feat(api:search): add endpoint /api/search/[searchStr]

  ## what
  - add endpoint `/api/search/[searchStr]`

  ## how
  - check if the `searchStr` is valid (using zod schema)
    - must be a string length of 1
  - if `searchStr` is not valid, return 400
  - if username exists, add SearchResult to an array
    - title: `User: [username]`
    - href: `/users/[username]`
  - if problem number exists, add SearchResult to an array
    - title: `Problem: [problem number] [problem title]`
    - href: `/problems/[problem number]`
  - return response using the SearchResult array

  ## why
  - this endpoint will be used to search for a problem number or a
    username

  ## where
  - ./src/app/api/search/[searchStr]/route.ts

  ## usage

src/app/api/search/[searchStr]/route.ts

@@ -0,0 +1,63 @@
+import { NextResponse } from "next/server";
+import { z } from "zod";
+
+import { searchSchema as schema } from "@/schema";
+import {
+  uhuntProblemNumUrl,
+  uhuntUsername2UidUrl,
+} from "@/utils/constants";
+import { Problem, SearchResultType } from "@/types";
+
+type getParamsType = {
+  params: z.infer<typeof schema>;
+};
+
+export const GET = async(_request: Request, {params}: getParamsType) => {
+  const { searchStr } = params;
+  const responseData: SearchResultType[] = []
+
+  // validate params
+  const schemaResponse = await schema.safeParseAsync(params);
+  if (!schemaResponse.success) {
+    const message = {
+      message: schemaResponse.error.issues[0].message,
+    };
+
+    return NextResponse.json(message, {
+      status: 400,
+    });
+  }
+
+  //----------------------------------------------------------------------------------------------//
+
+  // fetch username ID
+  const usernameUrl = uhuntUsername2UidUrl(searchStr);
+  const usernameResponse = await fetch(usernameUrl);
+  const usernameData: number = await usernameResponse.json();
+
+  // add search result to array if user exists
+  if (usernameData !== 0) {
+    responseData.push({
+      title: `User: '${searchStr}'`,
+      href: `/users/${searchStr}`
+    })
+  }
+
+  //----------------------------------------------------------------------------------------------//
+
+  // fetch problem number
+  const problemNumUrl = uhuntProblemNumUrl(searchStr)
+  const problemNumResponse = await fetch(problemNumUrl)
+  const problemNumData: Problem = await problemNumResponse.json()
+
+  if(Object.entries(problemNumData).length !== 0) {
+    const {num, title} = problemNumData
+    responseData.push({
+      title: `Problem: ${num} '${title}'`,
+      href: `/problems/${num}`
+    })
+  }
+
+  return Response.json(responseData)
+
+}