From 3577383945cbdb2190269a430ebd5b0173f1c3dc Mon Sep 17 00:00:00 2001
From: Cool-Katt <stani_s1@abv.bg>
Date: Wed, 23 Oct 2024 15:44:59 +0300
Subject: [PATCH] Add proof solution

---
 .../killer-sudoku-helper/.meta/proof.ci.js    | 28 +++++++++++++++++++
 1 file changed, 28 insertions(+)

diff --git a/exercises/practice/killer-sudoku-helper/.meta/proof.ci.js b/exercises/practice/killer-sudoku-helper/.meta/proof.ci.js
index e69de29bb2..570c87c060 100644
--- a/exercises/practice/killer-sudoku-helper/.meta/proof.ci.js
+++ b/exercises/practice/killer-sudoku-helper/.meta/proof.ci.js
@@ -0,0 +1,28 @@
+export const combinations = (cage) => {
+  const { sum, size, exclude } = cage;
+  const result = [];
+  const digits = [...Array(10).keys()]
+    .slice(1)
+    .filter((d) => !exclude.includes(d));
+
+  function findCombinations(remainingSum, index, combination) {
+    if (remainingSum === 0 && combination.length === size) {
+      result.push(combination);
+      return;
+    }
+
+    for (let i = index; i < digits.length; i++) {
+      const digit = digits[i];
+      if (digit > remainingSum) {
+        break;
+      }
+      if (combination.includes(digit)) {
+        continue;
+      }
+      findCombinations(remainingSum - digit, i + 1, [...combination, digit]);
+    }
+  }
+
+  findCombinations(sum, 0, []);
+  return result;
+};