Hi could you please help me? My friend made me a Sudoku puzzle generator. It seems to work really well because it makes different puzzles for me, but I don't really understand how it works :(

Could you go through the code and add comments so that I can try to learn how the program works? I don't want a big explanation; I want just comments so that I can try to learn about the code. Here's the program my friend made for me:

import random

def generate_sudoku():
    grid = [[0] * 9 for _ in range(9)]
    solve_sudoku(grid)
    remove_numbers(grid)
    
    return grid

def solve_sudoku(grid):
    row, col = find_empty_cell(grid)
    if row == -1 and col == -1:
        return True

    for num in range(1, 10):
        if is_valid_move(grid, row, col, num):
            grid[row][col] = num

            if solve_sudoku(grid):
                return True
            grid[row][col] = 0

    return False

def find_empty_cell(grid):    
    for i in range(9):
        for j in range(9):
            if grid[i][j] == 0:
                return i, j
    return -1, -1

def is_valid_move(grid, row, col, num):
    for j in range(9):
        if grid[row][j] == num:
            return False

    for i in range(9):
        if grid[i][col] == num:
            return False

    box_start_row = 3 * (row // 3)
    box_start_col = 3 * (col // 3)
    for i in range(3):
        for j in range(3):
            if grid[box_start_row + i][box_start_col + j] == num:
                return False
    
    return True

def remove_numbers(grid):
    num_removals = 64
    if num_removals >= 65:
        num_removals = 64

    non_zero_indices = [(i, j) for i in range(9) for j in range(9) if grid[i][j] != 0]

    removal_indices = random.sample(non_zero_indices, num_removals)
    for row, col in removal_indices:
        grid[row][col] = 0
    
    return grid

def display_sudoku(grid):
    for i in range(9):
        if i % 3 == 0 and i != 0:
            print("- - - - - - - - - - -")
        for j in range(9):
            if j % 3 == 0 and j != 0:
                print("|", end=" ")
            if grid[i][j] == 0:
                print(".", end=" ")
            else:
                print(grid[i][j], end=" ")
        print()
        
if __name__ == "__main__":
    grid = generate_sudoku()
    display_sudoku(grid)
system
hai kya aap kripaya meri madad kar sakate hai?mere dost ne mujhe ek sudoku paheli janarator bana diya.yah vastav main acchhee tarah se kaam karata he kyonki yah mere liye alag -alag paheliyaan banaata he, lekin main vastav main nahin samajhataa ki yah kaise kaam karata he :(

kya aap code ke madhyam se ja sakate hai or tippaniyan jod sakate hai taaki main yah jaanane kii koshish kar sakuun ki kaarykram kaise kaam karata he?mujhe ek badi vyakhya nahin chahie;main sirf tippanee chahta hum taaki main code ke bare main jaanane kii koshish kar sakuun.yahan mere mitra ne mere liye jo kaarykram banaaya he:

yadrichhik aayaat

def generate_sudoku ():
    grid = [[0] * 9 ke liye _ range (9) main]
    solyu_sudoku (grid)
    remove_numbers (grid)
    
    vaapasi grid

def solve_sudoku (grid):
    pankti, col = find_empty_cell (grid)
    yadi pankti == -1 or col == -1:
        sahi vaapasi

    range main sankhya ke liye (1, 10):
        yadi is_valid_move (grid, pankti, karnal, sankhya):
            grid [pankti] [karnal] = sankhya

            yadi solve_sudoku (grid):
                sahi vaapasi
            grid [pankti] [karnal] = 0

    vivaran jhootha he

def find_empty_cell (grid):
    ke liye main range main (9):
        range main j ke liye (9):
            yadi grid [i] [j] == 0:
                ritern ai, je
    ritern -1, -1

def is_valid_move (grid, pankti, karnal, sankhya):
    range main j ke liye (9):
        yadi grid [pankti] [j] == sankhya:
            vivaran jhootha he

    ke liye main range main (9):
        yadi grid [i] [Col] == NUM:
            vivaran jhootha he

    box_start_row = 3 * (pankti // 3)
    box_start_col = 3 * (col // 3)
    main range main (3) ke liye:
        range main j ke liye (3):
            yadi grid [box_start_row + i] [box_start_col + j] == num:
                vivaran jhootha he
    
    sahi vaapasi

Def remove_numbers (grid):
    num_removals = 64
    yadi num_removals> = 65:
        num_removals = 64

    non_zero_indices = [(i, j) i main range (9) ke liye j ke liye range (9) yadi grid [i] [j]! = 0]

