feat: Array Problems

Array/PascalsTriangle.js

@@ -0,0 +1,43 @@
+/**
+ * Pascal's Triangle
+ *
+ * Given an integer numRows, return the first numRows of Pascal's triangle.
+ * Each number is the sum of the two numbers directly above it.
+ *
+ * Time Complexity: O(n^2)
+ * Space Complexity: O(n^2)
+ *
+ * Approach:
+ * - Start with [[1]]
+ * - For each new row, first and last elements are always 1
+ * - Inner elements = sum of two elements directly above (prev[j-1] + prev[j])
+ *
+ * @param {number} numRows
+ * @returns {number[][]} first numRows of Pascal's triangle
+ */
+function generate(numRows) {
+    const triangle = [[1]];
+
+    for (let i = 1; i < numRows; i++) {
+        const prev = triangle[i - 1];
+        const row = [1];
+
+        for (let j = 1; j < i; j++) {
+            row.push(prev[j - 1] + prev[j]);
+        }
+
+        row.push(1);
+        triangle.push(row);
+    }
+
+    return triangle;
+}
+
+
+// ----------------------
+// Test
+// ----------------------
+
+const result = generate(5);
+
+console.log("Pascal's Triangle:", result);

Array/SortColors.js

@@ -0,0 +1,54 @@
+/**
+ * Dutch National Flag Algorithm (3 pointers)
+ *
+ * Sort an array containing only 0, 1, and 2 in-place.
+ * 0 → Red
+ * 1 → White
+ * 2 → Blue
+ *
+ * Time Complexity: O(n)
+ * Space Complexity: O(1)
+ *
+ * Approach:
+ * [0 .... low-1]   -> 0s
+ * [low ... mid-1]  -> 1s
+ * [mid ... high]   -> unsorted
+ * [high+1 ... n-1] -> 2s
+ *
+ * @param {number[]} nums
+ * @returns {number[]} sorted array (in-place)
+ */
+function sortColors(nums) {
+    let low = 0;
+    let mid = 0;
+    let high = nums.length - 1;
+
+    while (mid <= high) {
+        if (nums[mid] === 0) {
+            // swap low & mid
+            [nums[low], nums[mid]] = [nums[mid], nums[low]];
+            low++;
+            mid++;
+        } else if (nums[mid] === 1) {
+            mid++;
+        } else {
+            // nums[mid] === 2
+            // swap mid & high
+            [nums[mid], nums[high]] = [nums[high], nums[mid]];
+            high--;
+        }
+    }
+
+    return nums;
+}
+
+
+// ----------------------
+// Test
+// ----------------------
+
+const arr = [2, 0, 2, 1, 1, 0];
+
+const sorted = sortColors(arr);
+
+console.log("Sorted Array:", sorted);