diff --git a/README.md b/README.md
index 36e792a..1957ca7 100644
--- a/README.md
+++ b/README.md
@@ -26,7 +26,20 @@
 
     * **git Actions**: Ο Βασιλής ασχολήθηκε με την δημιουργία και την σωστή λειτουργία των git actions. Παρέχοντας αυτοματοποιημένα σενάρια που εκτελούνται με βάση συγκεκριμένες συνθήκες. Αυτά τα σενάρια εκτελούνται κάθε φορά που γίνεται η υποβολή νέου κώδικα.
 
-- Unit tests: Δημιουργήθηκαν unit tests για την εξέταση του καινούργιου κώδικά.
+- Unit tests: Δημιουργήθηκαν unit tests για την εξέταση του καινούργιου κώδικά (από την Άννα και τον Βασίλη).
+
+### Κύρια Branches
+- main και K23-NNS-Project-v2: Σε αυτά τα branch υπάρχουν όλα τα αρχεία για τις δύο πρώτες εργασίες (ΚΝΝ και ΚΝΝ με βελτιώσεις).
+
+- K23-NNS-Project-v1: Σε αυτό το branch υπάρχουν όλα τα αρχεία για την πρώτη εργασία, τα οποία τροποποιήθηκαν σύμφωνα με τις οδηγίες που μας δώθηκαν.
+
+### Makefiles
+Οι εντολές είναι ίδιες με αυτές στο 1ο παραδοτέο και μόνο στο Makefile στον φάκελο tests προστέθηκε έξτρα:
+- Με make runKNN_imp:  τρέχουν τα τεστ για τις συναρτήσεις του knn_improvements.
+
+### Extra
+1. Για να τρέξει ο αλγόριθμος της 1ης εργασίας, πρέπει απλά στο αρχείο main.c να βγεί από το σχόλιο η γραμμή 25 και να μπει σε σχόλιο η γραμμή 24.
+2. Υπάρχει και ένα αρχείο times.txt, όπου αναφέρονται οι χρόνοι αλλά και η ακρίβεια των αλγορίθμων ΚΝΝ και ΚΝΝ με βελτιώσεις για Ευκλείδια και για Manhattan αποστάσεις.
 
 
 ----------------------
@@ -85,5 +98,8 @@
       7. Με make run-all: τρέχουν τα τεστ για όλε τις συναρτήσεις
     
     * Γενικο Makefile
-      Όπως και παραπάνω οι make εντολές είναι ίδιες, απλά με make run-all τρέχει και ο αλγόριθμος αλλά και τα τεστ.
+      Όπως και παραπάνω οι make εντολές είναι ίδιες, και υπάρχουν έξτρα οι εντολές:
+      1. make all: τρέχoυν και ο αλγόριθμος αλλά και τα τεστ.
+      2. main-all: τρέχει ο αλγόριθμος με Ευκλείδια απόσταση αλλά και Manhattan
+      3. run-all-tests: τρέχουν μόνο τα τεστ.
 
diff --git a/include/MathematicalFunctions.h b/include/MathematicalFunctions.h
index 925a8a3..59042f4 100644
--- a/include/MathematicalFunctions.h
+++ b/include/MathematicalFunctions.h
@@ -1,9 +1,21 @@
-#include "Dimension.h"
+#ifndef MATHEMATICAL_FUNCTIONS_H
+#define MATHEMATICAL_FUNCTIONS_H
+
+#include <math.h>
+#include <stddef.h>
+#include <stdio.h>
+#include "Node.h"
 #include "common_types.h"
+#include <string.h>
 
 double euclidean_distance(Dimension* nodeDimension1 , Dimension* nodeDimension2);
 
 double manhattan_distance(Dimension* nodeDimension1 , Dimension* nodeDimension2);
 
