done

Author: DojeeDev

.github/workflows/test.yml

@@ -0,0 +1,11 @@
+name: Test Code
+on:
+  push:
+
+jobs:
+  test:
+    runs-on: ubuntu-latest
+    steps:
+    - uses: actions/checkout@v4
+    - run: npm i jsverify
+    - run: node code.test.js

README.md

@@ -20,3 +20,7 @@ this.
 
 What is the time complexity of your implementation (worst-case $\Theta$)? Add
 your answer, including your reasoning, to this markdown file.
+
+### Analysis
+
+Since comparisons take constant time and we consider n elements of the array the complexity is $\Theta(n)$

code.js

@@ -0,0 +1,17 @@
+var async = require("async");
+
+//sources: queried chat gpt what function in the async library would 
+//be useful for counting matches in an array and it suggested "each". Then I read the docs for the rest.
+function count(a, k) {
+  var m = 0;
+
+  async.each(
+    a,
+    (v, callback) => {
+      if (v == k) { m++; }
+      callback();
+    }
+  );
+
+  return m;
+}

code.test.js

@@ -0,0 +1,19 @@
+const fs = require('fs');
+const jsc = require('jsverify');
+
+eval(fs.readFileSync('code.js')+'');
+
+const testSum =
+    jsc.forall("array nat","nat", function(arr, key) {
+        return JSON.stringify(count(arr, key)) == JSON.stringify(syncCount(arr, key));
+    });
+
+jsc.assert(testSum);
+
+function syncCount(a, k) {
+  var m = 0;
+  for (var i = 0; i < a.length; i++) {
+    if (a[i] == k) { m++; }
+  }
+  return m;
+}

package-lock.json

@@ -0,0 +1,7 @@
+{
+  "dependencies": {
+    "async": "^3.2.6",
+    "fs": "^0.0.1-security",
+    "jsverify": "^0.8.4"
+  }
+}