Fibonacci square sum last digit

Mathematics_Algo/fibonacci_sum_squares.cpp

@@ -0,0 +1,32 @@
+#include <iostream>
+
+//Computes the last digit of  Fibonacci series square sum- F0^2 + F1^2 + · · · + Fn^2 in constant time.
+long long fibonacci_fast(int n)
+{
+
+    long long f[n];
+    f[0] = 0;
+    f[1] = 1;
+
+    for (int i = 2; i <= n; i++)
+    {
+        f[i] = (f[i - 1] + f[i - 2]) % 10;
+    }
+
+    return f[n];
+}
+long long fib_square(long long n)
+{
+    if (n < 1)
+        return 0;
+    long long x = fibonacci_fast(n % 60);
+    long long y = fibonacci_fast((n + 1) % 60);
+    long long z = (x * y) % 10;
+    return z;
+}
+int main()
+{
+    long long n = 0;
+    std::cin >> n;
+    std::cout << fib_square(n);
+}

README.md

@@ -26,6 +26,7 @@ The purpose of this repository is to get all the Algorithms required for Competi
   13) totient :- Total numbers from 1 to N whose gcd with N is 1.
   14) fibonacciNumber(n) :- Returns the nth Fibonacci Number in constant time.
   15)Spiral Search in 2d array (C++ code)
+  16) Computes the last digit of fibonacci square series F0^2 + F1^2 + · · · + Fn^2 in constant time.
 
 ## String_Algo
   1) isVowel :- Check whether a character is vowel or not.
@@ -34,3 +35,8 @@ The purpose of this repository is to get all the Algorithms required for Competi
 1)Spiral search in 2d array
 
 
+## Trees_Algo
+1) LCA.cpp
+2) Topview.cpp
+3) Bottomview.cpp
+4) Common_tree_traversal.cpp

Trees_Algo/common_tree_traversal_methods.cpp

@@ -0,0 +1,111 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <iostream>
+#include <bits/stdc++.h>
+#include <climits>
+using namespace std;
+
+struct node
+{
+    int data;
+    struct node *left;
+    struct node *right;
+};
+
+struct node *newnode(int data)
+{
+    struct node *p = new (struct node);
+    //struct node* p = (struct node*)malloc(sizeof(struct node));
+
+    p->data = data;
+    p->left = NULL;
+    p->right = NULL;
+    return p;
+}
+
+//Inorder (Left, Root, Right)
+//Preorder (Root, Left, Right)
+//Postorder (Left, Right, Root)
+//Levelorder
+int height(node *root)
+{
+    // Write your code here.
+    if (root == NULL)
+    {
+        return 0;
+    }
+    if (root->left == NULL && root->right == NULL)
+    {
+        return 0;
+    }
+    return std::max(height(root->left) + 1, height(root->right) + 1);
+}
+
+int printlevel(struct node *root, int level)
+{
+    if (root == NULL)
+        return 0;
+    if (level == 0)
+        cout << root->data << " ";
+    else
+    {
+        printlevel(root->left, level - 1);
+        printlevel(root->right, level - 1);
+    }
+}
+
+void levelOrder(struct node *root)
+
+{
+    int h = height(root);
+    for (int i = 0; i <= h; i++)
+    {
+        printlevel(root, i);
+    }
+}
+
+int preorder(struct node *root)
+{
+    if (root == NULL)
+        return 0;
+    cout << root->data << " ";
+    preorder(root->left);
+    preorder(root->right);
+}
+
+int inorder(struct node *root)
+{
+    if (root == NULL)
+        return 0;
+    inorder(root->left);
+    cout << root->data << " ";
+    inorder(root->right);
+}
+int postorder(struct node *root)
+{
+    if (root == NULL)
+        return 0;
+    postorder(root->left);
+    postorder(root->right);
+    cout << root->data << " ";
+}
+
+int main()
+{
+    struct node *root = newnode(3);
+    root->left = newnode(7);
+    root->right = newnode(5);
+    root->right->right = newnode(11);
+    root->left->left = newnode(9);
+
+    printf("\nTree traversed in preorder=\n");
+    preorder(root);
+    printf("\nTree traversed in inorder=\n");
+    inorder(root);
+    printf("\nTree traversed in postorder=\n");
+    postorder(root);
+    printf("\nTree traversed in levelorder=\n");
+    levelOrder(root);
+
+    return 0;
+}