برنامه محاسبه مثلث خیام پاسکال — راهنمای کاربردی

1//  C++ code for Pascal's Triangle 
2#include <stdio.h> 
3  
4// See https://www.geeksforgeeks.org/space-and-time-efficient-binomial-coefficient/  
5// for details of this function 
6int binomialCoeff(int n, int k); 
7  
8// Function to print first 
9// n lines of Pascal's  
10// Triangle 
11void printPascal(int n) 
12{ 
13    // Iterate through every line and 
14    // print entries in it 
15    for (int line = 0; line < n; line++) 
16    { 
17        // Every line has number of  
18        // integers equal to line  
19        // number 
20        for (int i = 0; i <= line; i++) 
21            printf("%d ", 
22                    binomialCoeff(line, i)); 
23        printf("\n"); 
24    } 
25} 
26  
27// See https://www.geeksforgeeks.org/space-and-time-efficient-binomial-coefficient/ 
28// for details of this function 
29int binomialCoeff(int n, int k) 
30{ 
31    int res = 1; 
32    if (k > n - k) 
33    k = n - k; 
34    for (int i = 0; i < k; ++i) 
35    { 
36        res *= (n - i); 
37        res /= (i + 1); 
38    } 
39      
40    return res; 
41} 
42  
43// Driver program  
44int main() 
45{ 
46    int n = 7; 
47    printPascal(n); 
48    return 0; 
49}

1// Java code for Pascal's Triangle 
2import java.io.*; 
3  
4class GFG { 
5      
6    // Function to print first 
7    // n lines of Pascal's Triangle 
8    static void printPascal(int n) 
9    { 
10          
11    // Iterate through every line 
12    // and print entries in it 
13    for (int line = 0; line < n; line++) 
14    { 
15        // Every line has number of  
16        // integers equal to line number 
17        for (int i = 0; i <= line; i++) 
18        System.out.print(binomialCoeff 
19                        (line, i)+" "); 
20                          
21        System.out.println(); 
22    } 
23    } 
24      
25    // Link for details of this function 
26    // https://www.geeksforgeeks.org/space-and-time-efficient-binomial-coefficient/ 
27    static int binomialCoeff(int n, int k) 
28    { 
29        int res = 1; 
30          
31        if (k > n - k) 
32        k = n - k; 
33              
34        for (int i = 0; i < k; ++i) 
35        { 
36            res *= (n - i); 
37            res /= (i + 1); 
38        } 
39        return res; 
40    } 
41      
42    // Driver code 
43    public static void main(String args[]) 
44    { 
45    int n = 7; 
46    printPascal(n); 
47    } 
48} 
49  
50/*This code is contributed by Nikita Tiwari.*/

1# Python 3 code for Pascal's Triangle 
2# A simple O(n^3)  
3# program for  
4# Pascal's Triangle 
5  
6# Function to print  
7# first n lines of 
8# Pascal's Triangle 
9def printPascal(n) : 
10      
11    # Iterate through every line  
12    # and print entries in it 
13    for line in range(0, n) : 
14          
15        # Every line has number of  
16        # integers equal to line 
17        # number 
18        for i in range(0, line + 1) : 
19            print(binomialCoeff(line, i), 
20                " ", end = "") 
21        print() 
22      
23  
24# See https://www.geeksforgeeks.org/space-and-time-efficient-binomial-coefficient/ 
25# for details of this function 
26def binomialCoeff(n, k) : 
27    res = 1
28    if (k > n - k) : 
29        k = n - k 
30    for i in range(0 , k) : 
31        res = res * (n - i) 
32        res = res // (i + 1) 
33      
34    return res 
35  
36# Driver program 
37n = 7
38printPascal(n) 
39  
40  
41# This code is contributed by Nikita Tiwari.

