From 1609abd3dbc0c980267a0029a424fa0c25766fa4 Mon Sep 17 00:00:00 2001
From: bhavishya <121548550+bhavishya3102@users.noreply.github.com>
Date: Tue, 17 Sep 2024 15:36:53 +0530
Subject: [PATCH 1/3] Update MathsForDSA.java

---
 .../code/MathsForDSA.java                     | 31 +++++++++++++++++++
 1 file changed, 31 insertions(+)

diff --git a/Lecture-011 - Maths for DSA - 1/code/MathsForDSA.java b/Lecture-011 - Maths for DSA - 1/code/MathsForDSA.java
index 96866d0..ab10354 100644
--- a/Lecture-011 - Maths for DSA - 1/code/MathsForDSA.java	
+++ b/Lecture-011 - Maths for DSA - 1/code/MathsForDSA.java	
@@ -1,3 +1,34 @@
+//         decimalno,base
+//         power=0 ans=0
+//         while(decimal_no>0){
+//            int rem=decimal_no%base;
+//            decimal_no=decimal_no/base;
+//            ans+=rem*Math.pow(10,power);
+//            power++;
+//         }
+//     }
+    
+    
+//     a,b
+//     while(b>0){
+//         if(b%2!=0){
+//             res=res*a;
+//         }
+//         b=b/2;
+//         a=a*a;
+//     }
+// }
+
+// 2,5
+// res=2
+// b=2
+// a=4
+// b=1
+// a=16
+// res=32
+// a=16*16
+// final-------------------res=32
+
 public class MathsForDSA {
     public static void main(String[] args) {
             decimalToAnyBase(5,2);

From 2a1152d8ea36180569a8ed9b89bf4ad10468628a Mon Sep 17 00:00:00 2001
From: bhavishya <121548550+bhavishya3102@users.noreply.github.com>
Date: Tue, 17 Sep 2024 15:45:06 +0530
Subject: [PATCH 2/3] Update MathsForDSA2.java

---
 .../code/MathsForDSA2.java                    | 36 ++++++++++++++-----
 1 file changed, 27 insertions(+), 9 deletions(-)

diff --git a/Lecture-012 - Maths for DSA - 2/code/MathsForDSA2.java b/Lecture-012 - Maths for DSA - 2/code/MathsForDSA2.java
index 4b9047c..8ebe2bb 100644
--- a/Lecture-012 - Maths for DSA - 2/code/MathsForDSA2.java	
+++ b/Lecture-012 - Maths for DSA - 2/code/MathsForDSA2.java	
@@ -76,23 +76,41 @@ public static void primeNumbers(int num){
         }
         System.out.println(num + " is a prime number ");
     }
-    public static void sieveAlgorithm(int num){
-        boolean arr[] = new boolean[num+1];
+  import java.util.Arrays;
+
+public class SieveOfEratosthenes {
+
+    public static void sieveAlgorithm(int num) {
+        if (num < 2) {
+            System.out.println("There are no primes less than 2.");
+            return;
+        }
+
+        boolean[] arr = new boolean[num + 1];
         Arrays.fill(arr, true);
-        int counter = 2;
-        while (counter<=num){
-            if(arr[counter] == true){
-                for(int factor = counter+counter; factor<=num; factor+=counter){
+        arr[0] = arr[1] = false; // 0 and 1 are not prime numbers
+
+        int limit = (int) Math.sqrt(num);
+        for (int counter = 2; counter <= limit; counter++) {
+            if (arr[counter]) {
+                for (int factor = counter * counter; factor <= num; factor += counter) {
                     arr[factor] = false;
                 }
             }
-            counter++;
         }
 
-        for(int i=2;i<=num;i++){
-            System.out.println(i +" : "+ arr[i]);
+        for (int i = 2; i <= num; i++) {
+            if (arr[i]) {
+                System.out.println(i + " : " + arr[i]);
+            }
         }
     }
+
+    public static void main(String[] args) {
+        sieveAlgorithm(30);
+    }
+}
+
     public static double newtonRaphsonSqRoot(int num){
         double tol = 0.0001;
         double root;

From b9c9eefc969afe6aed959a8c545243ab8e9b11bf Mon Sep 17 00:00:00 2001
From: bhavishya <121548550+bhavishya3102@users.noreply.github.com>
Date: Tue, 17 Sep 2024 15:54:33 +0530
Subject: [PATCH 3/3] Update MathsForDSA2.java

---
 .../code/MathsForDSA2.java                    | 20 +++++++++++--------
 1 file changed, 12 insertions(+), 8 deletions(-)

diff --git a/Lecture-012 - Maths for DSA - 2/code/MathsForDSA2.java b/Lecture-012 - Maths for DSA - 2/code/MathsForDSA2.java
index 8ebe2bb..dbd328a 100644
--- a/Lecture-012 - Maths for DSA - 2/code/MathsForDSA2.java	
+++ b/Lecture-012 - Maths for DSA - 2/code/MathsForDSA2.java	
@@ -40,16 +40,20 @@ public static void countDigitsViaLog(int num){
         int count = (int)Math.log10(num) + 1;
         System.out.println("Digits are :"+ count);
     }
-    public static void armstrongNumber(int num){
-        int res = 0;
-        int copy = num;
-        while (num>0){
-            int digit = num%10;
-            res = res + (int)Math.pow(digit,3);
+  public static void armstrongNumber(int num) {
+        int originalNum = num;
+        int numberOfDigits = Integer.toString(num).length();
+        int sum = 0;
+        
+        // Calculate the sum of each digit raised to the power of the number of digits
+        while (num > 0) {
+            int digit = num % 10;
+            sum += Math.pow(digit, numberOfDigits);
             num /= 10;
         }
-           System.out.println(res==copy);
-
+        
+        // Check if the sum is equal to the original number
+        System.out.println(sum == originalNum);
     }
     public static void printAllDivisors(int num){
         int counter = 1;