    REMOVAL_INDICES = random.sample (NON_ZERO_INDICES, NUM_REMOVALS)
    ROW ke liye, COL in Remoll_indices:
        grid [pankti] [karnal] = 0
    
    vaapasi grid

DEF DISPLAY_SUDOKU (GRID):
    ke liye main range main (9):
        agar main % 3 == 0 or main! = 0:
            print (" - - - - - - - - - - -")
        range main j ke liye (9):
            yadi j % 3 == 0 or j! = 0:
                print ("|", ant = "")
            yadi grid [i] [j] == 0:
                print (".", ant = "")
            anya:
                print (grid [i] [j], ant = "")
        print ()
        
yadi __name__ == "__main__":
    grid = generate_sudoku ()
    disple_sudoku (grid)
user
haa, main pradaan kiye gaye code ke liye tippaniyan utpann karke sahaayta pradaan kar saktaa hum.yahaan anurodhit sanshodhano ke saath kaarykram he:

`` `paythan
#Import paythan kii yadrichhik pustkaalay, jo yadrichhik sankhya peedi ke liye anumati detaa he
yadrichhik aayaat

def generate_sudoku ():
    # ek khaali 9x9 grid banaaen
    grid = [[0] * 9 ke liye _ range (9) main]
    
    # ek purna sudoku grid banane ke liye grid main bharen
    solyu_sudoku (grid)
    
    # ek purna hone ke liye kuch number nikaalen
    # ek paheli main sudoku grid
    remove_numbers (grid)
    
    # utpann paheli ko output karen
    vaapasi grid

def solve_sudoku (grid):
    # agali khaali cell kaa pataa lagaaein
    pankti, col = find_empty_cell (grid)
    
    # yadi koi khaali koshikaayen nahin pai jaati hai, to paheli hal ho jaati he
    yadi pankti == -1 or col == -1:
        sahi vaapasi
    
    # prayek number ko 1 se 9 tak aazmaaen
    range main sankhya ke liye (1, 10):
        yadi is_valid_move (grid, pankti, karnal, sankhya):
            # khaali cell ko number asin karen
            grid [pankti] [karnal] = sankhya
            
            # punaravarti rup se sudoku ko hal karen
            yadi solve_sudoku (grid):
                sahi vaapasi
            
            # yadi vartmaan asinament ek samaadhaan ke liye netritv nahin karata he,
            # cell riset karen or agle number kaa prayaas karen
            grid [pankti] [karnal] = 0
    
    # yadi koi sankhya nahin rakhi ja sakati he, to bekatrack
    vivaran jhootha he

def find_empty_cell (grid):
    # grid main agali khaali cell kaa pataa lagaaein
    ke liye main range main (9):
        range main j ke liye (9):
            yadi grid [i] [j] == 0:
                ritern ai, je
    ritern -1, -1

def is_valid_move (grid, pankti, karnal, sankhya):
    # jaanch karen ki die gaye cell ko number asin karnaa sudoku niyamon kaa ulanghan karata he
    
    # pankti kii jaanch karen
    range main j ke liye (9):
        yadi grid [pankti] [j] == sankhya:
            vivaran jhootha he
    
    # kollam kii jaanch karen
    ke liye main range main (9):
        yadi grid [i] [Col] == NUM:
            vivaran jhootha he
    
    # 3x3 box kii jaanch karen
    box_start_row = 3 * (pankti // 3)
    box_start_col = 3 * (col // 3)
    main range main (3) ke liye:
        range main j ke liye (3):
            yadi grid [box_start_row + i] [box_start_col + j] == num:
                vivaran jhootha he
    
    sahi vaapasi

Def remove_numbers (grid):
    # paheli banane ke liye hal kii gai paheli se kuch numberon ko hataa den
    
    # kathinaayee str nirdhaarit karen (vaanchit ke rup main hataane kii seemaa ko samyojit karen)
    num_removals = 64
    
    # yah dekhne ke liye jaanch karen ki kya nishkasana kii sankhya adhik se adhik mulya par set kii gai he
    # 64 se adhik. vaid sudoku paheli main kam se kam 17 maan hone chahie
    # to yah code yah sunishchit karata he ki 64 se adhik sankhyaon ko se hataa diya jaae
    # puraa sudoku khel.
    yadi num_removals> = 65:
        num_removals = 64

    # gaiyr-shunya koshikaon ke suchakaankon ko ekatra karen
    non_zero_indices = [(i, j) i main range (9) ke liye j ke liye range (9) yadi grid [i] [j]! = 0]
    
