import matplotlib.pyplot as plt
import numpy as np

##Exercice 1
def argmin(t) :

    ind_mini = 0
    mini = t[0]

    for i in range(len(t)):
        if t[i] < mini :
            mini = t[i]
            ind_mini = i

    return ind_mini


#complexité : O(n), n = len(t)




##Exercice 2
def argmindist(t):
    mini = float("inf")
    n = len(t)
    for i in range(n):
        for j in range(i):
            if abs(t[i] - t[j]) < mini :
                mini = abs(t[i] - t[j])
                k = i
                l = j

    return k, l


##Exercice 3
x = [1,0,-1,1]
y = [0,2,-1,0]
plt.figure()
plt.plot(x,y)
plt.axis("equal")
plt.show()

##Exercice 4
x = np.linspace(-1,1, 100)
y = np.exp(x)
plt.figure()
plt.plot(x,y)
plt.show()

##Exercice 5
x = np.linspace(-np.pi,np.pi, 100)
y = np.cos(x)
plt.figure()
plt.plot(x,y)
plt.show()


##Exercice 6
x = np.linspace(-np.pi,np.pi, 100)
y = np.cos(x) + np.sin(x)
plt.figure()
plt.plot(x,y)
plt.show()


##Exercice 9
x = np.linspace(-np.pi,np.pi, 100)
plt.figure()
plt.plot(x,np.cos(x), label="cos(x)")
plt.plot(x,np.sin(x), label="sin(x)")
plt.legend()
plt.show()


##Exercice 10
x = np.linspace(-np.pi,np.pi, 100)
plt.figure()
plt.plot(x,np.cos(x), label="cos(x)")
plt.legend()
plt.figure()
plt.plot(x,np.sin(x), label="sin(x)")
plt.legend()
plt.show()

##Exercice 11
def testcroi(t):
    n = len(t)
    for i in range(n-1):
        if t[i] > t[i+1] :
            return False

    return True