-double distance(Dimension* nodeDimension1 , Dimension* nodeDimension2, String distance_function);
+double calculate_norm(Dimension* head);
+
+double euclidean_distance_improved(Node* node1, Node* node2);
+
+double distance(Node* node1, Node* node2, String distance_function);
 
+#endif 
\ No newline at end of file
diff --git a/include/Node.h b/include/Node.h
index 12ece01..71b725f 100644
--- a/include/Node.h
+++ b/include/Node.h
@@ -13,6 +13,7 @@ typedef struct NodeNeighborsLinkedList NodeNeighborsLinkedList;
 
 typedef struct Node {
     int nodeNameInt;
+    double norm;
     Dimension* dimension;
     NodeNeighborsLinkedList* neighbors;
     NodeNeighborsLinkedList* reversedNeighbors;
@@ -26,4 +27,4 @@ void addNode(Node** headNode, Dimension* headDimension);
 
 void freeNode(Node* node);
 
-#endif 
+#endif 
\ No newline at end of file
diff --git a/main/Makefile b/main/Makefile
index aae02c2..817ba18 100644
--- a/main/Makefile
+++ b/main/Makefile
@@ -8,7 +8,7 @@ CC = gcc
 
 # Compile options. Το -I<dir> tells to compiler where to find the include files
 # -Werror when complite code add -Werror 
-CFLAGS = -Wall -Werror -g -I$(INCLUDE)
+CFLAGS = -Wall -g -I$(INCLUDE)
 LDFLAGS = -lm -fsanitize=address
 
 # .o files
@@ -22,6 +22,8 @@ ARGSEUCL = $(DATASETS)/00000020.bin 10 65 euclidean 0.8 0.001
 
 ARGSMAN = $(DATASETS)/00001000-4.bin 100 399 manhattan 0.1 0.001
 
+ARGSIMP = $(DATASETS)/asciiData3.bin 10 50 improved 0.1 0.001
+
 $(EXEC): $(OBJS)
 	$(CC) $(OBJS) -o $(EXEC) $(LDFLAGS)
 	@if [ -f $(EXEC).exe ]; then ln -sf $(EXEC).exe $(EXEC); fi
@@ -36,5 +38,9 @@ run-euclidean: $(EXEC)
 run-manhattan: $(EXEC)
 	./$(EXEC) $(ARGSMAN)
 
+run-euclidean-improved: $(EXEC)
+	./$(EXEC) $(ARGSIMP)
+
+
 valgrind: $(EXEC)
 	valgrind --error-exitcode=1 --leak-check=full --show-leak-kinds=all ./$(EXEC) $(ARGSEUCL)
\ No newline at end of file
diff --git a/modules/FindAllRightNeighborsAlgorithm.c b/modules/FindAllRightNeighborsAlgorithm.c
index 2446660..3b1dec5 100644
--- a/modules/FindAllRightNeighborsAlgorithm.c
+++ b/modules/FindAllRightNeighborsAlgorithm.c
@@ -38,6 +38,6 @@ void FindAllRightNeighbors(Graph * graph, String distance_function)
 
 
 void OrderNodesByNeighbor(Node *dest , Node *src, String distance_function){
-    addNeighbor(&dest->neighbors,src, distance(dest->dimension,src->dimension, distance_function));
+    addNeighbor(&dest->neighbors,src, distance(dest, src, distance_function));
     //Here or in the addNeigbor i would like to add a sorting method base on distance
 }
\ No newline at end of file
diff --git a/modules/Graph.c b/modules/Graph.c
index 4e0de9b..fe8b33d 100644
--- a/modules/Graph.c
+++ b/modules/Graph.c
@@ -62,6 +62,7 @@ Graph* createGraphFromBinaryFile(String filename, int dimensions) {
                 flag = 1;
                 break;
             }
+            // printf("coordinate-%f\n",coordinate);
             addDimension(&headDimension, i, coordinate);
         }
 
diff --git a/modules/MathematicalFunctions.c b/modules/MathematicalFunctions.c
index 1c7572b..fc83f99 100644
--- a/modules/MathematicalFunctions.c
+++ b/modules/MathematicalFunctions.c
@@ -1,9 +1,4 @@
-#include <math.h>
-#include <stddef.h>
-#include <stdio.h>
-#include "Dimension.h"
-#include "common_types.h"
-#include <string.h>
+#include "../include/MathematicalFunctions.h"
 
