# 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

Updated on: 11-Dec-2020

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