.idea/misc.xml

 <?xml version="1.0" encoding="UTF-8"?>
 <project version="4">
-  <component name="ProjectRootManager" version="2" languageLevel="JDK_18" default="true" project-jdk-name="18" project-jdk-type="JavaSDK">
+  <component name="ProjectRootManager" version="2" languageLevel="JDK_22" default="true" project-jdk-name="18" project-jdk-type="JavaSDK">
     <output url="file://$PROJECT_DIR$/out" />
   </component>
 </project>
\ No newline at end of file

src/App.java

@@ -2,7 +2,8 @@ import java.util.List;
 
 public class App {
     public static void main(String[] args) throws Exception {
-       Backpack backpack= new InstanceReader().read("src/sac0");
-        System.out.println(backpack);
+       Backpack backpack= new InstanceReader().read("src/sac4");
+       backpack.solve();
+       System.out.println("meilleur solution :" + backpack.getBestValue());
     }
 }

src/Backpack.java

+import java.util.Comparator;
 import java.util.List;
 
 public class Backpack {
-    int capacity;
-    List<Loot> loots;
+    private final int capacity;
+    private final List<Loot> loots;
+    private int bestValue = 0;
+    private int currentWeight = 0;
+    private int currentValue = 0;
 
     public Backpack(int capacity, List<Loot> loots) {
         this.capacity = capacity;
         this.loots = loots;
     }
 
+    public void solve() {
+        this.sortByRatio();
+        explore_from(0);
+        System.out.println("La valeur optimale est : " + bestValue);
+    }
+
     public String toString(){
         return capacity +"\n"+loots;
     }
+
+    /**
+    Méthode pour trier les objets par ordre décroissant selon leur ratio
+    */
+    public void sortByRatio(){
+        loots.sort(Comparator.comparing(Loot::getRatio).reversed());
+    }
+
+    public int solutionFractionnelle(int startIndex, int remainingCapacity) {
+        int sfValuee = 0;
+        int sfWeight = 0;
+
+        // On commence à partir de startIndex
+        for(int i = startIndex; i < loots.size(); i++) {
+            Loot loot = loots.get(i);
+            if(sfWeight + loot.getWeight() <= remainingCapacity){
+                // Si l'objet entier peut entrer dans le sac
+                sfValuee += loot.getValue();
+                sfWeight += loot.getWeight();
+            }
+            else {
+                // Si l'objet ne peut pas entrer entièrement dans le sac
+                int remainingWeight = remainingCapacity - sfWeight;
+                sfValuee += (int) (loot.getRatio() * remainingWeight);
+                break;
+            }
+        }
+        return sfValuee;
+    }
+
+    private void explore_from(int index) {
+        // Si on a exploré tous les objets
+        if (index >= loots.size()) {
+            if (currentValue > bestValue) {
+                bestValue = currentValue;
+            }
+            return;
+        }
+
+        // On calcule la borne supérieure pour ce nœud
+        int remainingCapacity = capacity - currentWeight;
+        int borneSuperieure = currentValue + solutionFractionnelle(index, remainingCapacity);
+
+        // Si la borne supérieure est inférieure à la meilleure solution
+        if (borneSuperieure <= bestValue) {
+            return;
+        }
+
+        // on essaye d'explorer avec l'objet
+        Loot currentLoot = loots.get(index);
+        if (currentWeight + currentLoot.getWeight() <= capacity) {
+            currentWeight += currentLoot.getWeight();
+            currentValue += currentLoot.getValue();
+            explore_from(index + 1);
+            currentWeight -= currentLoot.getWeight();
+            currentValue -= currentLoot.getValue();
+        }
+
+        // on explore sans l'objet
+        explore_from(index + 1);
+    }
+
+    public int getBestValue() {
+        return bestValue;
+    }
 }

src/InstanceReader.java

@@ -23,5 +23,4 @@ public class InstanceReader {
         return new Backpack(capacity,loots);
     }
 
-
 }

src/Loot.java

 public class Loot {
-    int weight, value;
+    private int weight, value;
+    private final float ratio;
 
     public Loot(int weight, int value) {
         this.weight = weight;
         this.value = value;
+        this.ratio = (float) value/weight;
     }
 
     public String toString(){
-        return weight+" "+value;
+        return weight+" "+value+" "+ratio;
+    }
+
+    public float getRatio(){
+        return ratio;
+    }
+
+    public int getWeight(){
+        return weight;
+    }
+
+    public int getValue(){
+        return value;
     }
 }

src/sacTest

+15
+5 40
+8 48
+4 36
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