### Exercice 1 ###

def estDedans(l,e):
    for el in l:
        if e==l:
            return True
    return False

def maximum(l):
    max = l[0]
    for e in l:
        if e>max:
            max = e
    return max

def count(l,e):
    s = 0
    for el in l:
        if el==e:
            s+=1
    return s
    
def moyenne(l):
    s = 0
    for el in l:
        s+=el
    return s/len(l)

def var(l):
    s = 0
    m = moyenne(l)
    for el in l:
        s+=(el-m)**2
    return sqrt(s/len(l))

def majoritaire(l):
    cmax = 0
    emax = l[0]
    for el in l:
        c = count(el,l)
        if c > cmax:
            emax = el
    return emax

### Exercice 2 ###

# Structure: liste de 2-tuples contenant (volume,masse)

# Algorithme naif: on teste tout
def pasTropLourd_lourd(l,m):
    selection = None #list
    vmax=0
    for i in range(2**len(l)):
        test = [l[k] for k in range(len(l)) if ((i>>k)%2)==1]
        mas = sum([t[1] for t in test])
        vol = sum([t[0] for t in test])
        if mas<=m and vol>vmax:
            selection = test
            vmax=vol
    return selection

# Bernard ici présent est en O(2^n)

def pasTropLourd(l,m):
    if(len(l)==0): return l
    if(len(l)==1): return l if l[0][1]<=m else []
    
    # Avec ou sans ?
    reste = l[1:]
    (vm,ms) = l[0]
    if ms>m:
        return pasTropLourd(reste,m)
    else:
        p1 = pasTropLourd(reste,m)
        p2 = pasTropLourd(reste,m-ms)
        v1 = sum([t[0] for t in p1])
        v2 = sum([t[0] for t in p2])+vm
        return p1 if v1>=v2 else p2+[(vm,ms)]
        
        
### Exercice 3 ###
import numpy as np

def bell(n):
    bin = np.zeros((n+1,n+1),dtype=int)
    bin[0,0] = 1
    for i in range(1,n+1):
        bin[i,0]=1
        bin[i,1:] = bin[i-1,1:] + bin[i-1,:-1]
    
    B = np.zeros((n+1,),dtype=int)
    B[0] = 1
    print(bin[5,:])
    for i in range(1,n+1):
        B[i] = np.dot(B,bin[i,:].T)
    return B