fix: correct NFDBP algo

Probas.py

@@ -9,7 +9,7 @@ import matplotlib.pyplot as pt
 
 def simulate_NFBP(N):
     """
-    Tries to simulate T_i, V_i and H_n for N packages of random size.
+    Tries to simulate T_i, V_i and H_n for N items of random size.
     """
     i = 0    # Nombre de boites
     R = [0]  # Remplissage de la i-eme boite
@@ -41,11 +41,12 @@ def simulate_NFBP(N):
     }
 
 
+# unused
 def stats_NFBP(R, N):
     """
-    Runs R runs of NFBP (for N packages) and studies distribution, variance, mean...
+    Runs R runs of NFBP (for N items) and studies distribution, variance, mean...
     """
-    print("Running {} NFBP simulations with {} packages".format(R, N))
+    print("Running {} NFBP simulations with {} items".format(R, N))
     I = []
     H = [[] for _ in range(N)]  # List of empty lists
     
@@ -55,24 +56,29 @@ def stats_NFBP(R, N):
         for n in range(N):
             H[n].append(sim["H"][n])
 
-    print("Mean number of boxes : {} (variance {})".format(mean(I), variance(I)))
+    print("Mean number of bins : {} (variance {})".format(mean(I), variance(I)))
 
     for n in range(N):
         print("Mean H_{} : {} (variance {})".format(n, mean(H[n]), variance(H[n])))
 
 def stats_NFBP_iter(R, N):
     """
-    Runs R runs of NFBP (for N packages) and studies distribution, variance, mean...
+    Runs R runs of NFBP (for N items) and studies distribution, variance, mean...
     Calculates stats during runtime instead of after to avoid excessive memory usage.
     """
-    P=R*N
-    print("Running {} NFBP simulations with {} packages".format(R, N))
+    P=R*N  # Total number of items
+    print("## Running {} NFBP simulations with {} items".format(R, N))
+    # number of bins
     ISum = 0  
     IVarianceSum = 0
+    # index of the bin containing the n-th item
     HSum = [0 for _ in range(N)] 
     HSumVariance = [0 for _ in range(N)]
+    # number of items in the i-th bin
     Sum_T=[0 for _ in range(N)]
+    # size of the first item in the i-th bin
     Sum_V=[0 for _ in range(N)]
+
     for i in range(R):
         sim = simulate_NFBP(N)
         ISum += sim["i"]
@@ -82,55 +88,56 @@ def stats_NFBP_iter(R, N):
             HSumVariance[n] += sim["H"][n]**2
         T=sim['T']
         V=sim['V']
-        for i in range(N):
+        # ensure that T, V have the same length as Sum_T, Sum_V
+        for i in range(N - sim['i']):
             T.append(0)
             V.append(0)
         Sum_T=[x+y for x,y in zip(Sum_T,T)]
         Sum_V=[x+y for x,y in zip(Sum_V,V)]
-            #we use round to approximate variations of continuous variable V
-       # Sum_V=  round(sim['V'],2))
+
     Sum_T=[x/R for x in Sum_T]
     Sum_V=[round(x/R,2) for x in Sum_V]
-    print(Sum_V)
+    #print(Sum_V)
     I = ISum/R
     IVariance = sqrt(IVarianceSum/(R-1) - I**2)
-    print("Mean number of boxes : {} (variance {})".format(I, IVariance),'\n')
+    print("Mean number of bins : {} (variance {})".format(I, IVariance),'\n')
+    # TODO clarify line below
     print(" {} * {} iterations of T".format(R,N),'\n')
     
