[IPT] TD 1: Exos 1 à 3.

SPE/IPT/TD1 Exos programmation/exo1.py

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+#!/usr/bin/env python3
+import random
+import numpy as np
+import matplotlib.pyplot as plt
+
+
+class Question:
+    def __init__(self,i=1, l=0, n=''):
+        self.name=n
+        self.level=l
+        self.number=i
+    def __enter__(self):
+        print('\n' + (self.level*2)*' ' + f"-> {self.number}. : {self.name} -- Début")
+        return self
+    def __exit__(self, exc_type, exc_value, exc_traceback):
+        print((self.level*2)*' ' + f"<- {self.number}. : {self.name} -- Fin\n") 
+with Question(1):
+    def tirer(n):
+        item = 0
+        for _ in range(n):
+            if random.random()<.5:
+                item +=1
+        return item
+
+    def proportion(n , N, k):
+        s = 0
+        for i in range(N):
+            if tirer(n) == k:
+                s += 1
+        return s/N
+    print('proportion(10, 100, 1) :', proportion(10, 100, 5))
+    n = 10
+    N = 100
+    plt.figure(0)
+    x = np.asarray(range(n+1))
+    y = np.asarray([proportion(n, N, k) for k in x])
+    plt.plot(x, y)
+    
+    
+    def binom(k, n):
+        return np.math.factorial(n)/(np.math.factorial(k)*np.math.factorial(n-k))
+    plt.figure(1)
+    x = np.asarray(range(n+1))
+    y = np.asarray([binom(k, n) for k in x])
+    plt.plot(x, y)
+    
+    #Version avec une proportion p : 
+    def tirer2(n, p):
+        item = 0
+        for _ in range(n):
+            if random.random()<p:
+                item +=1
+        return item
+
+    def proportion2(n, p, N, k):
+        s = 0
+        for i in range(N):
+            if tirer2(n, p) == k:
+                s += 1
+        return s/N
+    
+    p = .3
+    print('proportion2(10, p, 100, 1) :', proportion2(10, p, 100, 5))
+    n = 10
+    N = 100
+    plt.figure(2)
+    x = np.asarray(range(n+1))
+    y = np.asarray([proportion2(n, p, N, k) for k in x])
+    plt.plot(x, y)
+    
+    
+    def prop(k, n, p):
+        return binom(k, n) * (p**k) * (1-p)**(n-k)
+    plt.figure(3)
+    x = np.asarray(range(n+1))
+    y = np.asarray([prop(k, n, p) for k in x])
+    plt.plot(x, y)
+plt.show()
+

SPE/IPT/TD1 Exos programmation/exo2.py

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+#!/usr/bin/env python3
+
+
+class Question:
+    def __init__(self,i=1, l=0, n=''):
+        self.name=n
+        self.level=l
+        self.number=i
+    def __enter__(self):
+        print('\n' + (self.level*2)*' ' + f"-> {self.number}. : {self.name} -- Début")
+        return self
+    def __exit__(self, exc_type, exc_value, exc_traceback):
+        print((self.level*2)*' ' + f"<- {self.number}. : {self.name} -- Fin\n")
+
+with Question(2):
+    L = [True]*31
+    def modifier(L, p):
+        if p in (0,1):
+            L[p] = False
+        else:
+            for i in range(2*p,len(L), p):
+                L[i] = False
+    def premiers(n):
+        L = [True]*(n+1)
+        for i in range(n):
+            if L[i]:
+                modifier(L, i)
+        return [i for i, premier in enumerate(L) if premier]
+    print(premiers(823417)[-1])
+    print("Donc 823417 n'est pas premier.")

SPE/IPT/TD1 Exos programmation/exo3.py

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+#!/usr/bin/env python3
+
+
+class Question:
+    def __init__(self,i=1, l=0, n=''):
+        self.name=n
+        self.level=l
+        self.number=i
+    def __enter__(self):
+        print('\n' + (self.level*2)*' ' + f"-> {self.number}. : {self.name} -- Début")
+        return self
+    def __exit__(self, exc_type, exc_value, exc_traceback):
+        print((self.level*2)*' ' + f"<- {self.number}. : {self.name} -- Fin\n")
+
+import numpy as np
+import random
+with Question(3):
+    A = np.reshape(np.array([random.randint(0,9) for _ in range(9*9)]), (9,9))
+    B = np.reshape(np.array([random.randint(0,9) for _ in range(2*2)]), (2,2))
+    print(A)
+    print(B)
+    def motif(B, A):
+        for i in range(A.shape[0] - B.shape[0] + 1):
+            for j in range(A.shape[1] - B.shape[1] + 1):
+                diff = False
+                for k in range(B.shape[0]):
+                    for l in range(B.shape[1]):
+                        if B[k][l]!=A[i+k][j+l]:
+                            diff = True
+                            break
+                    if diff:
+                        break
+                if not diff:
+                    return True
+        return False
+    print(motif(B, A))
+    
+    def S(A, B):
+        s = 0
+        for i in range(A.shape[0]):
+            for j in range(A.shape[1]):
+                s += (A[i][j] - B[i][j])**2
+        return s
+    
+    def proche_motif(B, A):
+        M = np.zeros((A.shape[0] - B.shape[0] + 1, A.shape[1] - B.shape[1] + 1))
+        mini = (0,0)
+        for i in range(A.shape[0] - B.shape[0] + 1):
+            for j in range(A.shape[1] - B.shape[1] + 1):
+                M[i][j] = S(B, A[i: i +B.shape[0], j: j + B.shape[1]])
+                if M[mini[0]][mini[1]] > M[i][j]:
+                    mini = (i,j)
+        return A[mini[0]: mini[0] +B.shape[0], mini[1]: mini[1] + B.shape[1]]
+    print(proche_motif(B,A))
+    

SPE/IPT/TD1 Exos programmation/main.py

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+#!/usr/bin/env python3
+
+from exo1 import *
+from exo2 import *
+from exo3 import *