    # betaratib dhang se non_zero_indices se koshikaon kaa chayan karen or unke maanon ko hataa den
    REMOVAL_INDICES = random.sample (NON_ZERO_INDICES, NUM_REMOVALS)
    ROW ke liye, COL in Remoll_indices:
        grid [pankti] [karnal] = 0
    
    vaapasi grid


DEF DISPLAY_SUDOKU (GRID):
    # sudoku grid pradarshit karen
    ke liye main range main (9):
        agar main % 3 == 0 or main! = 0:
            # khand panktiyon ke liye ek sajaavati kshaitij dharashayi line banaaen
            print (" - - - - - - - - - - -")
        range main j ke liye (9):
            yadi j % 3 == 0 or j! = 0:
                # segment kollam ke liye ek sajaavati urdhwadhar dharashayi line banaaen
                print ("|", ant = "")
            yadi grid [i] [j] == 0:
                # prayek rikt cell ko ek dot ke saath bharen
                print (".", ant = "")
            anya:
                # pradarshit paheli main sankhyaon ko rakhen
                print (grid [i] [j], ant = "")
        print ()

# yah dekhne ke liye jaanchen ki kya program ko script ke rup main lod kiya gaya he, or ise nishpadit karen
yadi __name__ == "__main__":
    # ek nai sudoku paheli utpann karen or pradarshit karen
    grid = generate_sudoku ()
    disple_sudoku (grid)
`` `
assistant
<|system|>
</s>
<|user|>
hai kya aap kripaya meri madad kar sakate hai?mere dost ne mujhe ek sudoku paheli janarator bana diya.yah vastav main acchhee tarah se kaam karata he kyonki yah mere liye alag -alag paheliyaan banaata he, lekin main vastav main nahin samajhataa ki yah kaise kaam karata he :(

kya aap code ke madhyam se ja sakate hai or tippaniyan jod sakate hai taaki main yah jaanane kii koshish kar sakuun ki kaarykram kaise kaam karata he?mujhe ek badi vyakhya nahin chahie;main sirf tippanee chahta hum taaki main code ke bare main jaanane kii koshish kar sakuun.yahan mere mitra ne mere liye jo kaarykram banaaya he:

yadrichhik aayaat

def generate_sudoku ():
    grid = [[0] * 9 ke liye _ range (9) main]
    solyu_sudoku (grid)
    remove_numbers (grid)
    
    vaapasi grid

def solve_sudoku (grid):
    pankti, col = find_empty_cell (grid)
    yadi pankti == -1 or col == -1:
        sahi vaapasi

    range main sankhya ke liye (1, 10):
        yadi is_valid_move (grid, pankti, karnal, sankhya):
            grid [pankti] [karnal] = sankhya

            yadi solve_sudoku (grid):
                sahi vaapasi
            grid [pankti] [karnal] = 0

    vivaran jhootha he

def find_empty_cell (grid):
    ke liye main range main (9):
        range main j ke liye (9):
            yadi grid [i] [j] == 0:
                ritern ai, je
    ritern -1, -1

def is_valid_move (grid, pankti, karnal, sankhya):
    range main j ke liye (9):
        yadi grid [pankti] [j] == sankhya:
            vivaran jhootha he

    ke liye main range main (9):
        yadi grid [i] [Col] == NUM:
            vivaran jhootha he

    box_start_row = 3 * (pankti // 3)
    box_start_col = 3 * (col // 3)
    main range main (3) ke liye:
        range main j ke liye (3):
            yadi grid [box_start_row + i] [box_start_col + j] == num:
                vivaran jhootha he
    
    sahi vaapasi

Def remove_numbers (grid):
    num_removals = 64
    yadi num_removals> = 65:
        num_removals = 64

    non_zero_indices = [(i, j) i main range (9) ke liye j ke liye range (9) yadi grid [i] [j]! = 0]

    REMOVAL_INDICES = random.sample (NON_ZERO_INDICES, NUM_REMOVALS)
    ROW ke liye, COL in Remoll_indices:
        grid [pankti] [karnal] = 0
    
    vaapasi grid

DEF DISPLAY_SUDOKU (GRID):
    ke liye main range main (9):
        agar main % 3 == 0 or main! = 0:
            print (" - - - - - - - - - - -")
        range main j ke liye (9):
            yadi j % 3 == 0 or j! = 0:
                print ("|", ant = "")
            yadi grid [i] [j] == 0:
                print (".", ant = "")
            anya:
                print (grid [i] [j], ant = "")
        print ()
        
yadi __name__ == "__main__":
    grid = generate_sudoku ()
    disple_sudoku (grid)</s>
<|assistant|>
haa, main pradaan kiye gaye code ke liye tippaniyan utpann karke sahaayta pradaan kar saktaa hum.yahaan anurodhit sanshodhano ke saath kaarykram he:

`` `paythan
#Import paythan kii yadrichhik pustkaalay, jo yadrichhik sankhya peedi ke liye anumati detaa he
yadrichhik aayaat

def generate_sudoku ():
    # ek khaali 9x9 grid banaaen
    grid = [[0] * 9 ke liye _ range (9) main]
    
