Problem: BMP Histogram Matching and Evaluation Metrics

The problem focuses on BMP image histogram matching and analysis, involving finding BMP files, computing histograms/CDFs (including spatially weighted ones), mapping source pixels to reference via CDF matching, and calculating metrics like mapped values, average pixels, correlation coefficients, minimum distances, and Gaussian-weighted MSE, while handling file errors.


Input/Output: The problem takes two const string inputs: source_file (path to a source BMP image) and ref_file (path to a reference BMP image), plus an optional integer g (intensity value, 0 ≤ g < 255). It searches predefined directories to locate the BMP files, validates their format by checking the "BM" header, reads their pixel data, and computes spatially weighted histograms using Gaussian weights based on pixel distance to the image center. It calculates cumulative distribution functions (CDFs) scaled to 255 for both images, maps source intensities to reference via minimal absolute CDF distance, and generates a matched image. The problem outputs an integer mapped intensity value for g, a double average pixel value of the matched image, a double correlation coefficient between the matched histogram and reference histogram, a double minimum absolute CDF distance for g, and a double Gaussian-weighted mean squared error (MSE) between the matched image and reference. Errors like missing files or invalid BMPs return negative values or 0.0.

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

Sub-steps:
step_number: 1
step_description_prompt: Please write a C++ function named problem_10_1 that implements spatially weighted histogram matching between two BMP images and returns the matched value for a given input g. The function signature is int problem_10_1(const string& source_file, const string& ref_file, int g).

First, check if g is outside [0,255]; if so, return g. Define BMPFileHeader (with bfty[2], bfsize, bfreserved1, bfreserved2, bfoffbit) and BMPInfoHeader (bisize, biwidth, biheight, biplanes, bibitcount, bicompression, bisizeimage, bix, biy, biclrused, biclrimportant) using #pragma pack(push,2) and #pragma pack(pop) for structure alignment.

Search for source_file in paths "test_data/" + source_file, "../test_data/" + source_file, "../../test_data/" + source_file, "substep/test_data/" + source_file, and source_file itself. Repeat the same search for ref_file. If either file is not found, output an error message and return -1.

Read BMP headers from source_file. Check if the BMP signature (bfty[0] and bfty[1]) is "BM"; if not, output an error and return -1. Calculate width as biwidth, height as the absolute value of biheight, and aligned width aw as ((width + 3) / 4) * 4. If bibitcount is 8, skip 256 * 4 bytes (color palette) using seekg. Read source pixels into a dynamically allocated unsigned char array src_pixels of size aw * height.

Compute the spatially weighted histogram H for the source image: iterate over each pixel (i, j), get the intensity value val from src_pixels[(height-1-i)*aw + j]. Calculate weight using exp(-((i - center_i)^2 + (j - center_j)^2) / (2 * sigma^2)), where center_i = height / 2.0, center_j = width / 2.0, and sigma = max(width, height) / 4.0. Accumulate H[val] with the weight and sum all weights into total_weight.

Compute the cumulative distribution function S for the source: S[0] = H[0], S[i] = S[i-1] + H[i] for i from 1 to 255. Normalize S to [0, 255] by multiplying each element by 255.0 / (total_weight > 1e-10 ? total_weight : 1.0).

Repeat the above steps (read headers, check validity, read pixels, compute weighted histogram G, and CDF GS) for the reference file ref_file.

Create an array SG of size 256: for each i in 0-255, find the j in 0-255 that minimizes the absolute difference |S[i] - GS[j]|. Set SG[i] = j.

Deallocate src_pixels and ref_pixels using delete[]. Return SG[g].

Handle errors for file opening (output error and return -1 if files cannot be opened). Ensure all BMP reading steps (including seekg for palette if needed) are implemented.
function_header: int problem_10_1(const string& source_file, const string& ref_file, int g)
test_cases: // ==================== Main function: Testing ====================
int main() {
    srand(42);
    cout << fixed << setprecision(6);
    cout << "Problem 10.1" << endl;
    
    int correct_count = 0;
    
    // Test 1
    string src1 = "1.bmp", ref1 = "1.bmp";
    int g1 = 128;
    int result1 = problem_10_1(src1, ref1, g1);
    if (result1 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        int correct1 = 128;  // Expected value (updated from actual result)
        if (result1 == correct1) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }

    // Test 2
    string src2 = "a.bmp", ref2 = "a.bmp";
    int g2 = 64;
    int result2 = problem_10_1(src2, ref2, g2);
    if (result2 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        int correct2 = 64;  // Expected value (updated from actual result)
        if (result2 == correct2) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }

    // Test 3
    string src3 = "b.bmp", ref3 = "b.bmp";
    int g3 = 200;
    int result3 = problem_10_1(src3, ref3, g3);
    if (result3 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        int correct3 = 200;  // 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_10_2 that takes two const string references (source_file, ref_file) and returns a double. This function computes the mean pixel value of a histogram-matched image derived from a source BMP and a reference BMP.

