Problem: Gaussian-Weighted Band Difference Analysis

The problem involves processing binary image band data from file AA (with path validation and row flipping) to compute Gaussian-weighted metrics—such as sum, ratio, mean, standard deviation, and precision—for pixel differences or ratios between bands, returning quantitative results for change detection and statistical analysis.


Input/Output: The problem accepts integer parameters (band_num, threshold, band1, band2, band3) and a double parameter (ratio_threshold) depending on the subproblem. It locates the binary file AA in paths "test_data/AA", "../test_data/AA", "../../test_data/AA". For specified bands, it reads 600x600 data by skipping (band_num-1)*600*600 bytes and reversing row order. It computes metrics using Gaussian spatial weights (center at image/sub-center, sigma = max dimension/4): rounded weighted count of significant differences, weighted mean of valid pixels, weighted standard deviation of differences, weighted change ratio, weighted precision. Outputs are integers (rounded sums) or doubles (mean, std dev, ratio, precision); returns -1 (int) or -1.0 (double) if the file is not found.

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

Sub-steps:
step_number: 1
step_description_prompt: Please write a C++ function named problem_18_1 that takes two integers (band_num, threshold) as parameters and returns an integer. This function implements weighted change detection with Gaussian spatial weighting. The function signature is int problem_18_1(int band_num, int threshold);. First, search for the file "test_data/AA" in three paths: "test_data/AA", "../test_data/AA", "../../test_data/AA". If not found, output "Error: Cannot find data file AA" to cerr and return -1. Then read the specified band data (600 rows × 600 columns, binary mode): skip (band_num - 1) * 600 * 600 bytes, read each row into a buffer (unsigned char[600]), and store rows in reverse order (row i as 599 - i) into a 2D vector<unsigned char> band (600x600). Next, compute weighted count: for each i (0-599) and j (0-299), calculate absolute difference between band[i][j] and band[i][j+300]. If difference > threshold, compute Gaussian weight with center (300.0, 150.0) and sigma 150.0 (weight = exp(-((i-300.0)^2 + (j-150.0)^2)/(2*150*150))), add to weighted_count. Return (int)(weighted_count + 0.5). Use necessary headers and namespace std.
function_header: int problem_18_1(int band_num, int threshold)
test_cases: // ==================== Main function: Testing ====================
int main() {
    srand(42);
    cout << fixed << setprecision(6);
    cout << "Problem 18.1" << endl;
    
    int correct_count = 0;
    
    // Test 1
    int band1 = 1;
    int threshold1 = 20;

    int result1 = problem_18_1(band1, threshold1);
    if (result1 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        int correct1 = 2757;  // 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 = 30;

    int result2 = problem_18_1(band2, threshold2);
    if (result2 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        int correct2 = 33;  // 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 = 40;

    int result3 = problem_18_1(band3, threshold3);
    if (result3 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        int correct3 = 197;  // 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_18_2 that implements weighted change detection with Gaussian spatial weighting. The function is defined as int problem_18_2(int band1, int band2, double ratio_threshold); 

First, try to find the existing file from paths {"test_data/AA", "../test_data/AA", "../../test_data/AA"} using ifstream in binary mode. If no file is found, output "Error: Cannot find data file AA" to cerr and return -1. 

Then, read band1 and band2 data from the file into two 600x600 unsigned char 2D vectors b1 and b2. For each band, calculate the skip offset as (band-1)*600*600, use seekg to move to the band's start. Read each row into an unsigned char buffer of size 600, then store the row in reverse order (rows-1-i) into b1 or b2. 

Next, iterate over all pixels: if b1[i][j] > 0, compute ratio = (double)b2[i][j]/b1[i][j]. If ratio > 1+ratio_threshold or ratio < 1-ratio_threshold, calculate squared distance to center (center_i=600/2.0, center_j=600/2.0), sigma=max(600,600)/4.0, Gaussian weight=exp(-dist_sq/(2*sigma*sigma)), and accumulate weighted_count. 

Finally, return (int)(weighted_count + 0.5) (rounded). 

