Finding all possible ways of integer partitioning in JavaScript

The partition of a positive integer n is a way of writing n as a sum of positive integers. Two sums that differ only in the order of their summands are considered the same partition.

For example, 4 can be partitioned in five distinct ways −

4 3 + 1 2 + 2 2 + 1 + 1 1 + 1 + 1 + 1

We are required to write a JavaScript function that takes in a positive integer as the only argument. The function should find and return all the possible ways of partitioning that integer.

Example

Following is the code −

const findPartitions = (num = 1) => {    const arr = Array(num + 1).fill(null).map(() => {       return Array(num + 1).fill(null);    });    for (let j = 1; j <= num; j += 1) {       arr[0][j] = 0;    }    for (let i = 0; i <= num; i += 1) {       arr[i][0] = 1;    }    for (let i = 1; i <= num; i += 1) {       for (let j = 1; j <= num; j += 1) {          if (i > j) {             arr[i][j] = arr[i - 1][j];          }          else {             const exclusive = arr[i - 1][j];             const inclusive = arr[i][j - i];             arr[i][j] = exclusive + inclusive;          }       }    }    return arr[num][num]; }; console.log(findPartitions(4));

Output

Following is the output on console −

5