Function definition: double problem_10_2(const string& source_file, const string& ref_file);

Algorithm flow:
1. Resolve source and reference file paths by checking directories in this order: "test_data/", "../test_data/", "../../test_data/", "substep/test_data/", and the file name directly. Verify existence using ifstream in binary mode.
2. Open the source BMP in binary mode. Read BMPFileHeader (with #pragma pack(push, 2)) and BMPInfoHeader. Validate the BMP signature by checking if fh1.bfty[0] is 'B' and fh1.bfty[1] is 'M'.
3. Calculate image width (ih1.biwidth), height (absolute value of ih1.biheight), and padded width aw = ((width + 3) / 4) * 4. If ih1.bibitcount is 8, skip 256 * 4 bytes (palette) using seekg. Read source pixel data into a dynamically allocated array src_pixels (size aw * height).
4. Compute the source histogram H (256 bins) by iterating over pixels (rows are bottom-up: (height-1-i)*aw + j). Compute cumulative distribution S (normalized to 0-255) from H.
5. Repeat steps 2-4 for the reference BMP to get ref_pixels, histogram G, and cumulative distribution GS.
6. Create a lookup table SG (256 elements): for each i (0-255), find j (0-255) with the minimal absolute difference between S[i] and GS[j]; set SG[i] = j.
7. Apply SG to source pixels to generate matched_img (height x width, bottom-up row order).
8. Sum all pixels in matched_img, then return the mean (sum divided by width * height).
9. Clean up dynamically allocated arrays (src_pixels, ref_pixels).
10. Handle errors (file not found, invalid BMP) by outputting to cerr and returning -1.0.

Note: Use binary mode for file operations. Assume standard libraries (iostream, vector, string) are included. Other required functions are pre-defined.
function_header: double problem_10_2(const string& source_file, const string& ref_file)
test_cases: // ==================== Main function: Testing ====================
int main() {
    srand(42);
    cout << fixed << setprecision(6);
    cout << "Problem 10.2" << endl;
    
    int correct_count = 0;
    const double tolerance = 1e-5;
    
    // Test 1
    string src1 = "1.bmp", ref1 = "1.bmp";

    double result1 = problem_10_2(src1, ref1);
    if (result1 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct1 = 205.054980;  // Expected value (updated from actual result)
        if (abs(result1 - correct1) < tolerance) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 2
    string src2 = "a.bmp", ref2 = "a.bmp";

    double result2 = problem_10_2(src2, ref2);
    if (result2 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct2 = 238.082949;  // Expected value (updated from actual result)
        if (abs(result2 - correct2) < tolerance) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 3
    string src3 = "b.bmp", ref3 = "b.bmp";

    double result3 = problem_10_2(src3, ref3);
    if (result3 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct3 = 205.056859;  // 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: 3
step_description_prompt: Please write a C++ function named problem_10_3 that takes two const string& parameters (source_file, ref_file) and returns a double. This function calculates the correlation coefficient between the histogram of the source BMP image after histogram matching to the reference BMP image and the histogram of the reference BMP image.

double problem_10_3(const string& source_file, const string& ref_file);

Algorithm steps:
1. Search for source_file and ref_file in paths: "test_data/" + filename, "substep/test_data/" + filename, "../test_data/" + filename, "../../test_data/" + filename, or the filename itself. Use the first existing path for each.
2. Open the found files in binary mode. Read BMPFileHeader and BMPInfoHeader (use #pragma pack(push,2) to avoid struct padding), check if the header starts with 'B' and 'M'.
3. For each BMP: Calculate aligned width (aw = ((width + 3)/4)*4). If bibitcount is 8, skip the 256*4 color palette. Read pixel data into unsigned char arrays (note: pixels are stored bottom-to-top, so access with (height-1-i)*aw + j).
4. Compute the histogram H of the source image and its cumulative histogram S (normalized to 0-255 by total pixels * 255.0).
5. Compute the histogram G of the reference image and its cumulative histogram GS (same normalization as S).
6. Create a mapping SG where SG[i] is the j that minimizes |S[i] - GS[j]| for each i (0-255).
7. Apply SG to the source pixels to get the matched image's pixel values.
8. Compute histograms of the matched image (matched_hist) and the reference image (ref_hist).
9. Calculate the mean of matched_hist (mean_m) and ref_hist (mean_r) by averaging over 256 bins.
10. Compute numerator as sum of (matched_hist[i] - mean_m) * (ref_hist[i] - mean_r), denominator as sqrt(sum((matched_hist[i]-mean_m)^2) * sum((ref_hist[i]-mean_r)^2)).
11. Return numerator / denominator (return 0.0 if denominator < 1e-10).
12. Handle errors (file not found, cannot open, invalid BMP) by returning -1.0 and outputting to cerr. Free dynamically allocated memory (src_pixels, ref_pixels) with delete[].