Note: Use ios::binary for file operations. The file reading includes trying three paths, skipping previous bands, reading rows to buffer, and reversing row order. Assume required functions/headers are available.
function_header: int problem_18_2(int band1, int band2, double ratio_threshold)
test_cases: // ==================== Main function: Testing ====================
int main() {
    srand(42);
    cout << fixed << setprecision(6);
    cout << "Problem 18.2" << endl;
    
    int correct_count = 0;
    
    // Test 1
    int band1_1 = 1, band2_1 = 2;
    double ratio_threshold1 = 0.2;

    int result1 = problem_18_2(band1_1, band2_1, ratio_threshold1);
    if (result1 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        int correct1 = 128799;  // 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;
    double ratio_threshold2 = 0.3;

    int result2 = problem_18_2(band1_2, band2_2, ratio_threshold2);
    if (result2 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        int correct2 = 11163;  // 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;
    double ratio_threshold3 = 0.25;

    int result3 = problem_18_2(band1_3, band2_3, ratio_threshold3);
    if (result3 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        int correct3 = 59987;  // 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_18_3 with parameters int band_num and int threshold that returns a double. The function first checks three file paths ("test_data/AA", "../test_data/AA", "../../test_data/AA") to find the existing "AA" file; if no file exists, output "Error: Cannot find data file AA" to cerr and return -1.0. Then, read a 600x600 band from the file: skip (band_num - 1) * 600 * 600 bytes from the start, read each row into a buffer, reverse the row order when storing into a 2D vector<vector<unsigned char>> band (size 600x600). Next, for each i (0<=i<600) and j (0<=j<300), calculate the absolute difference between band[i][j] and band[i][j+300]; if the difference exceeds threshold, compute Gaussian weight as exp(-((i - 300.0)^2 + (j - 150.0)^2)/(2*sigma^2)) where sigma = max(600, 300)/4. Sum the weighted band[i][j] and the weights. Return weighted_sum / weight_sum if weight_sum > 1e-10, else return 0.0. Ensure functions like ifstream, ios::binary, ios::beg, cerr, exp, max are available.</think>Wait, let's check: half_cols is cols/2 = 300, so j is 0 to 299. Center i is 600/2.0=300.0, center j is 300/2.0=150.0. Yes. Sigma is max(600,300)/4=600/4=150. Correct. File reading part: skip (band_num-1)*600*600, read each row into buf, reverse rows (rows-1-i). Correct. Error message: yes. Parameters: correct. Return values: correct. All rules followed.</think>Please write a C++ function named problem_18_3 with parameters int band_num and int threshold that returns a double. The function first checks three file paths ("test_data/AA", "../test_data/AA", "../../test_data/AA") to find the existing "AA" file; if no file is found, output "Error: Cannot find data file AA" to cerr and return -1.0. Then, read a 600x600 band from the file: skip (band_num - 1) * 600 * 600 bytes from the start, read each row into a buffer, reverse the row order when storing into a 2D vector<vector<unsigned char>> band (rows: 600, cols: 600). Next, compute the weighted mean of band[i][j] (j in the first half of cols) where the absolute difference between band[i][j] and band[i][j + (cols/2)] exceeds threshold. The weight is a Gaussian spatial weight with center at (rows/2.0, (cols/2)/2.0) and sigma = max(rows, cols/2) / 4. Sum the weighted band[i][j] values and the weights. Return the ratio of weighted_sum to weight_sum if weight_sum > 1e-10, otherwise return 0.0. Ensure functions like ifstream, ios::binary, ios::beg, cerr, exp, and max are available.
function_header: double problem_18_3(int band_num, int threshold)
test_cases: // ==================== Main function: Testing ====================
int main() {
    srand(42);
    cout << fixed << setprecision(6);
    cout << "Problem 18.3" << endl;
    
    int correct_count = 0;
    const double tolerance = 1e-5;
    
    // Test 1
    int band1 = 1;
    int threshold1 = 20;

    double result1 = problem_18_3(band1, threshold1);
    if (result1 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct1 = 95.900764;  // 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 = 30;

    double result2 = problem_18_3(band2, threshold2);
    if (result2 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct2 = 58.955924;  // 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 = 40;

    double result3 = problem_18_3(band3, threshold3);
    if (result3 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct3 = 73.733703;  // 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: 4
step_description_prompt: Please write a C++ function named problem_18_4 that takes an integer band_num as input and returns a double. This function calculates the weighted standard deviation of absolute differences between left and right halves of a specific band from a binary file, using Gaussian spatial weighting.

