y = var('y')
'''
Group Members
=============
'''

userids = ['Thormundur15'] # fill in this array with strings of usernames
def m5p1(G):
    '''Return the size of the largest clique
    '''
    maxcount = 1
    for i in G:
        stack = [i]
        for j in G[i]:
            if(set(stack) <= set(G[j])):
                stack.append(j)
        if(len(stack) > maxcount):
            maxcount = len(stack)
    return maxcount

def myfunction(stack, constack, G):
    diff = list(set(stack) - set(G))
    for i in diff:
        if(i not in stack and i not in constack):
            newstack [i]
            newconstack = []
            for j in stack:
                newstack.append(j)
            for j in constack:
                newconstack.append(j)
            for j in G[i]:
                newconstack.append(j)
            myfunction(newstack, newconstack, G)
    return len(stack)

def m5p2(G):
    '''Return the size of the largest independent set
    '''
    largest = 1
    for i in G:
        independentSet = [i]
        listSC = [i]
        for k in G[i]:
            listSC.append(k)
        count = 0
        oArr = G.copy()
        for k in range(0, i):
            temp = oArr[0]
            for j in xrange(0, len(oArr)-1):
                oArr[j] = oArr[j+1]
            oArr[len(oArr)-1] = temp
        for k in oArr:
            if(k not in listSC):
                independentSet.append(k)
                count += 1
            if(k in independentSet):
                for j in oArr[k]:
                    listSC.append(j)
        if(largest < count):
            largest = count
    return largest

def lowCost(U, S, cost, Allcost):
    if(len(U) == 0):
        Allcost.append(cost)
        return cost
    else:
        for i in range(len(S)):
            for j in range(len(S[i])):
                if(S[i][j] in U):
                    lowCost(list(set(U) - set(S[i])), S, cost+1, Allcost)
                    break
    return min(Allcost)

def m5p3(U, S):
    '''Return the lowest number of subsets from S to cover U
    '''
    return lowCost(U, S, 0, [])

def m5p4(xmin, xmax, ymin, ymax):
    '''Return a lambda function for the square bounded by xmin-xmax and ymin-ymax
    '''
    return lambda px, py: px >= xmin and px <= xmax and py >= ymin and py <= ymax

def m5p5(x0, y0, r):
    '''Return a lambda function for the square with center (x0, y0) and side length 2r
    '''
    return lambda px, py: px >= x0 - r and px <= x0 + r and py >= y0 - r and py <= y0 + r

def m5p6(x0, y0, r):
    '''Return a lambda function for the disc with center (x0, y0) and radius r
    '''
    return lambda px, py: True

def m5p7((a0, b0, r), n=5000, xmin=-1, xmax=1, ymin=-1, ymax=1):
    '''Return an approximation of the area covered by P (a disc) inside the rectangle
    '''
    return -1

def m5p8(f, n=1000, xmin=-1, xmax=1, ymin=-1, ymax=1, zmax=1):
    '''Return an approximation of the volume between the function and the xy-plane
    '''
    return -1