Note: BMPFileHeader and BMPInfoHeader are defined with #pragma pack(push,2) and #pragma pack(pop). Dynamically allocate memory for pixel arrays with new[]. Output error messages to cerr for file not found, cannot open, or invalid BMP.
function_header: double problem_10_3(const string& source_file, const string& ref_file)
test_cases: // ==================== Main function: Testing ====================
int main() {
    srand(42);
    cout << fixed << setprecision(6);
    cout << "Problem 10.3" << endl;
    
    int correct_count = 0;
    const double tolerance = 1e-5;
    
    // Test 1
    string src1 = "1.bmp", ref1 = "1.bmp";

    double result1 = problem_10_3(src1, ref1);
    if (result1 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct1 = 1.000000;  // Updated with actual result
        if (abs(result1 - correct1) < tolerance) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 2
    string src2 = "a.bmp", ref2 = "a.bmp";

    double result2 = problem_10_3(src2, ref2);
    if (result2 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct2 = 1.000000;  // Updated with actual result
        if (abs(result2 - correct2) < tolerance) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 3
    string src3 = "b.bmp", ref3 = "b.bmp";

    double result3 = problem_10_3(src3, ref3);
    if (result3 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct3 = 1.000000;  // Updated with 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_10_4 that calculates the minimum absolute distance between the cumulative spatially weighted histogram value of a given gray level g from a source BMP image and any cumulative spatially weighted histogram value from a reference BMP image. It returns 0.0 if g is out of [0, 255], -1.0 on file errors or invalid BMPs, and the minimum distance otherwise.

Function definition: double problem_10_4(const string& source_file, const string& ref_file, int g);

Algorithm flow:
1. Return 0.0 immediately if g is less than 0 or greater than or equal to 256.
2. Define BMPFileHeader (with char bfty[2], int bfsize, short bfreserved1, short bfreserved2, int bfoffbit) and BMPInfoHeader (with int bisize, int biwidth, int biheight, short biplanes, short bibitcount, int bicompression, int bisizeimage, int bix, int biy, int biclrused, int biclrimportant) using #pragma pack(push, 2) before and #pragma pack(pop) after to ensure structure alignment.
3. Search for source_file and ref_file in the paths "test_data/", "substep/test_data/", "../test_data/", "../../test_data/", and the file name directly. Open the first existing file. If no file is found, output an error message to cerr and return -1.0.
4. For the source BMP:
   a. Open the file in binary mode, read BMPFileHeader and BMPInfoHeader. Check if the BMP signature (bfty[0] == 'B' and bfty[1] == 'M'); if not, output an error to cerr and return -1.0.
   b. Calculate width as biwidth, height as the absolute value of biheight, and aligned width (aw) as ((width + 3) / 4) * 4. If the BMP is 8-bit (bibitcount == 8), skip the color palette by seeking 256 * 4 bytes from the current position. Read pixel data into a dynamically allocated unsigned char array src_pixels.
5. Compute the spatially weighted histogram H for the source image:
   a. Set center_i = height / 2.0, center_j = width / 2.0, sigma = max(width, height) / 4.0.
   b. Iterate over each pixel (i from 0 to height-1, j from 0 to width-1):
      - Calculate actual_row = height - 1 - i (to reverse BMP's bottom-up pixel storage).
      - Get the pixel value val from src_pixels[actual_row * aw + j].
      - Compute weight as exp(-((i - center_i)² + (j - center_j)²) / (2.0 * sigma * sigma)).
      - Accumulate H[val] with weight and total_weight with weight.
6. Compute the cumulative histogram S for the source:
   a. Calculate cumulative sum of H to get S (S[0] = H[0], S[i] = S[i-1] + H[i] for i ≥ 1).
   b. Normalize S to the range [0, 255] using S[i] = S[i] * 255.0 / (total_weight > 1e-10 ? total_weight : 1.0).
7. Repeat steps 4-6 for the reference BMP file (ref_file) to get the cumulative spatially weighted histogram GS.
8. Calculate the minimum absolute distance min_dist between S[g] and any value in GS (0 ≤ j < 256).
9. Delete the dynamically allocated src_pixels and ref_pixels arrays. Return min_dist.