Function definition: double problem_18_4(int band_num);

Algorithm flow:
1. Check three file paths in order: "test_data/AA", "../test_data/AA", "../../test_data/AA". Open the first existing binary file. If no file is found, output "Error: Cannot find data file AA" to cerr and return -1.0.
2. Read the specified band (band_num) with 600 rows and 600 columns: Skip (band_num - 1) * 600 * 600 bytes from the file start. Read each row, reverse row order (store as rows-1 - i).
3. Compute Gaussian weights: center_i = 600 / 2.0, center_j = (600 / 2) / 2.0, sigma = max(600, 600 / 2) / 4.0.
4. Calculate weighted sum of absolute differences between left (j) and right (j + 300) halves using Gaussian weights, then get the weighted mean.
5. Compute weighted variance of these differences, then return the square root of the variance.

Ensure binary file reading, vector operations, and Gaussian weight calculations follow the above steps. Assume necessary headers and types (vector, ifstream, ios::binary, exp, sqrt, max) are available.
function_header: double problem_18_4(int band_num)
test_cases: // ==================== Main function: Testing ====================
int main() {
    srand(42);
    cout << fixed << setprecision(6);
    cout << "Problem 18.4" << endl;
    
    int correct_count = 0;
    const double tolerance = 1e-5;
    
    // Test 1
    int band1 = 1;

    double result1 = problem_18_4(band1);
    if (result1 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct1 = 5.940436;  // 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_18_4(band2);
    if (result2 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct2 = 4.205419;  // 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_18_4(band3);
    if (result3 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct3 = 7.831254;  // 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: 5
step_description_prompt: Write a C++ function named problem_18_5 that takes two integers (band_num, threshold) and returns a double. This function calculates the weighted change ratio with Gaussian spatial weighting based on the specified band data and threshold.
Function definition: double problem_18_5(int band_num, int threshold);
Steps:
1. Attempt to open the binary file "AA" from three paths: "test_data/AA", "../test_data/AA", "../../test_data/AA". If found, store the path; if not, output "Error: Cannot find data file AA" to cerr and return -1.0.
2. Read 600x600 band data from the file: skip (band_num - 1) * 600 * 600 bytes from the start, read each row of 600 bytes, and store rows in reverse order (rows-1-i).
3. Use center (300.0, 150.0) and sigma = 150. Iterate over all rows and first 300 columns: compute absolute difference between the pixel and its corresponding pixel in the second half of columns, compute distance squared to the center, calculate weight as exp(-dist_sq/(2*sigma*sigma)). Accumulate weighted_count if difference > threshold, and accumulate weight_sum.
4. Return weighted_count / weight_sum if weight_sum > 1e-10; else return 0.0.
function_header: double problem_18_5(int band_num, int threshold)
test_cases: // ==================== Main function: Testing ====================
int main() {
    srand(42);
    cout << fixed << setprecision(6);
    cout << "Problem 18.5" << endl;
    
    int correct_count = 0;
    const double tolerance = 1e-5;
    
    // Test 1
    int band1 = 1;
    int threshold1 = 20;

    double result1 = problem_18_5(band1, threshold1);
    if (result1 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct1 = 0.029929;  // 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 = 30;

    double result2 = problem_18_5(band2, threshold2);
    if (result2 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct2 = 0.000355;  // 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 = 40;

    double result3 = problem_18_5(band3, threshold3);
    if (result3 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct3 = 0.002143;  // 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_18_6 that implements weighted change detection with Gaussian spatial weighting using three spectral bands from a binary file, returning the rounded weighted count of changed pixels exceeding a threshold. The function is defined as int problem_18_6(int band1, int band2, int band3, int threshold). First, locate the binary file "AA" in paths {"test_data/AA", "../test_data/AA", "../../test_data/AA"}; if not found, output "Error: Cannot find data file AA" to cerr and return -1. Read three 600x600 bands (each as a consecutive 600x600 block) from the file: for each band N (band1, band2, band3), skip (N-1)*600*600 bytes, read each row into a buffer, then store in a 2D vector<vector<unsigned char>> with vertical flip (using rows-1-i instead of i). For each pixel (i,j), if abs((int)b1[i][j] - (int)b2[i][j]) > threshold or abs((int)b2[i][j] - (int)b3[i][j]) > threshold, calculate Gaussian weight (center at (300.0, 300.0), sigma = 150.0, weight = exp(-((i-300.0)*(i-300.0)+(j-300.0)*(j-300.0))/(2*sigma*sigma))). Sum these weights, round to the nearest integer (add 0.5 then cast to int), and return the result. Assume standard libraries (vector, ifstream, ios, cerr, exp) are available.
function_header: int problem_18_6(int band1, int band2, int band3, int threshold)
test_cases: // ==================== Main function: Testing ====================
int main() {
    srand(42);
    cout << fixed << setprecision(6);
    cout << "Problem 18.6" << endl;
    
