From b768376ff074e019da356f86205e453c1649faed Mon Sep 17 00:00:00 2001
From: Loosetooth <loosetooth@protonmail.com>
Date: Sun, 2 Feb 2025 23:52:26 +0100
Subject: [PATCH] first solution

---
 5kyu/smallest-possible-sum/description.md | 26 ++++++++++
 5kyu/smallest-possible-sum/solution.ts    | 58 +++++++++++++++++++++++
 5kyu/smallest-possible-sum/tests.ts       |  8 ++++
 3 files changed, 92 insertions(+)
 create mode 100644 5kyu/smallest-possible-sum/description.md
 create mode 100644 5kyu/smallest-possible-sum/solution.ts
 create mode 100644 5kyu/smallest-possible-sum/tests.ts

diff --git a/5kyu/smallest-possible-sum/description.md b/5kyu/smallest-possible-sum/description.md
new file mode 100644
index 0000000..d8432ee
--- /dev/null
+++ b/5kyu/smallest-possible-sum/description.md
@@ -0,0 +1,26 @@
+Description
+Given an array X of positive integers, its elements are to be transformed by running the following operation on them as many times as required:
+
+if X[i] > X[j] then X[i] = X[i] - X[j]
+
+When no more transformations are possible, return its sum ("smallest possible sum").
+
+For instance, the successive transformation of the elements of input X = [6, 9, 21] is detailed below:
+
+X_1 = [6, 9, 12] # -> X_1[2] = X[2] - X[1] = 21 - 9
+X_2 = [6, 9, 6]  # -> X_2[2] = X_1[2] - X_1[0] = 12 - 6
+X_3 = [6, 3, 6]  # -> X_3[1] = X_2[1] - X_2[0] = 9 - 6
+X_4 = [6, 3, 3]  # -> X_4[2] = X_3[2] - X_3[1] = 6 - 3
+X_5 = [3, 3, 3]  # -> X_5[1] = X_4[0] - X_4[1] = 6 - 3
+The returning output is the sum of the final transformation (here 9).
+
+Example
+solution([6, 9, 21]) #-> 9
+Solution steps:
+[6, 9, 12] #-> X[2] = 21 - 9
+[6, 9, 6] #-> X[2] = 12 - 6
+[6, 3, 6] #-> X[1] = 9 - 6
+[6, 3, 3] #-> X[2] = 6 - 3
+[3, 3, 3] #-> X[1] = 6 - 3
+Additional notes:
+There are performance tests consisted of very big numbers and arrays of size at least 30000. Please write an efficient algorithm to prevent timeout.
\ No newline at end of file
diff --git a/5kyu/smallest-possible-sum/solution.ts b/5kyu/smallest-possible-sum/solution.ts
new file mode 100644
index 0000000..36eb1c7
--- /dev/null
+++ b/5kyu/smallest-possible-sum/solution.ts
@@ -0,0 +1,58 @@
+// idea: keep the array sorted
+// whenever we execute the subtraction, place the result in the correct position
+
+/**
+ * Inserts the value in a sorted array to keep it sorted.
+ * The sort direction is assumed to be ascending.
+ * @param arr The sorted array
+ * @param value The value to insert
+ */
+const sortInsert = (arr: number[], value: number): void => {
+  let i = 0;
+  while (i < arr.length && arr[i] < value) {
+    i++;
+  }
+
+  arr.splice(i, 0, value);
+}
+
+/**
+ * Does a single operation on the given array.
+ * Keeps the array sorted.
+ * @returns True if the array is all the same, false otherwise.
+ */
+const operate = (arr: number[]): boolean => {
+  // last element is the largest
+  // find the first element that is not the largest
+  let i = arr.length - 1;
+  while (i >= 0 && arr[i] === arr[arr.length - 1]) {
+    i--;
+  }
+
+  if (i < 0) {
+    // all elements are the same
+    return true;
+  }
+
+  // subtract
+  const value = arr[arr.length - 1] - arr[i];
+
+  // remove the last element
+  arr.pop();
+
+  // insert the value in the correct position
+  sortInsert(arr, value);
+
+  return false;
+}
+
+export function solution(numbers: number[]): number {
+  numbers.sort((a, b) => a - b);
+  let done = false;
+  while (!done) {
+    done = operate(numbers);
+  }
+
+  // sum the numbers
+  return numbers.reduce((acc, num) => acc + num, 0);
+}
\ No newline at end of file
diff --git a/5kyu/smallest-possible-sum/tests.ts b/5kyu/smallest-possible-sum/tests.ts
new file mode 100644
index 0000000..25aed6c
--- /dev/null
+++ b/5kyu/smallest-possible-sum/tests.ts
@@ -0,0 +1,8 @@
+// See https://www.chaijs.com for how to use Chai.
+import { assert } from "chai";
+
+import { solution } from "./solution";
+
+describe('Example test', function() {
+  it('[6,9,12]', () => assert.strictEqual(solution([6,9,21]),9));
+});
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