Notes: Use ifstream with ios::binary for BMP reading. Output error messages to cerr when files cannot be found, opened, or are invalid BMPs. Handle 8-bit BMP color palette skipping. Ensure aligned width calculation for BMP row padding. Reverse BMP's bottom-up pixel order with actual_row.
function_header: double problem_10_4(const string& source_file, const string& ref_file, int g)
test_cases: // ==================== Main function: Testing ====================
int main() {
    srand(42);
    cout << fixed << setprecision(6);
    cout << "Problem 10.4" << endl;
    
    int correct_count = 0;
    const double tolerance = 1e-5;
    
    // Test 1
    string src1 = "1.bmp", ref1 = "1.bmp";
    int g1 = 128;
    double result1 = problem_10_4(src1, ref1, g1);
    if (result1 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct1 = 0.000000;  // Updated with actual result
        if (abs(result1 - correct1) < tolerance) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }

    // Test 2
    string src2 = "a.bmp", ref2 = "a.bmp";
    int g2 = 64;
    double result2 = problem_10_4(src2, ref2, g2);
    if (result2 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct2 = 0.000000;  // Updated with actual result
        if (abs(result2 - correct2) < tolerance) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }

    // Test 3
    string src3 = "b.bmp", ref3 = "b.bmp";
    int g3 = 200;
    double result3 = problem_10_4(src3, ref3, g3);
    if (result3 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct3 = 0.000000;  // Updated with 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_10_5 that takes two const string& parameters (source_file, ref_file) and returns a double. This function calculates the spatially weighted Mean Squared Error (MSE) between a source BMP image and a reference BMP image after performing spatially weighted histogram matching.

Function definition: double problem_10_5(const string& source_file, const string& ref_file);

Algorithm flow:
1. Search for valid paths of source_file and ref_file in "test_data/", "substep/test_data/", "../test_data/", "../../test_data/", and the file name directly. If no valid path is found, output an error message and return -1.0.
2. Open the source BMP file in binary mode, read BMPFileHeader (with #pragma pack(push,2)) and BMPInfoHeader, verify it's a valid BMP (bfty[0] == 'B' and bfty[1] == 'M'). If invalid, output error and return -1.0.
3. Calculate width as ih1.biwidth, height as abs(ih1.biheight), aligned width as ((width + 3)/4)*4. If the image is 8-bit (bibitcount == 8), skip the color palette (seekg(256*4, ios::cur)). Read pixels into a dynamically allocated unsigned char array (src_pixels) with row inversion (actual_row = height - 1 - i).
4. Compute the spatially weighted histogram H for the source image: Use Gaussian weight (sigma = max(width, height)/4.0, center at (height/2.0, width/2.0)), accumulate H[val] with weight = exp(-dist_sq/(2*sigma²)) where dist_sq is the squared distance from the center. Calculate total_weight.
5. Compute cumulative distribution function S of H, normalize S to 0-255.
6. Repeat steps 2-5 for the reference BMP file to get cumulative distribution function GS.
7. Create mapping SG: For each gray level i (0-255), find j in 0-255 that minimizes |S[i] - GS[j]|, set SG[i] = j.
8. Generate a matched image using the source image's size: Map each source pixel value via SG.
9. Calculate weighted MSE between the matched image and reference image: Use the same Gaussian weight as step 4, sum weight * (matched_val - ref_val)², divide by total weight.
10. Free dynamically allocated memory (src_pixels, ref_pixels) and return the MSE.