    int correct_count = 0;
    
    // Test 1
    int band1_1 = 1, band2_1 = 2, band3_1 = 3;
    int threshold1 = 20;

    int result1 = problem_18_6(band1_1, band2_1, band3_1, threshold1);
    if (result1 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        int correct1 = 128797;  // 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, band3_2 = 4;
    int threshold2 = 30;

    int result2 = problem_18_6(band1_2, band2_2, band3_2, threshold2);
    if (result2 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        int correct2 = 3747;  // 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, band3_3 = 5;
    int threshold3 = 40;

    int result3 = problem_18_6(band1_3, band2_3, band3_3, threshold3);
    if (result3 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        int correct3 = 2971;  // 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_18_7 that takes three integers (band1, band2, threshold) and returns a double. This function calculates the weighted precision of change detection between two bands using Gaussian spatial weighting.
The function is defined as double problem_18_7(int band1, int band2, int threshold);
Algorithm steps: 1. Check three paths ("test_data/AA", "../test_data/AA", "../../test_data/AA") in order to find the existing file. If no file exists, output "Error: Cannot find data file AA" to cerr and return -1.0. 2. For band1, skip (band1-1)*600*600 bytes from the file start, read each row (600 unsigned char per row), and store in a 600x600 vector with vertical flip (rows-1-i). Repeat for band2 using (band2-1)*600*600 bytes. 3. Iterate over all 600x600 pixels: compute absolute difference between b1[i][j] and b2[i][j]. Mark "actual" if difference >20, "detected" if difference >threshold. Calculate Gaussian weight with center (300.0,300.0) and sigma=150.0 (max(600,600)/4). Accumulate weighted_total_changes for actual pixels and weighted_true_positives for actual+detected pixels. 4. Return weighted_true_positives / weighted_total_changes if weighted_total_changes >1e-10, else 0.0.
Note: Use ifstream in binary mode to read files. Use seekg to skip bytes, read() to get row data. Use vectors of vectors for band data storage. Gaussian weight formula: exp(-( (i-300.0)^2 + (j-300.0)^2 )/(2*150.0*150.0) ).
function_header: double problem_18_7(int band1, int band2, int threshold)
test_cases: // ==================== Main function: Testing ====================
int main() {
    srand(42);
    cout << fixed << setprecision(6);
    cout << "Problem 18.7" << endl;
    
    int correct_count = 0;
    const double tolerance = 1e-5;
    
    // Test 1
    int band1_1 = 1, band2_1 = 2;
    int threshold1 = 20;

    double result1 = problem_18_7(band1_1, band2_1, threshold1);
    if (result1 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct1 = 1.000000;  // Expected value (updated from actual result)
        if (abs(result1 - correct1) < tolerance) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 2
    int band1_2 = 2, band2_2 = 3;
    int threshold2 = 30;

    double result2 = problem_18_7(band1_2, band2_2, threshold2);
    if (result2 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct2 = 0.031411;  // Expected value (updated from actual result)
        if (abs(result2 - correct2) < tolerance) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 3
    int band1_3 = 3, band2_3 = 4;
    int threshold3 = 40;

