first solution

5kyu/smallest-possible-sum/solution.ts

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+// 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);
+}