1// C# code for Pascal's Triangle 
2using System; 
3  
4class GFG { 
5      
6    // Function to print first 
7    // n lines of Pascal's Triangle 
8    static void printPascal(int n) 
9    { 
10          
11    // Iterate through every line 
12    // and print entries in it 
13    for (int line = 0; line < n; line++) 
14    { 
15        // Every line has number of  
16        // integers equal to line number 
17        for (int i = 0; i <= line; i++) 
18        Console.Write(binomialCoeff 
19                        (line, i)+" "); 
20                          
21        Console.WriteLine(); 
22    } 
23    } 
24      
25    // Link for details of this function 
26    // https://www.geeksforgeeks.org/space-and-time-efficient-binomial-coefficient/ 
27    static int binomialCoeff(int n, int k) 
28    { 
29        int res = 1; 
30          
31        if (k > n - k) 
32        k = n - k; 
33              
34        for (int i = 0; i < k; ++i) 
35        { 
36            res *= (n - i); 
37            res /= (i + 1); 
38        } 
39        return res; 
40    } 
41      
42    // Driver code 
43    public static void Main() 
44    { 
45    int n = 7; 
46    printPascal(n); 
47    } 
48} 
49  
50/*This code is contributed by vt_m.*/

1<?php 
2// PHP implementation for 
3// Pascal's Triangle 
4  
5// for details of this function 
6function binomialCoeff($n, $k) 
7{ 
8    $res = 1; 
9    if ($k > $n - $k) 
10    $k = $n - $k; 
11    for ($i = 0; $i < $k; ++$i) 
12    { 
13        $res *= ($n - $i); 
14        $res /= ($i + 1); 
15    } 
16return $res; 
17} 
18  
19// Function to print first 
20// n lines of Pascal's  
21// Triangle 
22function printPascal($n) 
23{ 
24    // Iterate through every line and 
25    // print entries in it 
26    for ($line = 0; $line < $n; $line++) 
27    { 
28        // Every line has number of  
29        // integers equal to line  
30        // number 
31        for ($i = 0; $i <= $line; $i++) 
32                echo "".binomialCoeff($line, $i)." "; 
33                  
34        echo "\n"; 
35    } 
36} 
37  
38// Driver Code 
39$n=7; 
40printPascal($n); 
41  
42// This code is contributed by Mithun Kumar 
43?>

1// C++ program for Pascal’s Triangle 
2// A O(n^2) time and O(n^2) extra space  
3// method for Pascal's Triangle 
4#include <bits/stdc++.h> 
5using namespace std; 
6  
7void printPascal(int n) 
8{ 
9      
10    // An auxiliary array to store  
11    // generated pscal triangle values 
12    int arr[n][n];  
13  
14    // Iterate through every line and  
15    // print integer(s) in it 
16    for (int line = 0; line < n; line++) 
17    { 
18        // Every line has number of integers  
19        // equal to line number 
20        for (int i = 0; i <= line; i++) 
21        { 
22        // First and last values in every row are 1 
23        if (line == i || i == 0) 
24            arr[line][i] = 1; 
25        // Other values are sum of values just  
26        // above and left of above 
27        else
28            arr[line][i] = arr[line - 1][i - 1] +  
29                            arr[line - 1][i]; 
30        cout << arr[line][i] << " "; 
31        } 
32        cout << "\n"; 
33    } 
34} 
35  
36// Driver code 
37int main() 
38{ 
39    int n = 5; 
40    printPascal(n); 
41    return 0; 
42} 
43  
44// This code is Contributed by Code_Mech.

1// C program for Pascal’s Triangle 
2// A O(n^2) time and O(n^2) extra space  
3// method for Pascal's Triangle 
4void printPascal(int n) 
5{ 
6// An auxiliary array to store  
7// generated pscal triangle values 
8int arr[n][n];  
9  
10// Iterate through every line and print integer(s) in it 
11for (int line = 0; line < n; line++) 
12{ 
13    // Every line has number of integers  
14    // equal to line number 
15    for (int i = 0; i <= line; i++) 
16    { 
17    // First and last values in every row are 1 
18    if (line == i || i == 0) 
19        arr[line][i] = 1; 
20    // Other values are sum of values just  
21    // above and left of above 
22    else 
23        arr[line][i] = arr[line-1][i-1] + arr[line-1][i]; 
24    printf("%d ", arr[line][i]); 
25    } 
26    printf("\n"); 
27} 
28} 
29// Driver code 
30int main() 
31{ 
32int n = 5; 
33    printPascal(n); 
34    return 0; 
35}

