# 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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