diff --git a/.idea/misc.xml b/.idea/misc.xml
index 80cd069..e5e2ec5 100644
--- a/.idea/misc.xml
+++ b/.idea/misc.xml
@@ -7,4 +7,5 @@
       </list>
     </option>
   </component>
+  <component name="ProjectRootManager" version="2" project-jdk-name="11" project-jdk-type="JavaSDK" />
 </project>
\ No newline at end of file
diff --git a/be-graphes-algos/src/main/java/org/insa/graphs/algorithm/utils/BinaryHeap.java b/be-graphes-algos/src/main/java/org/insa/graphs/algorithm/utils/BinaryHeap.java
index 7a17c6b..832f3e9 100644
--- a/be-graphes-algos/src/main/java/org/insa/graphs/algorithm/utils/BinaryHeap.java
+++ b/be-graphes-algos/src/main/java/org/insa/graphs/algorithm/utils/BinaryHeap.java
@@ -1,4 +1,5 @@
 package org.insa.graphs.algorithm.utils;
+import java.util.HashMap;
 
 import java.util.ArrayList;
 
@@ -16,6 +17,9 @@ public class BinaryHeap<E extends Comparable<E>> implements PriorityQueue<E> {
     // Number of elements in heap.
     private int currentSize;
 
+    // a hash map for the element - index link
+    private HashMap<E, Integer> map;
+
     // The heap array.
     protected final ArrayList<E> array;
 
@@ -25,6 +29,7 @@ public class BinaryHeap<E extends Comparable<E>> implements PriorityQueue<E> {
     public BinaryHeap() {
         this.currentSize = 0;
         this.array = new ArrayList<E>();
+        this.map = new HashMap<E, Integer>();
     }
 
     /**
@@ -35,6 +40,7 @@ public class BinaryHeap<E extends Comparable<E>> implements PriorityQueue<E> {
     public BinaryHeap(BinaryHeap<E> heap) {
         this.currentSize = heap.currentSize;
         this.array = new ArrayList<E>(heap.array);
+        this.map = new HashMap<E, Integer>(heap.map);
     }
 
     /**
@@ -50,6 +56,9 @@ public class BinaryHeap<E extends Comparable<E>> implements PriorityQueue<E> {
         else {
             this.array.set(index, value);
         }
+
+        // we need to add the correspondence between index - value
+        map.put(value,index);
     }
 
     /**
@@ -137,15 +146,36 @@ public class BinaryHeap<E extends Comparable<E>> implements PriorityQueue<E> {
 
     @Override
     public void remove(E x) throws ElementNotFoundException {
-    	// index of is not optimized but it's better than nothing. We will come back to improve it if we have time at the end
-    	int i = this.array.indexOf(x);
-    	if (i == -1 || i > this.currentSize - 1) {
+    	/* LEGACY CODE :
+    	Index of is not optimized but it's better than nothing. We will come back to improve it if we have time at the end
+    	int i = this.array.indexOf(x) */
+
+
+        int i = -1;
+
+        // check if it is in the hashMap
+        if (this.map.get(x) != null){
+            i = this.map.get(x);
+        } else {
+            throw new ElementNotFoundException(x);
+        }
+
+        // check if the value makes sense
+        if (i > this.currentSize - 1 || i == -1) {
     		throw new ElementNotFoundException(x);
     	}
         E lastItem = this.array.get(--this.currentSize);
         this.arraySet(i, lastItem);
         this.percolateDown(i);
         this.percolateUp(i);
+
+
+
+        // since we removed the element we need to make sure it's not referenced in the hashMap (hence putting it to -1)
+        // since usually (not sure for the case of java, depends on how collisions are handled) the deletion of a pair
+        // costs more than changing its value so could just set it to -1 but keeping it increases the chances of collisions
+        // We therefore chose to remove it
+        this.map.remove(x);
     }
 
     @Override
@@ -161,6 +191,7 @@ public class BinaryHeap<E extends Comparable<E>> implements PriorityQueue<E> {
         E lastItem = this.array.get(--this.currentSize);
         this.arraySet(0, lastItem);
         this.percolateDown(0);
+        this.map.remove(minItem);
         return minItem;
     }