-    for n in range(N):
+    for n in range(min(N, 10)):
         Hn = HSum[n]/R # moyenne
         HVariance = sqrt(HSumVariance[n]/(R-1) - Hn**2) # Variance
-        print("Index of box containing the {}th package (H_{}) : {} (variance {})".format(n, n, Hn, HVariance))
+        print("Index of bin containing the {}th item (H_{}) : {} (variance {})".format(n, n, Hn, HVariance))
     HSum=[x/R for x in HSum]
-    print(HSum)
+    # print(HSum)
 #Plotting
     fig = plt.figure()
     #T plot
     x =  np.arange(N)
-    print(x)
+    # print(x)
     ax = fig.add_subplot(221)
     ax.bar(x,Sum_T, width=1,label='Empirical values', edgecolor="blue", linewidth=0.7,color='red')
     ax.set(xlim=(0, N), xticks=np.arange(0, N),ylim=(0,3), yticks=np.linspace(0, 3, 5))
     ax.set_ylabel('Items')
-    ax.set_xlabel('Boxes (1-{})'.format(N))
-    ax.set_title('T histogram for {} packages (Number of packages in each box)'.format(P))
+    ax.set_xlabel('Bins (1-{})'.format(N))
+    ax.set_title('T histogram for {} items (Number of items in each bin)'.format(P))
     ax.legend(loc='upper left',title='Legend')
     #V plot
     bx = fig.add_subplot(222) 
     bx.bar(x,Sum_V, width=1,label='Empirical values', edgecolor="blue", linewidth=0.7,color='orange')
     bx.set(xlim=(0, N), xticks=np.arange(0, N),ylim=(0, 1), yticks=np.linspace(0, 1, 10))
     bx.set_ylabel('First item size')
-    bx.set_xlabel('Boxes (1-{})'.format(N))
-    bx.set_title('V histogram for {} packages (first package size of each box)'.format(P))
+    bx.set_xlabel('Bins (1-{})'.format(N))
+    bx.set_title('V histogram for {} items (first item size of each bin)'.format(P))
     bx.legend(loc='upper left',title='Legend')
     #H plot
     #We will simulate this part for a asymptotic study
     cx = fig.add_subplot(223)
     cx.bar(x,HSum, width=1,label='Empirical values', edgecolor="blue", linewidth=0.7,color='green')
     cx.set(xlim=(0, N), xticks=np.arange(0, N),ylim=(0, 10), yticks=np.linspace(0, N, 5))
-    cx.set_ylabel('Box ranking of n-item')
+    cx.set_ylabel('Bin ranking of n-item')
     cx.set_xlabel('n-item (1-{})'.format(N))
-    cx.set_title('H histogram for {} packages'.format(P))
+    cx.set_title('H histogram for {} items'.format(P))
     xb=linspace(0,N,10)
     yb=Hn*xb/10
     wb=HVariance*xb/10
@@ -141,7 +148,8 @@ def stats_NFBP_iter(R, N):
 
 def simulate_NFDBP(N):
     """
-    Tries to simulate T_i, V_i and H_n for N packages of random size.
+    Tries to simulate T_i, V_i and H_n for N items of random size.
+    Next Fit Dual Bin Packing : bins should overflow
     """
     i = 0    # Nombre de boites
     R = [0]  # Remplissage de la i-eme boite
@@ -150,20 +158,18 @@ def simulate_NFDBP(N):
     H = []   # Rang de la boite contenant le n-ieme paquet
     for n in range(N):
         size = random()
-        R[i] += size
-        T[i] += 1
-        if R[i] + size >= 1:
+        if R[i] >= 1:
             # Il y n'y a plus de la place dans la boite pour le paquet.
-            # On passe à la boite suivante (qu'on initialise)
+            # On passe à la boite suivante (qu'on initialise).
             i += 1
             R.append(0)
             T.append(0)
-            V.append(0)
-
-        if V[i] == 0:
             # C'est le premier paquet de la boite
-            V[i] = size
+            V.append(size)
         H.append(i)
+        R[i] += size
+        T[i] += 1
+
 
     return {
         "i": i,
@@ -176,10 +182,10 @@ def simulate_NFDBP(N):
 
 def stats_NFDBP(R, N,t_i):
     """
-    Runs R runs of NFDBP (for N packages) and studies distribution, variance, mean...
+    Runs R runs of NFDBP (for N items) and studies distribution, variance, mean...
     """
-    print("Running {} NFDBP simulations with {} packages".format(R, N))
-    P=N*R
+    print("## Running {} NFDBP simulations with {} items".format(R, N))
+    P=N*R  # Total number of items
     I = [] 
     H = [[] for _ in range(N)]  # List of empty lists
     T=[]
@@ -203,7 +209,7 @@ def stats_NFDBP(R, N,t_i):
     Sum_T=[x/R for x in Sum_T] #Experimental [Ti=k]
     Sum_T=[x*100/(sum(Sum_T)) for x in Sum_T] #Pourcentage de la repartition des items 
     
