How do I count the combinations of a 2D array by each row?

Counting combinations in a 2D array by each row involves understanding that each row’s elements can be combined independently. The total number of combinations for a row is the product of the number of elements in each subset of each row (considering that you can choose no element, one element, two elements, and so on up to the total number of elements in that subset).

Let's clarify with a simple example. Suppose you have the following 2D array:

[ [1, 2], [3, 4, 5], [6] ]

In this case, for the first row `[1, 2]`, the combinations are: `{}`, `{1}`, `{2}`, `{1, 2}` which is 2² = 4 combinations. For the second row `[3, 4, 5]`, we have: `{}`, `{3}`, `{4}`, `{5}`, `{3, 4}`, `{3, 5}`, `{4, 5}`, `{3, 4, 5}` which gives us 2³ = 8 combinations. For the third row `[6]`, the combinations are: `{}`, `{6}`, so there are 2¹ = 2 combinations.

To calculate the total combinations across all rows, we multiply the number of combinations for each row. In this example, it would be 4 8 2 = 64.

Here is a JavaScript example of how to calculate the number of combinations per row:

function countRowCombinations(arr) {
   return arr.map(row => Math.pow(2, row.length));
}

This function will return an array where each number represents the total number of combinations for each row. If you need to calculate the total number of combinations across all rows, you must multiply the result, as the combination of each row is independent to the others.

Here is how to calculate the total combinations across all rows:

function calculateTotalCombinations(arr) {
   const rowCombinations = countRowCombinations(arr);
   return rowCombinations.reduce((acc, curr) => acc curr, 1);
}

Let's demonstrate a complete usage example:

const array2D = [
   [1, 2],
   [3, 4, 5],
   [6]
];

const rowCombinations = countRowCombinations(array2D);
const totalCombinations = calculateTotalCombinations(array2D);

console.log("Combinations per row:", rowCombinations); // Output: [4, 8, 2]
console.log("Total combinations:", totalCombinations); // Output: 64


This approach is effective for determining how many combinations are possible by independently selecting items from each row of a 2D array.

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