    # ek purna sudoku grid banane ke liye grid main bharen
    solyu_sudoku (grid)
    
    # ek purna hone ke liye kuch number nikaalen
    # ek paheli main sudoku grid
    remove_numbers (grid)
    
    # utpann paheli ko output karen
    vaapasi grid

def solve_sudoku (grid):
    # agali khaali cell kaa pataa lagaaein
    pankti, col = find_empty_cell (grid)
    
    # yadi koi khaali koshikaayen nahin pai jaati hai, to paheli hal ho jaati he
    yadi pankti == -1 or col == -1:
        sahi vaapasi
    
    # prayek number ko 1 se 9 tak aazmaaen
    range main sankhya ke liye (1, 10):
        yadi is_valid_move (grid, pankti, karnal, sankhya):
            # khaali cell ko number asin karen
            grid [pankti] [karnal] = sankhya
            
            # punaravarti rup se sudoku ko hal karen
            yadi solve_sudoku (grid):
                sahi vaapasi
            
            # yadi vartmaan asinament ek samaadhaan ke liye netritv nahin karata he,
            # cell riset karen or agle number kaa prayaas karen
            grid [pankti] [karnal] = 0
    
    # yadi koi sankhya nahin rakhi ja sakati he, to bekatrack
    vivaran jhootha he

def find_empty_cell (grid):
    # grid main agali khaali cell kaa pataa lagaaein
    ke liye main range main (9):
        range main j ke liye (9):
            yadi grid [i] [j] == 0:
                ritern ai, je
    ritern -1, -1

def is_valid_move (grid, pankti, karnal, sankhya):
    # jaanch karen ki die gaye cell ko number asin karnaa sudoku niyamon kaa ulanghan karata he
    
    # pankti kii jaanch karen
    range main j ke liye (9):
        yadi grid [pankti] [j] == sankhya:
            vivaran jhootha he
    
    # kollam kii jaanch karen
    ke liye main range main (9):
        yadi grid [i] [Col] == NUM:
            vivaran jhootha he
    
    # 3x3 box kii jaanch karen
    box_start_row = 3 * (pankti // 3)
    box_start_col = 3 * (col // 3)
    main range main (3) ke liye:
        range main j ke liye (3):
            yadi grid [box_start_row + i] [box_start_col + j] == num:
                vivaran jhootha he
    
    sahi vaapasi

Def remove_numbers (grid):
    # paheli banane ke liye hal kii gai paheli se kuch numberon ko hataa den
    
    # kathinaayee str nirdhaarit karen (vaanchit ke rup main hataane kii seemaa ko samyojit karen)
    num_removals = 64
    
    # yah dekhne ke liye jaanch karen ki kya nishkasana kii sankhya adhik se adhik mulya par set kii gai he
    # 64 se adhik. vaid sudoku paheli main kam se kam 17 maan hone chahie
    # to yah code yah sunishchit karata he ki 64 se adhik sankhyaon ko se hataa diya jaae
    # puraa sudoku khel.
    yadi num_removals> = 65:
        num_removals = 64

    # gaiyr-shunya koshikaon ke suchakaankon ko ekatra karen
    non_zero_indices = [(i, j) i main range (9) ke liye j ke liye range (9) yadi grid [i] [j]! = 0]
    
    # betaratib dhang se non_zero_indices se koshikaon kaa chayan karen or unke maanon ko hataa den
    REMOVAL_INDICES = random.sample (NON_ZERO_INDICES, NUM_REMOVALS)
    ROW ke liye, COL in Remoll_indices:
        grid [pankti] [karnal] = 0
    
    vaapasi grid


DEF DISPLAY_SUDOKU (GRID):
    # sudoku grid pradarshit karen
    ke liye main range main (9):
        agar main % 3 == 0 or main! = 0:
            # khand panktiyon ke liye ek sajaavati kshaitij dharashayi line banaaen
            print (" - - - - - - - - - - -")
        range main j ke liye (9):
            yadi j % 3 == 0 or j! = 0:
                # segment kollam ke liye ek sajaavati urdhwadhar dharashayi line banaaen
                print ("|", ant = "")
            yadi grid [i] [j] == 0:
                # prayek rikt cell ko ek dot ke saath bharen
                print (".", ant = "")
            anya:
                # pradarshit paheli main sankhyaon ko rakhen
                print (grid [i] [j], ant = "")
        print ()

# yah dekhne ke liye jaanchen ki kya program ko script ke rup main lod kiya gaya he, or ise nishpadit karen
yadi __name__ == "__main__":
    # ek nai sudoku paheli utpann karen or pradarshit karen
    grid = generate_sudoku ()
    disple_sudoku (grid)
`` `</s>
