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2571-find-the-pivot-integer/README.md

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+<p>Given a positive integer <code>n</code>, find the <strong>pivot integer</strong> <code>x</code> such that:</p>
+
+<ul>
+	<li>The sum of all elements between <code>1</code> and <code>x</code> inclusively equals the sum of all elements between <code>x</code> and <code>n</code> inclusively.</li>
+</ul>
+
+<p>Return <em>the pivot integer </em><code>x</code>. If no such integer exists, return <code>-1</code>. It is guaranteed that there will be at most one pivot index for the given input.</p>
+
+<p>&nbsp;</p>
+<p><strong class="example">Example 1:</strong></p>
+
+<pre>
+<strong>Input:</strong> n = 8
+<strong>Output:</strong> 6
+<strong>Explanation:</strong> 6 is the pivot integer since: 1 + 2 + 3 + 4 + 5 + 6 = 6 + 7 + 8 = 21.
+</pre>
+
+<p><strong class="example">Example 2:</strong></p>
+
+<pre>
+<strong>Input:</strong> n = 1
+<strong>Output:</strong> 1
+<strong>Explanation:</strong> 1 is the pivot integer since: 1 = 1.
+</pre>
+
+<p><strong class="example">Example 3:</strong></p>
+
+<pre>
+<strong>Input:</strong> n = 4
+<strong>Output:</strong> -1
+<strong>Explanation:</strong> It can be proved that no such integer exist.
+</pre>
+
+<p>&nbsp;</p>
+<p><strong>Constraints:</strong></p>
+
+<ul>
+	<li><code>1 &lt;= n &lt;= 1000</code></li>
+</ul>

2571-find-the-pivot-integer/solution.js

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+/**
+ * @param {number} n
+ * @return {number}
+ */
+var pivotInteger = function(n) {
+    for(let i=1;i<=n;i++){
+        // using arithmetic progression
+        let leftSum = (i * (i+1)) / 2; // sum of elements from 1 to i
+        let rightSum = ((n*(n+1)) / 2 ) - ((i * (i-1)) / 2); // sum of elements from i to n
+
+        if(leftSum === rightSum){
+            return i;
+        }
+    }
+    return -1;
+};