Corrected explanations and included an example (#75)

This commit is contained in:
Nnadozie Okeke
2018-06-22 12:31:57 +01:00
committed by Oleksii Trekhleb
parent 2334583635
commit 16b6ea506a

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@ -17,9 +17,10 @@ export default function integerPartition(number) {
partitionMatrix[0][numberIndex] = 0;
}
// Let's fill the first row. It represents the number of way of how we can form
// number zero out of numbers 0, 1, 2, ... Obviously there is only one way we could
// form number 0 and it is with number 0 itself.
// Let's fill the first column. It represents the number of ways we can form
// number zero out of numbers 0, 0 and 1, 0 and 1 and 2, 0 and 1 and 2 and 3, ...
// Obviously there is only one way we could form number 0
// and it is with number 0 itself.
for (let summandIndex = 0; summandIndex <= number; summandIndex += 1) {
partitionMatrix[summandIndex][0] = 1;
}
@ -35,7 +36,18 @@ export default function integerPartition(number) {
} else {
// The number of combinations would equal to number of combinations of forming the same
// number but WITHOUT current summand number plus number of combinations of forming the
// previous number but WITH current summand.
// <current number - current summand> number but WITH current summand.
// Example: number of ways to form number 4 using summands 1, 2 and 3 is the sum of
// {number of ways to form 4 with sums that begin with 1 +
// number of ways to form 4 with sums that begin with 2 and include 1} +
// {number of ways to form 4 with sums that begin with 3 and include 2 and 1}
// Taking these sums to proceed in descending order of intergers, this gives us:
// With 1: 1+1+1+1 -> 1 way
// With 2: 2+2, 2+1+1 -> 2 ways
// With 3: 3 + (4-3) <= convince yourself that number of ways to form 4 starting
// with 3 is == number of ways to form 4-3 where 4-3 == <current number-current summand>
// Helper: if there are n ways to get (4-3) then 4 can be represented as 3 + first way,
// 3 + second way, and so on until the 3 + nth way. So answer for 4 is: 1 + 2 + 1 = 4 ways
const combosWithoutSummand = partitionMatrix[summandIndex - 1][numberIndex];
const combosWithSummand = partitionMatrix[summandIndex][numberIndex - summandIndex];