    double result3 = problem_18_7(band1_3, band2_3, threshold3);
    if (result3 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct3 = 0.015537;  // 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 use C++ code to generate a function named problem_18_8 that calculates a rounded integer of the weighted count of pixels where band2 value minus band1 value exceeds a threshold, using Gaussian spatial weighting. The function is defined as int problem_18_8(int band1, int band2, int threshold). Algorithm flow: 1. Check paths "test_data/AA", "../test_data/AA", "../../test_data/AA" in order to find the binary file "AA"; if not found, output "Error: Cannot find data file AA" via cerr and return -1. 2. Read band1 data (600x600 unsigned char) from the file: open the file in binary mode, skip (band1 - 1) * 600 * 600 bytes using seekg, read each row and store it as rows - 1 - i. 3. Read band2 data from the same file using the same method as band1. 4. Iterate over all 600x600 pixels, if (int)b2[i][j] - (int)b1[i][j] > threshold, calculate the weight using the Gaussian formula where the center is (300, 300) and sigma is 150, then add the weight to weighted_count. 5. Return (int)(weighted_count + 0.5). Note: When reading the file, open it in binary mode, use seekg to skip the correct number of bytes for each band, and flip the rows when storing the data.
function_header: int problem_18_8(int band1, int band2, int threshold)
test_cases: // ==================== Main function: Testing ====================
int main() {
    srand(42);
    cout << fixed << setprecision(6);
    cout << "Problem 18.8" << endl;
    
    int correct_count = 0;
    
    // Test 1
    int band1_1 = 1, band2_1 = 2;
    int threshold1 = 20;

    int result1 = problem_18_8(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 = 30;

    int result2 = problem_18_8(band1_2, band2_2, threshold2);
    if (result2 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        int correct2 = 17;  // 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 = 40;

    int result3 = problem_18_8(band1_3, band2_3, threshold3);
    if (result3 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        int correct3 = 436;  // 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_18_9 that calculates a combined change detection score using Gaussian-weighted metrics from a binary data file, returning a double value (0-1, or -1.0 on file error).
Function definition: double problem_18_9(int band1, int band2, int threshold);
Algorithm flow:
1. Search for binary file "AA" in paths {"test_data/AA", "../test_data/AA", "../../test_data/AA"}; if none exists, output "Error: Cannot find data file AA" to cerr and return -1.0.
2. Read 600x600 unsigned char data for band1: skip (band1-1)*600*600 bytes in binary mode, read each row into an unsigned char buffer, then store in band with rows flipped (rows-1 - i).
3. Compute Gaussian weights with center (300.0, 150.0) and sigma = 150.0 (max(600, 300)/4).
4. Calculate weighted_change_count (sum weights where |band[i][j]-band[i][j+300]|>threshold for j<300) and weight_sum_change.
5. Compute change_percentage = weighted_change_count / (weight_sum_change > 1e-10 ? weight_sum_change : 1.0).
6. Calculate weighted_sum_diff, mean_diff = weighted_sum_diff / (weight_sum_diff > 1e-10 ? weight_sum_diff : 1.0), variance_diff = sum(weight*(diff-mean_diff)^2)/weight_sum_diff, then change_intensity = sqrt(variance_diff).
7. Normalize change_count (rounded weighted_change_count) to min(1.0, change_count/100000.0) and intensity to min(1.0, change_intensity/50.0).
8. Return normalized_count*0.3 + change_percentage*0.4 + normalized_intensity*0.3.
Note: Use binary mode for file operations, manage buffer memory, and include necessary headers for vectors, file streams, math functions, and algorithms.
function_header: double problem_18_9(int band1, int band2, int threshold)
test_cases: // ==================== Main function: Testing ====================
int main() {
    srand(42);
    cout << fixed << setprecision(6);
    cout << "Problem 18.9" << endl;
    
    int correct_count = 0;
    const double tolerance = 1e-5;
    
    // Test 1
    int band1_1 = 1, band2_1 = 2;
    int threshold1 = 20;

    double result1 = problem_18_9(band1_1, band2_1, threshold1);
    if (result1 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct1 = 0.055885;  // Expected value (updated from actual result)
        if (abs(result1 - correct1) < tolerance) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 2
    int band1_2 = 2, band2_2 = 3;
    int threshold2 = 30;

    double result2 = problem_18_9(band1_2, band2_2, threshold2);
    if (result2 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct2 = 0.025474;  // Expected value (updated from actual result)
        if (abs(result2 - correct2) < tolerance) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 3
    int band1_3 = 3, band2_3 = 4;
    int threshold3 = 40;

    double result3 = problem_18_9(band1_3, band2_3, threshold3);
    if (result3 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct3 = 0.048436;  // 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: