diff --git a/Euler Totient Function/etf.cpp b/Euler Totient Function/etf.cpp
index 5c99e1c..02891b1 100644
--- a/Euler Totient Function/etf.cpp	
+++ b/Euler Totient Function/etf.cpp	
@@ -8,15 +8,15 @@ void cal_etf()
 {
     for(int i = 1 ;i <= MAXN ; i++ )
     	etf[i]=i;
-    for(int i=2 ; i<= MAXN ; i++ )
-        if ( etf[i] == i)
-            for(int j = 2*i ; j <= MAXN ; j += i)
-            	etf[j] -=  etf[j]/ i ;
-    
-    etf[1]=1;
-    for(int i=2 ; i<= MAXN ; i++) {	
-        if ( etf[i]==i) //if that number is prime
-    		etf[i] = i-1;
+    }
+
+    for(int i=2;i<=MAXN;i++){
+        if(etf[i]==i){
+            etf[i]=i-1;
+            for(int j=2;j*i<=MAXN;j++){
+                etf[j*i]=(1-(1/i));
+            }
+        }
     }
 }
 
diff --git a/Fibonacci/fast_doubling.cpp b/Fibonacci/fast_doubling.cpp
index a157574..9724040 100644
--- a/Fibonacci/fast_doubling.cpp
+++ b/Fibonacci/fast_doubling.cpp
@@ -1,28 +1,45 @@
 /* Fast Doubling Method - Fibonacci */
 #include <bits/stdc++.h>
-#define REP(i,n) for (int i = 1; i <= n; i++)
 using namespace std;
 
-typedef long long ll;
+#define MOD 1000000007;
+long long int a,b,c,d;
 
-map<long long, long long> F;
-
-ll m=1000000007;
-
-long long f(long long n) {
-	if (F.count(n))
-		return F[n];
-	long long k = n / 2;
-	if (n % 2 == 0) { // n=2*k
-		return F[n] = (f(k) * f(k) + f(k - 1) * f(k - 1)) % m;
-	} else { // n=2*k+1
-		return F[n] = (f(k) * f(k + 1) + f(k - 1) * f(k)) % m;
-	}
+void fast_fib(long long int n,long long int ans[])
+{
+    if(n == 0)
+    {
+        ans[0] = 0;
+        ans[1] = 1;
+        return;
+    }
+    fast_fib((n/2),ans);
+    a = ans[0];             /* F(n) */
+    b = ans[1];             /* F(n+1) */
+    c = 2*b - a;
+    if(c < 0)
+        c += MOD;
+    c = (a * c) % MOD;      /* F(2n) */
+    d = (a*a + b*b) % MOD;  /* F(2n + 1) */
+    if(n%2 == 0)
+    {
+        ans[0] = c;
+        ans[1] = d;
+    }
+    else
+    {
+        ans[0] = d;
+        ans[1] = c+d;
+    }
 }
 
 int main()
 {
-    F[0] = F[1] = 1;
-    ll n;cin >> n; // This answers the term n
-    cout << f(n-1);
+
+    long long int n;        /* nth value to be found */
+    cin>>n;
+    long long int ans[2]={0};
+    fast_fib(n,ans);
+    cout<<ans[0]<<endl
+    return 0;
 }
diff --git a/Longest Increasing Subsequence/LIS.cpp b/Longest Increasing Subsequence/LIS.cpp
index 9714c10..5563c21 100644
--- a/Longest Increasing Subsequence/LIS.cpp	
+++ b/Longest Increasing Subsequence/LIS.cpp	
@@ -12,10 +12,24 @@ int LIS()
     for(int i=0;i<n;i++)
     {
         cin>>elem;
-        //vector<int>::iterator it = upper_bound(d.begin(),d.end(),elem); // non-decreasing
-        vector<int>::iterator it = lower_bound(d.begin(),d.end(),elem); // strictly increasing
-        if(it == d.end()) d.push_back(elem);
-        else *it=elem;
+        d.push_back(elem);
     }
-    cout<<d.size();
+    int dp[n];
+    for(int i=0;i<n;i++){
+        dp[i]=1;
+    }
+    for(int i=2;i<n;i++){
+        for(int j=i-1;j>=0;j--){
+            if(d[i]>=d[j]){
+                dp[i]=max(dp[i],dp[j]+1);
+            }
+        }
+    }
+    int ans=INT_MIN;
+    for(int i=0;i<n;i++){
+        if(ans<dp[i]){
+            ans=dp[i];
+        }
+    }
+    cout<<ans<<endl;
 }
diff --git a/Sieve of Eratosthenes/sieve.cpp b/Sieve of Eratosthenes/sieve.cpp
index a3a8362..0f2a10b 100644
--- a/Sieve of Eratosthenes/sieve.cpp	
+++ b/Sieve of Eratosthenes/sieve.cpp	
@@ -10,8 +10,8 @@ void sieveOptimized(int N) {
             if (isPrime[i]) {
             // For further optimization, You can do instead of j += i, j += (2 * i).
             // Proof is left to reader :)
-            for (int j = i * i; j <= N; j += i) 
-                isPrime[j] = 0;
+            for (int j = 2; (j*i) <= N; j += 1) 
+                isPrime[j*i] = 0;
         }
     }
 }