Enhance Prefix Sum pattern description and examples

Updated the description of the Prefix Sum pattern for clarity and added examples for different programming languages. Also, added a new problem to the list of related problems.

Author: javydevx

src/data/patterns.json

@@ -72,14 +72,55 @@
     },
     {
       "title": "Prefix Sum",
-      "description": "Used for range sum, subarrays with given sum.",
+      "description": "Used for fast range sum queries and subarray sum problems. There are two common implementations: (1) with an extra 0 at the start, and (2) without it (0-based).",
       "templates": {
-        "python": "prefix = [0] * (len(arr) + 1)\nfor i in range(len(arr)):\n    prefix[i + 1] = prefix[i] + arr[i]",
-        "javascript": "const prefix = new Array(arr.length + 1).fill(0);\nfor (let i = 0; i < arr.length; i++) {\n    prefix[i + 1] = prefix[i] + arr[i];\n}",
-        "java": "int[] prefix = new int[arr.length + 1];\nfor (int i = 0; i < arr.length; i++) {\n    prefix[i + 1] = prefix[i] + arr[i];\n}",
-        "go": "prefix := make([]int, len(arr)+1)\nfor i := 0; i < len(arr); i++ {\n    prefix[i+1] = prefix[i] + arr[i]\n}"
+        "python": "# Version 1: With extra 0 at the start (simpler range queries)\n" +
+               "prefix = [0] * (len(arr) + 1)\n" +
+               "for i in range(len(arr)):\n" +
+               "    prefix[i + 1] = prefix[i] + arr[i]\n\n" +
+               "# Version 2: Without extra 0 (0-based indexing)\n" +
+               "prefix = [0] * len(arr)\n" +
+               "prefix[0] = arr[0]\n" +
+               "for i in range(1, len(arr)):\n" +
+               "    prefix[i] = prefix[i - 1] + arr[i]",
+    
+        "javascript": "// Version 1: With extra 0 at the start (simpler range queries)\n" +
+                  "const prefix = new Array(arr.length + 1).fill(0);\n" +
+                  "for (let i = 0; i < arr.length; i++) {\n" +
+                  "    prefix[i + 1] = prefix[i] + arr[i];\n" +
+                  "}\n\n" +
+                  "// Version 2: Without extra 0 (0-based indexing)\n" +
+                  "const prefix2 = new Array(arr.length).fill(0);\n" +
+                  "prefix2[0] = arr[0];\n" +
+                  "for (let i = 1; i < arr.length; i++) {\n" +
+                  "    prefix2[i] = prefix2[i - 1] + arr[i];\n" +
+                  "}",
+
+        "java": "// Version 1: With extra 0 at the start (simpler range queries)\n" +
+             "int[] prefix = new int[arr.length + 1];\n" +
+             "for (int i = 0; i < arr.length; i++) {\n" +
+             "    prefix[i + 1] = prefix[i] + arr[i];\n" +
+             "}\n\n" +
+             "// Version 2: Without extra 0 (0-based indexing)\n" +
+             "int[] prefix2 = new int[arr.length];\n" +
+             "prefix2[0] = arr[0];\n" +
+             "for (int i = 1; i < arr.length; i++) {\n" +
+             "    prefix2[i] = prefix2[i - 1] + arr[i];\n" +
+             "}",
+
+        "go": "// Version 1: With extra 0 at the start (simpler range queries)\n" +
+          "prefix := make([]int, len(arr)+1)\n" +
+          "for i := 0; i < len(arr); i++ {\n" +
+          "    prefix[i+1] = prefix[i] + arr[i]\n" +
+          "}\n\n" +
+          "// Version 2: Without extra 0 (0-based indexing)\n" +
+          "prefix2 := make([]int, len(arr))\n" +
+          "prefix2[0] = arr[0]\n" +
+          "for i := 1; i < len(arr); i++ {\n" +
+          "    prefix2[i] = prefix2[i-1] + arr[i]\n" +
+          "}"
       },
-      "problems": ["Subarray Sum Equals K", "Range Sum Query"]
+      "problems": ["Subarray Sum Equals K", "Range Sum Query", "Continuous Subarray Sum"]
     },
     {
       "title": "Backtracking",