File reading notes: Read BMP files in binary mode (ios::binary). Handle BMPFileHeader with #pragma pack(push,2) and #pragma pack(pop). For 8-bit BMP, skip the 256*4-byte color palette. Calculate aligned width as ((width + 3)/4)*4. Read pixels with row inversion (actual_row = height - 1 - i). Handle division by zero by using 1.0 if total_weight or weight_sum is less than 1e-10.
function_header: double problem_10_5(const string& source_file, const string& ref_file)
test_cases: // ==================== Main function: Testing ====================
int main() {
    srand(42);
    cout << fixed << setprecision(6);
    cout << "Problem 10.5" << endl;
    
    int correct_count = 0;
    const double tolerance = 1e-5;
    
    // Test 1
    string src1 = "1.bmp", ref1 = "1.bmp";
    double result1 = problem_10_5(src1, ref1);
    if (result1 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct1 = 0.000000;  // Updated with actual result
        if (abs(result1 - correct1) < tolerance) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }

    // Test 2
    string src2 = "a.bmp", ref2 = "a.bmp";
    double result2 = problem_10_5(src2, ref2);
    if (result2 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct2 = 0.000000;  // Updated with actual result
        if (abs(result2 - correct2) < tolerance) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }

    // Test 3
    string src3 = "b.bmp", ref3 = "b.bmp";
    double result3 = problem_10_5(src3, ref3);
    if (result3 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct3 = 0.000000;  // Updated with 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_10_6 that calculates the total number of pixels with a gray level ≤ the given gray_level in the specified band of a 600x600 image. The function is defined as int problem_10_6(int band_num, int gray_level). Algorithm steps: 1. Return 0 if gray_level is < 0 or ≥ 256. 2. Try to open the file from paths "test_data/AA", "../test_data/AA", "../../test_data/AA" in order; if no file is found, output "Error: Cannot find data file AA" to cerr and return -1. 3. Read the specified band: skip (band_num - 1) * 600 * 600 bytes from the start of the file (using ios::binary mode), read each row into a buffer, then store rows in reverse order (rows - 1 - i) into a 2D vector<vector<unsigned char>> of size 600x600. 4. Compute a histogram of 256 bins based on the image data. 5. Calculate the cumulative sum of histogram values from bin 0 to bin gray_level, return this sum.
function_header: int problem_10_6(int band_num, int gray_level)
test_cases: // ==================== Main function: Testing ====================
int main() {
    srand(42);
    cout << fixed << setprecision(6);
    cout << "Problem 10.6" << endl;
    
    int correct_count = 0;
    
    // Test 1
    int band1 = 1, gray1 = 128;

    int result1 = problem_10_6(band1, gray1);
    if (result1 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        int correct1 = 359900;  // Expected value (updated from actual result)
        if (result1 == correct1) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 2
    int band2 = 2, gray2 = 64;

    int result2 = problem_10_6(band2, gray2);
    if (result2 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        int correct2 = 359772;  // Expected value (updated from actual result)
        if (result2 == correct2) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
// Test 3
    int band3 = 3, gray3 = 200;

    int result3 = problem_10_6(band3, gray3);
    if (result3 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        int correct3 = 360000;  // 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_10_7 which takes an int parameter band_num and returns a double, it calculates the ratio of the maximum frequency of pixel values to the total number of pixels in a specified band from a binary data file.
The function definition is double problem_10_7(int band_num);
Algorithm flow: 1. Check three file paths "test_data/AA", "../test_data/AA", "../../test_data/AA" to find the existing one using ifstream in binary mode; if no file is found, output "Error: Cannot find data file AA" to cerr and return -1.0. 2. Set rows=600 and cols=600, create a 2D vector band of unsigned char with size rows×cols. 3. Open the found binary file, skip (band_num - 1) * rows * cols bytes using seekg, read each row into a dynamically allocated unsigned char buffer of size cols, then assign the buffer content to the band vector in reverse row order (band[rows - 1 - i][j] = buf[j] for each column j in row i). 4. Create a histogram vector of 256 int elements initialized to 0, count the frequency of each pixel value in band. 5. Find the maximum value in histogram using max_element, calculate and return (double)max_freq / (rows * cols).
Note that functions like ifstream, max_element are assumed to be defined. The file reading operations use binary mode, and you need to handle file existence check, skipping bytes, and row reversal correctly.
function_header: double problem_10_7(int band_num)
test_cases: // ==================== Main function: Testing ====================
int main() {
    srand(42);
    cout << fixed << setprecision(6);
    cout << "Problem 10.7" << endl;
    
    int correct_count = 0;
    const double tolerance = 1e-5;
    
    // Test 1
    int band1 = 1;

    double result1 = problem_10_7(band1);
    if (result1 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct1 = 0.070661;  // 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_10_7(band2);
    if (result2 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct2 = 0.106689;  // 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_10_7(band3);
    if (result3 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        double correct3 = 0.058069;  // 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: