Interview Preparation Kit --> Miscellaneous --> Time_Complexity-Primality

Author: keshavsingh3197

HackerRank/Interview Preparation Kit/Miscellaneous/Miscellaneous.ipynb

@@ -8,15 +8,6 @@
     "![Flipping bits](Flipping_bits.png)"
    ]
   },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "n=b"
-   ]
-  },
   {
    "cell_type": "code",
    "execution_count": 17,
@@ -67,6 +58,83 @@
     "    print(int('1'*(32-len(x))+s,2))"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Time Complexity: Primality\n",
+    " ***Every prime number can represented in form of 6n+1 or 6n-1 except 2 and 3, where n is natural number***\n",
+    " \n",
+    " \n",
+    "![Time_Complexity-Primality](Time_Complexity-Primality.png)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "n=b"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdin",
+     "output_type": "stream",
+     "text": [
+      " 2\n",
+      " 23\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Prime\n"
+     ]
+    },
+    {
+     "name": "stdin",
+     "output_type": "stream",
+     "text": [
+      " 67\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Prime\n"
+     ]
+    }
+   ],
+   "source": [
+    "def isPrime(n):\n",
+    "    if n<=1:\n",
+    "        return False\n",
+    "    if n<=3:\n",
+    "        return True\n",
+    "    if n%2==0 or n%3==0:\n",
+    "        return False\n",
+    "    i=5\n",
+    "    while i*i<=n:\n",
+    "        if n%i==0 or n%(i+2)==0:\n",
+    "            return False\n",
+    "        i+=6\n",
+    "    return True\n",
+    "for _ in range(int(input())):\n",
+    "    n=int(input())\n",
+    "    if isPrime(n):\n",
+    "        print('Prime')\n",
+    "    else:\n",
+    "        print('Not Prime')"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,

HackerRank/Interview Preparation Kit/Miscellaneous/Time_Complexity-Primality.png

@@ -0,0 +1,19 @@
+def isPrime(n):
+    if n<=1:
+        return False
+    if n<=3:
+        return True
+    if n%2==0 or n%3==0:
+        return False
+    i=5
+    while i*i<=n:
+        if n%i==0 or n%(i+2)==0:
+            return False
+        i+=6
+    return True
+for _ in range(int(input())):
+    n=int(input())
+    if isPrime(n):
+        print('Prime')
+    else:
+        print('Not Prime')