 /// @brief Basic use of euclidian distance theorym the distance as cost
 /// @param nodeDimension1 
@@ -38,7 +33,7 @@ double manhattan_distance(Dimension* nodeDimension1 , Dimension* nodeDimension2)
     Dimension* tempDimension1 = nodeDimension1;
     Dimension* tempDimension2 = nodeDimension2;
     
-    double distance = 0;
+    double distance = 0.0;
 
     while (tempDimension1 != NULL && tempDimension2 != NULL) {
         
@@ -51,19 +46,55 @@ double manhattan_distance(Dimension* nodeDimension1 , Dimension* nodeDimension2)
     return distance;
 }
 
+//isws boleyei node1, node2
+double calculate_norm(Dimension* head) { 
+    double norm = 0.0;
+
+    while (head != NULL) {
+        // printf("head->value-%f\n", head->value);
+        //norm = x1*x1 + x2*x2 + ......
+        norm += head->value*head->value;
+        head = head->next;
+    }
+    // printf("norm-%f\n",norm);
+    return norm;
+}
+
+double euclidean_distance_improved(Node* node1, Node* node2){
+    //x^2+y^2-2xy
+    double norm1 = node1->norm;
+    double norm2 = node2->norm;
+
+    Dimension* tempDimension1 = node1->dimension;
+    Dimension* tempDimension2 = node2->dimension;
+
+    double mult = 0.0;
+
+    while (tempDimension1 != NULL) {
+        mult += tempDimension1->value*tempDimension2->value;
+        tempDimension1 = tempDimension1->next;
+        tempDimension2 = tempDimension2->next;
+    }
+    printf("improved cost-%f\n",norm1+norm2-2.0*mult);
+    return norm1+norm2-2.0*mult;
+}
+
 /// @brief This function decides with mathematical therym (formula ) we are going to use
 ///  and returns it cost
 /// @param nodeDimension1 
 /// @param nodeDimension2 
 /// @param distance_function 
 /// @return 
-double distance(Dimension* nodeDimension1 , Dimension* nodeDimension2, String distance_function){
+double distance(Node* node1 , Node* node2, String distance_function){
     double cost = 0.0;
-    if(strcmp(distance_function, "euclidean") == 0){
-        cost = euclidean_distance(nodeDimension1, nodeDimension2);
+    if(strcmp(distance_function, "euclidean") == 0) {
+        cost = euclidean_distance(node1->dimension, node2->dimension);
+    }
+    else if(strcmp(distance_function, "manhattan") == 0) {
+        cost = manhattan_distance(node1->dimension, node2->dimension);
     }
-    else if(strcmp(distance_function, "manhattan") == 0){
-        cost = manhattan_distance(nodeDimension1, nodeDimension2);
+    else if(strcmp(distance_function, "improved") == 0) {
+        cost = euclidean_distance_improved(node1, node2);
     }
     return cost;
 }
diff --git a/modules/Node.c b/modules/Node.c
index 479136a..d57ed5e 100644
--- a/modules/Node.c
+++ b/modules/Node.c
@@ -1,5 +1,5 @@
 #include "../include/Node.h"
-
+#include "../include/MathematicalFunctions.h"
 
 /// @brief Initialzation of a node
 /// @return 
@@ -24,6 +24,9 @@ Node* initNode() {
 void addNode(Node** headNode, Dimension* headDimension) {
     Node* newNode = initNode();
     newNode->dimension = headDimension;
+    // printf("head->value-%f\n", headDimension->value);
+    newNode->norm = calculate_norm(headDimension);
+
     if (*headNode == NULL) {
         newNode->nodeNameInt = 0;
         *headNode = newNode;
diff --git a/modules/knn.c b/modules/knn.c
index f727712..cdc3df3 100644
--- a/modules/knn.c
+++ b/modules/knn.c
@@ -73,7 +73,7 @@ void checkNeighborofNeighbors(Graph** graph, Node** sourceNode, NodeNeighborsLin
 
         double cost = 0.0;
         if(matrixNodes[neighborName][sourceName] == -1.00){
-            cost = distance((*sourceNode)->dimension, tempNeighbors->node->dimension, distance_function);
+            cost = distance(*sourceNode, tempNeighbors->node, distance_function);
             matrixNodes[neighborName][sourceName] = cost;
         }
         else{
@@ -133,7 +133,7 @@ void KRandomNodes(Graph** graph, int K, String distance_function) {
                 neighborNode = neighborNode->next;
             }
 
-            double cost = distance(currentNode->dimension, neighborNode->dimension, distance_function);
+            double cost = distance(currentNode, neighborNode, distance_function);
             
             addNeighbor(&(currentNode->neighbors), neighborNode, cost);
             addNeighbor(&(neighborNode->reversedNeighbors), currentNode, cost);
diff --git a/modules/knn_improvements.c b/modules/knn_improvements.c
index a493506..72f6114 100644
--- a/modules/knn_improvements.c
+++ b/modules/knn_improvements.c
@@ -118,7 +118,7 @@ void localJoin(Node** node, String distance_function, int pK) {
             int nodeName2 = tempNeig->node->nodeNameInt;
 
             if ( nodeName1 != nodeName2 && incrementalSearch(tempNeig, temp) == 1 ) {
-                double cost = distance(temp->node->dimension, tempNeig->node->dimension, distance_function);
+                double cost = distance(temp->node, tempNeig->node, distance_function);
                 addCost(&((*node)->cost), nodeName1, nodeName2, cost);
 
                 // Update the flags
@@ -133,7 +133,7 @@ void localJoin(Node** node, String distance_function, int pK) {
             int nodeName4 = tempRev->node->nodeNameInt;
 
             if (nodeName3 != nodeName4 && incrementalSearch(tempRev, temp) == 1) {
-                double cost = distance(temp->node->dimension, tempRev->node->dimension, distance_function);
+                double cost = distance(temp->node, tempRev->node, distance_function);
                 addCost(&((*node)->cost), nodeName3, nodeName4, cost);
 
                 // Update the flags
diff --git a/times.txt b/times.txt
index 6a52c13..8c00e57 100644
--- a/times.txt
+++ b/times.txt
@@ -1,10 +1,38 @@
+-------------------------------------------------------
+
+
+/* FOR KNN */
+
+datasets/00001000-4.bin 100 399 euclidean 0.2 0.001
+Time for KNN algorithm: 717.410187 sec
+~ Acurate by 100.000000 % ~
+~ Acurate Supper  by 100.000000 % ~
+
+
+--------------------------------------------------------
+
+
+datasets/00001000-4.bin 100 399 manhattan 0.1 0.001
+Time for KNN algorithm: 711.582880 sec
+~ Acurate by 100.000000 % ~
+~ Acurate Supper  by 100.000000 % ~
+
+
+---------------------------------------------------------
+---------------------------------------------------------
+
+
+/* FOR KNN IMPROVEMENTS */
+
+
 datasets/00001000-4.bin 100 399 euclidean 0.2 0.001
 Time for KNN algorithm: 10.568234 sec
 ~ Acurate by 97.468672 % ~
 ~ Acurate Supper  by 55.828070 % ~
 
 
--------------------------------------------------------
+--------------------------------------------------------
+
 
 
 datasets/00001000-4.bin 100 399 manhattan 0.1 0.001