fourth solution

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

@@ -1,5 +1,19 @@
-// idea: find lowest number, subtract it from all other numbers,
-// repeat until all numbers are the same
+// idea: do not ever sort
+// simply keep looping from left to right and back to left
+// whenever a smaller number is found,
+// subtract as many multiples of that number from the rest of the array
+
+const subtractMultiples = (a: number, b: number): number => {
+  // subtract a from b as many times as possible
+  const mod = b % a;
+  if (mod === 0) {
+    // figure out how many times a can be subtracted from b
+    const div = b / a - 1;
+    return b - a * div;
+  } else {
+    return mod;
+  }
+}
 
 /**
  * Does a single operation on the given array.
@@ -7,46 +21,36 @@
  * @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
-  const first = arr[0]; // smallest
 
-  // if all numbers are the same, return true
-  // if the array is sorted, it is enough to compare the first and last elements
-  if(arr[arr.length - 1] === first) return true;
+  let step = 1;
+  let i = 0;
+  let done = false;
+  let hasChangedDuringLoop = false;
+  while (!done) {
+    if (i + step >= arr.length || i + step < 0) {
+      // reverse direction
+      step = -step;
+      if (!hasChangedDuringLoop) {
+        done = true;
+      }
+      hasChangedDuringLoop = false;
+    }
 
-  // if the first number is 1, set all numbers to 1
-  if(first === 1) {
-    for(let i = 1; i < arr.length; i++) {
-      arr[i] = 1;
-    }
-    return true;
-  }
-  
-  // subtract as many multiples of the smallest number from all the rest
-  let i = 1;
-  while (i < arr.length) {
-    if(arr[i] <= first) {
-      i++;
-      continue;
-    }
-    
-    const mod = arr[i] % first;
+    const first = arr[i];
+    const next = arr[i + step];
 
-    if (mod === 0) {
-      // figure out how many times the first number can be subtracted from the current number
-      const div = arr[i] / first - 1;
-      arr[i] = arr[i] - first * div;
-    } else {
-      arr[i] = mod;
+    if (first > next) {
+      arr[i] = subtractMultiples(next, first);
+      hasChangedDuringLoop = true;
+    } else if (first < next) {
+      arr[i + step] = subtractMultiples(first, next);
+      hasChangedDuringLoop = true;
     }
-    i++;
+
+    i += step;
   }
 
-  // sort the array
-  arr.sort((a, b) => a - b);
-
-  return false;
+  return true;
 }
 
 export function solution(numbers: number[]): number {