Initial data commit

Task/Zumkeller-numbers/TypeScript/zumkeller-numbers.ts

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+/**
+ * return an array of divisors of a number(n)
+ * @params {number} n The number to find divisors from
+ * @return {number[]} divisors of n
+*/
+function getDivisors(n: number): number[] {
+    //initialize divisors array
+    let divisors: number[] = [1, n]
+    //loop through all numbers from 2 to sqrt(n)
+    for (let i = 2; i*i <= n; i++) {
+      // if i is a divisor of n
+      if (n % i == 0) {
+        // add i to divisors array
+        divisors.push(i);
+        // quotient of n/i is also a divisor of n
+        let j = n/i;
+        // if quotient is not equal to i
+        if (i != j) {
+          // add quotient to divisors array
+          divisors.push(j);
+        }
+      }
+    }
+
+    return divisors
+  }
+
+  /**
+   * return sum of an array of number
+   * @param {number[]} arr The array we need to sum
+   * @return {number} sum of arr
+   */
+  function getSum(arr: number[]): number {
+    return arr.reduce((prev, curr) => prev + curr, 0)
+  }
+
+  /**
+   * check if there is a subset of divisors which sums to a specific number
+   * @param {number[]} divs The array of divisors
+   * @param {number} sum The number to check if there's a subset of divisors which sums to it
+   * @return {boolean} true if sum is 0, false if divisors length is 0
+   */
+  function isPartSum(divs: number[], sum: number): boolean {
+    // if sum is 0, the partition is sum up to the number(sum)
+    if (sum == 0) return true;
+    //get length of divisors array
+    let len = divs.length;
+    // if divisors array is empty the partion doesnt not sum up to the number(sum)
+    if (len == 0) return false;
+    //get last element of divisors array
+    let last = divs[len - 1];
+    //create a copy of divisors array without the last element
+    const newDivs = [...divs];
+    newDivs.pop();
+    // if last element is greater than sum
+    if (last > sum) {
+      // recursively check if there's a subset of divisors which sums to sum using the new divisors array
+      return isPartSum(newDivs, sum);
+    }
+    // recursively check if there's a subset of divisors which sums to sum using the new divisors array
+    // or if there's a subset of divisors which sums to sum - last using the new divisors array
+    return isPartSum(newDivs, sum) || isPartSum(newDivs, sum - last);
+  }
+
+  /**
+   * check if a number is a Zumkeller number
+   * @param {number} n The number to check if it's a Zumkeller number
+   * @returns {boolean} true if n is a Zumkeller number, false otherwise
+   */
+  function isZumkeller(n: number): boolean {
+    // get divisors of n
+    let divs = getDivisors(n);
+    // get sum of divisors of n
+    let sum = getSum(divs);
+    // if sum is odd can't be split into two partitions with equal sums
+    if (sum % 2 == 1) return false;
+    // if n is odd use 'abundant odd number' optimization
+    if (n % 2 == 1) {
+      let abundance = sum - 2 * n
+      return abundance > 0 && abundance%2 == 0;
+    }
+
+    // if n and sum are both even check if there's a partition which totals sum / 2
+    return isPartSum(divs, sum/2);
+  }
+
+  /**
+   * find x zumkeller numbers
+   * @param {number} x The number of zumkeller numbers to find
+   * @returns {number[]} array of x zumkeller numbers
+   */
+  function getXZumkelers(x: number): number[] {
+    let zumkellers: number[] = [];
+    let i = 2;
+    let count= 0;
+    while (count < x) {
+        if (isZumkeller(i)) {
+            zumkellers.push(i);
+            count++;
+        }
+        i++;
+    }
+
+    return zumkellers;
+  }
+
+  /**
+   * find x Odd Zumkeller numbers
+   * @param {number} x The number of odd zumkeller numbers to find
+   * @returns {number[]} array of x odd zumkeller numbers
+   */
+  function getXOddZumkelers(x: number): number[] {
+    let oddZumkellers: number[] = [];
+    let i = 3;
+    let count = 0;
+    while (count < x) {
+      if (isZumkeller(i)) {
+        oddZumkellers.push(i);
+        count++;
+      }
+      i += 2;
+    }
+
+    return oddZumkellers;
+  }
+
+  /**
+   * find x odd zumkeller number which are not end with 5
+   * @param {number} x The number of odd zumkeller numbers to find
+   * @returns {number[]} array of x odd zumkeller numbers
+   */
+  function getXOddZumkellersNotEndWith5(x: number): number[] {
+    let oddZumkellers: number[] = [];
+    let i = 3;
+    let count = 0;
+    while (count < x) {
+      if (isZumkeller(i) && i % 10 != 5) {
+        oddZumkellers.push(i);
+        count++;
+      }
+      i += 2;
+    }
+
+    return oddZumkellers;
+  }
+
+//get the first 220 zumkeller numbers
+console.log("First 220 Zumkeller numbers: ", getXZumkelers(220));
+
+//get the first 40 odd zumkeller numbers
+console.log("First 40 odd Zumkeller numbers: ", getXOddZumkelers(40));
+
+//get the first 40 odd zumkeller numbers which are not end with 5
+console.log("First 40 odd Zumkeller numbers which are not end with 5: ", getXOddZumkellersNotEndWith5(40));