-    print("Mean number of boxes : {} (variance {})".format(mean(I), variance(I)))
+    print("Mean number of bins : {} (variance {})".format(mean(I), variance(I)))
 
     for n in range(N):
         print("Mean H_{} : {} (variance {})".format(n, mean(H[n]), variance(H[n])))
@@ -214,8 +220,7 @@ def stats_NFDBP(R, N,t_i):
         T_maths.append(1/(factorial(u-1))-1/factorial(u))
     E=0
     sigma2=0
-    print("hep")
-    print(T_maths)
+    # print(T_maths)
     for p in range(len(T_maths)):
         E=E+(p+1)*T_maths[p]
         sigma2=((T_maths[p]-E)**2)/(len(T_maths)-1)
@@ -231,8 +236,8 @@ def stats_NFDBP(R, N,t_i):
     ax.bar(x,Sum_T, width=1,label='Empirical values', edgecolor="blue", linewidth=0.7,color='red')
     ax.set(xlim=(0, N), xticks=np.arange(0, N),ylim=(0,20), yticks=np.linspace(0, 20, 2))
     ax.set_ylabel('Items(n) in %')
-    ax.set_xlabel('Boxes (1-{})'.format(N))
-    ax.set_title('Items percentage for each box and {} packages (Number of packages in each box)'.format(P))
+    ax.set_xlabel('Bins (1-{})'.format(N))
+    ax.set_title('Items percentage for each bin and {} items (Number of items in each bin)'.format(P))
     ax.legend(loc='upper left',title='Legend')
 
     #Mathematical P(Ti=k) plot. It shows the Ti(t_i) law with the probability of each number of items.
@@ -241,8 +246,8 @@ def stats_NFDBP(R, N,t_i):
     bx.hist(Tk[t_i],bins=10, width=1,label='Empirical values', edgecolor="blue", linewidth=0.7,color='red')
     bx.set(xlim=(0, N), xticks=np.arange(0, N),ylim=(0,len(Tk[t_i])), yticks=np.linspace(0, 1, 1))
     bx.set_ylabel('P(T{}=i)'.format(t_i))
-    bx.set_xlabel('Boxes i=(1-{}) in %'.format(N))
-    bx.set_title('T{} histogram for {} packages (Number of packages in each box)'.format(t_i,P))
+    bx.set_xlabel('Bins i=(1-{}) in %'.format(N))
+    bx.set_title('T{} histogram for {} items (Number of items in each bin)'.format(t_i,P))
     bx.legend(loc='upper left',title='Legend')
 
     #Loi mathematique
@@ -251,11 +256,13 @@ def stats_NFDBP(R, N,t_i):
     cx.bar(x,T_maths, width=1,label='Theoretical values', edgecolor="blue", linewidth=0.7,color='red')
     cx.set(xlim=(0, N), xticks=np.arange(0, N),ylim=(0,100), yticks=np.linspace(0, 100, 10))
     cx.set_ylabel('P(T{}=i)'.format(t_i))
-    cx.set_xlabel('Boxes i=(1-{})'.format(N))
+    cx.set_xlabel('Bins i=(1-{})'.format(N))
     cx.set_title('Theoretical T{} values in %'.format(t_i))
     cx.legend(loc='upper left',title='Legend')
     plt.show()
 
+# unused
+def basic_demo():
     N = 10 ** 1
     sim = simulate_NFBP(N)
 
@@ -277,6 +284,6 @@ for j in range(sim["i"] + 1):
                                                                                                    sim["T"][j],
                                                                                                    sim["V"][j]))
 
-print()
 stats_NFBP_iter(10**3, 10)
+print('\n\n')
 stats_NFDBP(10 ** 3, 10,1)