In this tutorial, we will learn how to find the binomial coefficients of two integers using JavaScript. Before learning about binomial coefficient we should know what binomial coefficient is and what it refers to.
What is the binomial coefficient?
Binomial coefficient refers to the positive integer that appears as a coefficient in the binomial theorem.
The binomial coefficient C(n, k) can be defined as the coefficient of x^k in the expansion of (1 x)^n.
The binomial coefficients of two numbers n and k represent the number of combinations of r items that can be selected from a set of n items.
For example, we can say that if you want to select 3 balls from a set of 5 balls, the number of ways to do this would be C(5,2).
The formula for the binomial coefficient of C(n,k) is -
C(n,k) = n!/(n-k)!*k!
Find binomial coefficients in JavaScript
Now we will learn how to find binomial coefficients using JavaScript. Here we will provide two variables n and k and using the code we will calculate the binomial coefficient using some conditions provided.
step
We need to follow certain steps to write code to calculate the binomial coefficient of two integers n and k.
Step 1 - Create a function that accepts two parameters n and k, which will be further used to evaluate the binomial coefficients.
Step 2 - Now we check if both parameters are numbers using Number.isNaN() method.
Step 3 - Now we create an if loop which has two conditions depending on the value of the integer k, the first condition is if k is greater than 0 and the other condition is the value of k A value less than the integer n. If either condition is true, the function returns the value zero.
Step 4 - Now we create an if loop again with two other conditions depending on the value of the integer k, the first condition is if k is equal to 1 and the other conditions are of k The value is equal to the value integer n. If either condition is true, the function returns the value 1.
Step 5 - Now we create a final if loop with two conditions depending on the value of the integer k, the first condition is if k is equal to 1 and the other condition is The value of k is equal to value n-1. If either condition is true, the function returns the value n.
Step 6 - Here we will write logic to find the binomial coefficients of two integers n and k. To find the binomial coefficients we need to create a for loop starting with j = 2 until the condition j
Step 7 - After evaluating the value of the integer result, we will use the Math.round() function to find the rounding of the result.
Step 8 - In the final step we will provide the values of the two integers n and k from which we want to evaluate the binomial coefficients.
Example
We can use the following HTML code to calculate the binomial coefficient of two integers n and k using JavaScript
<!DOCTYPE html>
<html>
<head>
<h2 id="Tutorials-Point"> Tutorials Point </h2>
</head>
<body>
<script>
function Calculate (n, k){
if(Number.isNaN (n) || Number.isNaN (k)){
return NaN;
}
if(k < 0 || k > n){
return 0
}
if(k === 0 || k === n){
return 1
}
if(k === 1 || k === n - 1){
return n
}
let result = n;
for(let j = 2; j <= k; j++){
result *= (n - j + 1) / j;
}
return Math.round(result);
}
document.write("Binomial Coefficient of 15 and 6 is : " + Calculate(15, 6))
</script>
</body>
</html>
Throughout the scenario, we must understand that to find the binomial coefficients of two integers n and k, we need to first check some conditions given above and then apply logic to calculate the binomial coefficients.
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