diff --git a/Project-Euler/Problem044.js b/Project-Euler/Problem044.js
index 04d531d569..e2530da7ef 100644
--- a/Project-Euler/Problem044.js
+++ b/Project-Euler/Problem044.js
@@ -8,37 +8,57 @@
* It can be seen that P4 + P7 = 22 + 70 = 92 = P8. However, their difference, 70 − 22 = 48, is not pentagonal.
* Find the pair of pentagonal numbers, Pj and Pk, for which their sum and difference are pentagonal and D = |Pk − Pj| is minimised; what is the value of D?
*
- * @author ddaniel27
+ * @author utkarsh-shrivastav77
*/
-function problem44 (k) {
- if (k < 1) {
+function getPentagonalNumber(n) {
+ return n * (3 * n - 1) / 2;
+}
+
+// The function takes a limit parameter that determines the maximum pentagonal number to consider. It first defines a getPentagonalNumber function to calculate the nth pentagonal number using the given formula.
+
+function findMinPentagonalDifference(limit) {
+
+ if (limit < 1) {
throw new Error('Invalid Input')
}
- while (true) {
- k++
- const n = k * (3 * k - 1) / 2 // calculate Pk
+ // Then, it initializes two arrays: pentagonalNumbers to store the pentagonal numbers and pentagonalIndices to store their indices. We use a Set for pentagonalIndices to ensure that checking if a number is pentagonal is O(1) on average.
+
+ const pentagonalNumbers = [];
+ const pentagonalIndices = new Set();
+
+ // The function then iterates over all pairs of indices in pentagonalNumbers and checks if their sum and difference are also pentagonal. If they are, it checks if the difference D is smaller than the current minimum difference minD. If it is, it updates minD to the new minimum value and minPair to the corresponding pair of pentagonal numbers.
+
+ for (let i = 1; i <= limit; i++) {
+ const pentagonalNumber = getPentagonalNumber(i);
+ pentagonalNumbers.push(pentagonalNumber);
+ pentagonalIndices.add(pentagonalNumber);
+ }
+
+ let minD = Infinity;
+ let minPair;
- for (let j = k - 1; j > 0; j--) {
- const m = j * (3 * j - 1) / 2 // calculate all Pj < Pk
- if (isPentagonal(n - m) && isPentagonal(n + m)) { // Check sum and difference
- return n - m // return D
+ for (let j = 1; j < pentagonalNumbers.length; j++) {
+ for (let k = j + 1; k < pentagonalNumbers.length; k++) {
+ const sum = pentagonalNumbers[j] + pentagonalNumbers[k];
+ const diff = pentagonalNumbers[k] - pentagonalNumbers[j];
+ if (pentagonalIndices.has(sum) && pentagonalIndices.has(diff)) {
+ if (diff < minD) {
+ minD = diff;
+ minPair = [pentagonalNumbers[j], pentagonalNumbers[k]];
+ }
}
}
}
+
+ return minD;
}
-/**
- * Function to check if a number is pentagonal or not
- * This function solves n
- * applying the solution for a quadratic function
- * @see {@link https://en.wikipedia.org/wiki/Quadratic_function}
- */
+// You can call the function like this to find the minimum difference between a pair of pentagonal numbers whose sum and difference are also pentagonal up to the pentagonal number limit of 10000
+
+
+export { findMinPentagonalDifference }
+
-function isPentagonal (n) {
- const pent = (Math.sqrt(24 * n + 1) + 1) / 6
- return pent === Math.floor(pent)
-}
-export { problem44 }
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