

    double result1 = problem_17_9(band1);
    if (result1 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct1 = 0.502214;  // Expected value (updated from actual result)
        if (abs(result1 - correct1) < tolerance) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 2
    int band2 = 2;

    double result2 = problem_17_9(band2);
    if (result2 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct2 = 0.474309;  // Expected value (updated from actual result)
        if (abs(result2 - correct2) < tolerance) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 3
    int band3 = 3;

    double result3 = problem_17_9(band3);
    if (result3 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct3 = 0.327776;  // Expected value (updated from actual result)
        if (abs(result3 - correct3) < tolerance) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }

    
    if (correct_count == 3) {
        cout << "Completely correct!" << endl;
    }
    
    return 0;
}

General solution:

General tests: