Problem: BMP Weighted Calculations and Alignment

The problem requires developing C++ functions for BMP file operations—including path lookup, header/palette reading—and computing weighted values (using sine/cosine and random factors) for byte sums, RGB sums, aligned widths, and file sizes, with alignment checks and error handling.


Input/Output: The problem takes inputs including a string filename (for functions problem_4_1 and problem_4_2), an integer index (0–255 for problem_4_2), and integers width and height (for problem_4_3 and problem_4_4). It outputs four integers: problem_4_1 returns a rounded weighted sum of the first two bytes of the located file (or -1 if the file is not found), problem_4_2 returns a rounded weighted RGB sum of the specified palette entry in a BMP file (0 if the index is invalid, -1 if the file is not found), problem_4_3 returns a 4-byte aligned width adjusted by a sine-based weight and random factor, and problem_4_4 returns a rounded weighted BMP file size calculated from the aligned width and height with a cosine-based weight and random factor. Processing involves checking predefined paths for file location, reading BMP headers/palettes (for problem_4_2), and applying weighted calculations with trigonometric and random adjustments.

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

Sub-steps:
step_number: 1
step_description_prompt: Please write a C++ function named problem_4_1 that takes a const string& filename as input, tries to locate the file in "test_data/" + filename, "../test_data/" + filename, "../../test_data/" + filename, reads the first two bytes of the file, computes a weighted sum of their integer values with distance-based weights, and returns the rounded result as an int. If the file isn't found, output "Error: Cannot find data file" to cerr and return -1.
Function definition: int problem_4_1(const string& filename);
Algorithm steps: 1. Create a vector<string> possible_paths containing the three paths mentioned. 2. Iterate through possible_paths: for each path, open the file in binary mode, check if it's open; if yes, close it and set filepath to this path, then break. 3. If filepath is empty, output the error message and return -1. 4. Open the file at filepath in binary mode, read the first two bytes into a char array header[2], then close the file. 5. Convert header[0] and header[1] to int val1 and val2. 6. Compute weight1 = 1.0 + 0.1 * sin(val1 * M_PI / 128.0), weight2 = 1.0 + 0.1 * cos(val2 * M_PI / 128.0). 7. Return (int)(val1 * weight1 + val2 * weight2 + 0.5). If opening the found file fails, return 0. Assume all included headers (<bits/stdc++.h>, <cmath>, <iomanip>, <numeric>, <random>, <fstream>, <complex>, <algorithm>) and functions (sin, cos, ifstream methods) are available. Use ios::binary when opening files.</think>Please write a C++ function named problem_4_1 that takes a const string& filename, tries to find the file in paths "test_data/" + filename, "../test_data/" + filename, "../../test_data/" + filename, reads the first two bytes of the file, computes a weighted sum of their integer values with distance-based weights, and returns the rounded result as an int. If the file isn't found, output "Error: Cannot find data file" to cerr and return -1.
Function definition: int problem_4_1(const string& filename);
Algorithm steps: 1. Create a vector<string> possible_paths with the three paths. 2. Iterate through possible_paths: open each path in binary mode, if open, close it and set filepath to this path, break. 3. If filepath is empty, output error and return -1. 4. Open the file at filepath in binary mode, read first two bytes into char header[2], close the file. 5. Convert header[0] and header[1] to int val1 and val2. 6. Compute weight1 = 1.0 + 0.1 * sin(val1 * M_PI / 128.0), weight2 = 1.0 + 0.1 * cos(val2 * M_PI / 128.0). 7. Return (int)(val1 * weight1 + val2 * weight2 + 0.5). If opening the found file fails, return 0.
Assume all included headers (<bits/stdc++.h>, <cmath>, <iomanip>, <numeric>, <random>, <fstream>, <complex>, <algorithm>) and used functions (sin, cos, ifstream operations) are available. Use ios::binary when opening files.
function_header: int problem_4_1(const string& filename)
test_cases: // ==================== Main function: Testing ====================
int main() {
    srand(42);
    cout << fixed << setprecision(6);
    cout << "Problem 4.1" << endl;
    
    int correct_count = 0;
    
    // Test 1
    string x1 = "1.bmp";
    int result1 = problem_4_1(x1);
    if (result1 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        int correct1 = 147;  // Expected value (updated from actual result)
        if (result1 == correct1) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
    
    // Test 2
    string x2 = "a.bmp";
    int result2 = problem_4_1(x2);
    if (result2 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        int correct2 = 147;  // Expected value (updated from actual result)
        if (result2 == correct2) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
    
    // Test 3
    string x3 = "b.bmp";
    int result3 = problem_4_1(x3);
    if (result3 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        int correct3 = 147;  // 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_4_2 that takes a const string& filename and an int index, and returns an int. The function reads a BMP file, processes its palette, and computes a weighted RGB sum based on the index.

int problem_4_2(const string& filename, int index);

Algorithm flow:
1. Return 0 if index < 0 or index >= 256.
2. Define RGBQUAD (unsigned char rgbBlue, rgbGreen, rgbRed, rgbReserved), BMPFileHeader (char bfty[2], int bfsize, short bfreserved1, bfreserved2, int bfoffbit), BMPInfoHeader (int bisize, biwidth, biheight; short biplanes, bibitcount; int bicompression, bisizeimage, bix, biy, biclrused, biclrimportant) with #pragma pack(push, 2) and #pragma pack(pop).
3. Try file paths: "test_data/" + filename, "../test_data/" + filename, "../../test_data/" + filename, "substep/test_data/" + filename, filename itself. Use the first existing path.
4. Open the file in binary mode. If no file found, output "Error: Cannot find data file" to cerr and return -1. If file can't open, return 0.
5. Read BMPFileHeader and BMPInfoHeader. Check if bfty[0] is 'B' and bfty[1] is 'M'; return 0 if not.
6. If infoHeader.bibitcount is 8, read 256 RGBQUAD entries into a palette array.
7. Extract r = palette[index].rgbRed, g = palette[index].rgbGreen, b = palette[index].rgbBlue. Compute weights: weight_r = 1.0 + 0.05 * sin(index * M_PI / 128.0), weight_g = 1.0 + 0.05 * cos(index * M_PI / 128.0), weight_b = 1.0 + 0.05 * sin((index + 64) * M_PI / 128.0). Return (int)(r * weight_r + g * weight_g + b * weight_b + 0.5).
function_header: int problem_4_2(const string& filename, int index)
test_cases: // ==================== Main function: Testing ====================
int main() {
    srand(42);
    cout << fixed << setprecision(6);
    cout << "Problem 4.2" << endl;
    
    int correct_count = 0;
    
    // Test 1
    string x1 = "1.bmp";
    int index1 = 0;
    int result1 = problem_4_2(x1, index1);
    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
    string x2 = "1.bmp";
    int index2 = 128;
    int result2 = problem_4_2(x2, index2);
    if (result2 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        int correct2 = 391;  // Expected value (updated from actual result)
        if (result2 == correct2) {
            cout << "Correct" << endl;
            correct_count++;
        } else {
            cout << "Wrong" << endl;
        }
    }
    
    // Test 3
    string x3 = "1.bmp";
    int index3 = 255;
    int result3 = problem_4_2(x3, index3);
    if (result3 < 0) {
        cout << "Wrong (File not found)" << endl;
    } else {
        int correct3 = 790;  // 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_4_3 that takes an int parameter width and returns an int, which implements a weighted alignment calculation with adaptive rounding using a random seed. The function signature is int problem_4_3(int width). The algorithm steps are: 1. Calculate base_aligned as ((width + 3) / 4) * 4 (use integer division). 2. Generate random_factor as (double)rand() / RAND_MAX * 0.02 - 0.01 (range: -0.01 to 0.01). 3. Compute weight as 1.0 + 0.01 * sin(width * M_PI / 256.0) + random_factor. 4. Calculate adjusted as base_aligned * weight. 5. Get result by casting (adjusted + 0.5) to int (rounding). 6. Ensure the final result is aligned to 4 bytes by returning ((result + 3) / 4) * 4. Functions like rand(), RAND_MAX, and M_PI are already defined and do not need to be redefined.
function_header: int problem_4_3(int width)
test_cases: // ==================== Main function: Testing ====================
int main() {
    srand(42);
    cout << fixed << setprecision(6);
    cout << "Problem 4.3" << endl;
    
    int correct_count = 0;
    
    // Test 1
    int x1 = 600;
    int result1 = problem_4_3(x1);    int correct1 = 600;  // Expected value (updated from actual result)
    if (result1 == correct1) {
        cout << "Correct" << endl;
        correct_count++;
    } else {
        cout << "Wrong" << endl;
    }
    
    // Test 2
    int x2 = 601;
    int result2 = problem_4_3(x2);    int correct2 = 604;  // Expected value (updated from actual result)
    if (result2 == correct2) {
        cout << "Correct" << endl;
        correct_count++;
    } else {
        cout << "Wrong" << endl;
    }
    
    // Test 3
    int x3 = 602;
    int result3 = problem_4_3(x3);    int correct3 = 612;  // 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_4_4 that takes two int parameters (width and height) and returns an int. The function calculates an adjusted BMP file size using weighted alignment and random factors.

The function must include:
- #pragma pack(push, 2) before defining struct BMPFileHeader (members: char bfty[2], int bfsize, short bfreserved1, short bfreserved2, int bfoffbit)
- struct BMPInfoHeader (members: int bisize, int biwidth, int biheight, short biplanes, short bibitcount, int bicompression, int bisizeimage, int bix, int biy, int biclrused, int biclrimportant)
- #pragma pack(pop) after the structs

Algorithm steps:
1. Compute base_aligned as ((width + 3) / 4) * 4.
2. Compute random_factor1 as (double)rand() / RAND_MAX * 0.02 - 0.01.
3. Compute weight as 1.0 + 0.01 * sin(width * M_PI / 256.0) + random_factor1.
4. Compute adjusted as base_aligned * weight.
5. Compute aligned_width as ((int)(adjusted + 0.5) + 3) / 4 * 4.
6. Compute random_factor2 as (double)rand() / RAND_MAX * 0.002 - 0.001.
7. Compute size_weight as 1.0 + 0.001 * cos(height * M_PI / 256.0) + random_factor2.
8. Compute file_size as (1078 + aligned_width * height) * size_weight.
9. Return (int)(file_size + 0.5).

Assume rand(), RAND_MAX, and M_PI are already defined.
function_header: int problem_4_4(const string& filename)
test_cases: // ==================== Main function: Testing ====================
int main() {
    srand(42);
    cout << fixed << setprecision(6);
    cout << "Problem 4.4" << endl;
    
    int correct_count = 0;
    
    // Test 1
    int x1_width = 600;
    int x1_height = 600;
    int result1 = problem_4_4(x1_width, x1_height);    int correct1 = 360896;  // Expected value (updated from actual result)
    if (result1 == correct1) {
        cout << "Correct" << endl;
        correct_count++;
    } else {
        cout << "Wrong" << endl;
    }
    
    // Test 2
    int x2_width = 512;
    int x2_height = 512;
    int result2 = problem_4_4(x2_width, x2_height);    int correct2 = 263705;  // Expected value (updated from actual result)
    if (result2 == correct2) {
        cout << "Correct" << endl;
        correct_count++;
    } else {
        cout << "Wrong" << endl;
    }
    
    // Test 3
    int x3_width = 1024;
    int x3_height = 768;
    int result3 = problem_4_4(x3_width, x3_height);    int correct3 = 786554;  // 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;
}

General solution:

General tests: