Merge pull request #561 from trinity97/master

Added O(logn) algorithm to find fibonacci term

Author: t2013anurag

NthFibonacci/NthFibonacci.java

@@ -0,0 +1,87 @@
+import java.io.BufferedReader;
+import java.io.IOException;
+import java.io.InputStream;
+import java.io.InputStreamReader;
+import java.util.StringTokenizer;
+
+public class NthFibonacci {
+    public static void main(String[] args) throws IOException {
+        Reader.init(System.in);
+        System.out.println("Enter the number of term to be printed:");
+        long n = Reader.nextLong();
+        System.out.println(smartfib(n)[1][0]);
+    }
+
+    public static long[][] smartfib(long n){
+        long a[][]=new long[2][2];
+        a[0]= new long[]{1, 1};
+        a[1]= new long[]{1,0};
+        if (n==0){
+            a[1][0]=0;
+            return a;
+        }
+        if (n==1){
+            return a;
+        }
+        if (n%2==1){
+            return product(square(smartfib(((n-1)/2))),a);
+        }
+        return square(smartfib((n/2)));
+    }
+    public static long[][] square(long a[][]){
+        long b[][]=new long[2][2];
+        for (int i=0;i<2;i++){
+            for (int j=0;j<2;j++){
+                long sum=0;
+                for(int k=0;k<2;k++){
+                    sum+=(a[i][k]*a[k][j]);
+                }
+                b[i][j]=sum;
+            }
+        }
+        return b;
+    }
+    public static long[][] product(long a[][],long b[][]){
+        long c[][]=new long[2][2];
+        for (int i=0;i<2;i++){
+            for (int j=0;j<2;j++){
+                long sum=0;
+                for(int k=0;k<2;k++){
+                    sum+=(a[i][k]*b[k][j]);
+                }
+                c[i][j]=sum;
+            }
+        }
+        return c;
+    }
+}
+
+class Reader {
+    static BufferedReader reader;
+    static StringTokenizer tokenizer;
+
+    static void init(InputStream input) {
+        reader = new BufferedReader(
+                new InputStreamReader(input) );
+        tokenizer = new StringTokenizer("");
+    }
+
+    static String next() throws IOException {
+        while ( ! tokenizer.hasMoreTokens() ) {
+            tokenizer = new StringTokenizer(
+                    reader.readLine() );
+        }
+        return tokenizer.nextToken();
+    }
+
+    static int nextInt() throws IOException {
+        return Integer.parseInt( next() );
+    }
+
+    static double nextDouble() throws IOException {
+        return Double.parseDouble( next() );
+    }
+    static long nextLong() throws IOException {
+        return Long.parseLong( next() );
+    }
+}

NthFibonacci/README.md

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+## The Nth Fibonacci Term
+### Algorithm
+
+The Fibonacci Sequence is the series of numbers:
+
+`1, 1, 2, 3, 5, 8, 13, 21, 34, ...`
+
+The next number is found by adding up the two numbers before it.
+
+* The 2 is found by adding the two numbers before it (1+1)
+* The 3 is found by adding the two numbers before it (1+2),
+* And the 5 is (2+3),
+* and so on!
+
+### Output of the program
+* `Enter the number of term to be printed: 10`
+* `Output: 55`