# Maximum of all the integers in the given level of Pascal triangle

Given an integer L, the task is to find the maximum of all the integers present at the given level in Pascal’s triangle.
A Pascal triangle with 6 levels is shown below:

1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1

Examples:

Input: L = 3
Output: 3
0th level -> 1
1st level -> 1 1
2nd level -> 1 2 1
3rd level -> 1 3 3 1

Input: L = 5
Output: 10

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: It is known that each row in a Pascal Triangle is Binomial Coefficients and the kth coefficient in a binomial expansion for the level n is nCk. Also, the middle element of any level is always the greatest that is k = floor(n / 2).
Hence the maximum of all the integers present at the given level in Pascal’s triangle is binomialCoeff(n, n / 2).

Below is the implementation of the above approach:

## C++

 // C++ implementation of the approach #include using namespace std;    // Function for the binomial coefficient int binomialCoeff(int n, int k) {     int C[n + 1][k + 1];     int i, j;        // Calculate value of Binomial Coefficient     // in bottom up manner     for (i = 0; i <= n; i++) {         for (j = 0; j <= min(i, k); j++) {                // Base Cases             if (j == 0 || j == i)                 C[i][j] = 1;                // Calculate value using previously             // stored values             else                 C[i][j] = C[i - 1][j - 1] + C[i - 1][j];         }     }        return C[n][k]; }    // Function to return the maximum // value in the nth level // of the Pascal's triangle int findMax(int n) {     return binomialCoeff(n, n / 2); }    // Driver code int main() {     int n = 5;        cout << findMax(n);        return 0; }

## Java

 // Java implementation of the approach    class GFG {     // Function for the binomial coefficient     static int binomialCoeff(int n, int k)     {         int [][] C = new int[n + 1][k + 1];         int i, j;                // Calculate value of Binomial Coefficient         // in bottom up manner         for (i = 0; i <= n; i++) {             for (j = 0; j <= Math.min(i, k); j++) {                        // Base Cases                 if (j == 0 || j == i)                     C[i][j] = 1;                        // Calculate value using previously                 // stored values                 else                     C[i][j] = C[i - 1][j - 1] + C[i - 1][j];             }         }                return C[n][k];     }            // Function to return the maximum     // value in the nth level     // of the Pascal's triangle     static int findMax(int n)     {         return binomialCoeff(n, n / 2);     }            // Driver code     public static void main (String[] args) {                    int n = 5;                System.out.println(findMax(n));            }    }       // This code is contributed by ihritik

## C#

 // C# implementation of the approach    using System; class GFG {     // Function for the binomial coefficient     static int binomialCoeff(int n, int k)     {         int [ , ] C = new int[n + 1, k + 1];         int i, j;                // Calculate value of Binomial Coefficient         // in bottom up manner         for (i = 0; i <= n; i++) {             for (j = 0; j <= Math.Min(i, k); j++) {                        // Base Cases                 if (j == 0 || j == i)                     C[i, j] = 1;                        // Calculate value using previously                 // stored values                 else                     C[i, j] = C[i - 1, j - 1] + C[i - 1, j];             }         }                return C[n, k];     }            // Function to return the maximum     // value in the nth level     // of the Pascal's triangle     static int findMax(int n)     {         return binomialCoeff(n, n / 2);     }            // Driver code     public static void Main () {                    int n = 5;                Console.WriteLine(findMax(n));            }    }       // This code is contributed by ihritik

## Python3

 # Python3 implementation of the approach    # Function for the binomial coefficient def binomialCoeff(n, k):     C = [[0 for i in range(k + 1)]              for i in range(n + 1)]        # Calculate value of Binomial Coefficient     # in bottom up manner     for i in range(n + 1):         for j in range(min(i, k) + 1):                            # Base Cases             if (j == 0 or j == i):                 C[i][j] = 1                # Calculate value using previously             # stored values             else:                 C[i][j] = C[i - 1][j - 1] + C[i - 1][j]        return C[n][k]    # Function to return the maximum # value in the nth level # of the Pascal's triangle def findMax(n):     return binomialCoeff(n, n // 2)    # Driver code n = 5    print(findMax(n))    # This code is contributed by Mohit Kumar

Output:

10

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