1// java program for Pascal's Triangle 
2// A O(n^2) time and O(n^2) extra  
3// space method for Pascal's Triangle 
4import java.io.*; 
5  
6class GFG { 
7    public static void main (String[] args) { 
8        int n = 5; 
9        printPascal(n); 
10    } 
11  
12public static void printPascal(int n) 
13{ 
14// An auxiliary array to store generated pascal triangle values 
15int[][] arr = new int[n][n];  
16  
17// Iterate through every line and print integer(s) in it 
18for (int line = 0; line < n; line++) 
19{ 
20    // Every line has number of integers equal to line number 
21    for (int i = 0; i <= line; i++) 
22    { 
23    // First and last values in every row are 1 
24    if (line == i || i == 0) 
25        arr[line][i] = 1; 
26    else // Other values are sum of values just above and left of above 
27        arr[line][i] = arr[line-1][i-1] + arr[line-1][i]; 
28    System.out.print(arr[line][i]); 
29    } 
30    System.out.println(""); 
31} 
32} 
33}

1// C# program for Pascal's Triangle 
2// A O(n^2) time and O(n^2) extra  
3// space method for Pascal's Triangle 
4using System; 
5  
6class GFG  
7{ 
8public static void printPascal(int n) 
9{ 
10      
11// An auxiliary array to store  
12// generated pascal triangle values 
13int[,] arr = new int[n, n];  
14  
15// Iterate through every line 
16// and print integer(s) in it 
17for (int line = 0; line < n; line++) 
18{ 
19    // Every line has number of  
20    // integers equal to line number 
21    for (int i = 0; i <= line; i++) 
22    { 
23          
24    // First and last values  
25    // in every row are 1 
26    if (line == i || i == 0) 
27        arr[line, i] = 1; 
28    else // Other values are sum of values 
29         // just above and left of above 
30        arr[line, i] = arr[line - 1, i - 1] +  
31                       arr[line - 1, i]; 
32    Console.Write(arr[line, i]); 
33    } 
34Console.WriteLine(""); 
35} 
36} 
37  
38// Driver Code 
39public static void Main ()  
40{ 
41    int n = 5; 
42    printPascal(n); 
43} 
44} 
45  
46// This code is contributed  
47// by Akanksha Rai(Abby_akku)

1<?php 
2// PHP program for Pascal’s Triangle 
3// A O(n^2) time and O(n^2) extra space  
4// method for Pascal's Triangle 
5function printPascal($n) 
6{ 
7    // An auxiliary array to store  
8    // generated pscal triangle values 
9    $arr = array(array());  
10      
11    // Iterate through every line and  
12    // print integer(s) in it 
13    for ($line = 0; $line < $n; $line++) 
14    { 
15        // Every line has number of integers  
16        // equal to line number 
17        for ($i = 0; $i <= $line; $i++) 
18        { 
19            // First and last values in every row are 1 
20            if ($line == $i || $i == 0) 
21                $arr[$line][$i] = 1; 
22                  
23            // Other values are sum of values just  
24            // above and left of above 
25            else
26                $arr[$line][$i] = $arr[$line - 1][$i - 1] +  
27                                $arr[$line - 1][$i]; 
28            echo $arr[$line][$i] . " "; 
29        } 
30        echo "\n"; 
31    } 
32} 
33  
34// Driver code 
35$n = 5; 
36printPascal($n); 
37  
38// This code is contributed 
39// by Akanksha Rai 
40?>

1// C++ program for Pascal’s Triangle 
2// A O(n^2) time and O(1) extra space  
3// function for Pascal's Triangle 
4#include <bits/stdc++.h> 
5  
6using namespace std; 
7void printPascal(int n) 
8{ 
9      
10for (int line = 1; line <= n; line++) 
11{ 
12    int C = 1; // used to represent C(line, i) 
13    for (int i = 1; i <= line; i++)  
14    { 
15          
16        // The first value in a line is always 1 
17        cout<< C<<" ";  
18        C = C * (line - i) / i;  
19    } 
20    cout<<"\n"; 
21} 
22} 
23  
24// Driver code 
25int main() 
26{ 
27    int n = 5; 
28    printPascal(n); 
29    return 0; 
30} 
31  
32// This code is contributed by Code_Mech