# loop to construct array of 50 fibonacci numbers

a = 1
b = 1
n = 0  # controls length of array to be built:
FIB = [1] # array to be built, starting with 1
while n<50:
    FIB.append(b)
    (a,b) = (b,a+b)
    n += 1
#
print FIB
print len(FIB)  # 51 why?

#### alternative:

FIB = 50*[0]  # notation means create array of 50 zeros
FIB[0] = 1
FIB[1] = 1
i = 2  # next fib index
while i<len(FIB):
    FIB[i] = FIB[i-1] + FIB[i-2]
    i = i+1
#while

print FIB
print len(FIB)

#### MUST DISTINGUISH BETWEEN INDEX AND VALUE ******************


### which one is better?  50*[0] method is more efficient for large arrays
# but sometimes you can't tell the length of array in advance, sometimes it
# can change.

# function to add up all the elements of an array:
def sum(A):  # add up all elements of an array A
    ax = 0  # running sum, accumulator
    i = 0 # array index
    while i<len(A):
        ax = ax + A[i]
        i = i+1
    #while
    return ax
# sum

print sum([2,4,6,1,7])


### alternative to while loop: for loop:
#  for x in A: ax = ax+x

### A for loop operates on the VALUES OF THE ARRAY, NOT INDEX

## Anything you can do with a for loop you can also do with a while loop
## a while loop is more flexible - can stop before end of array, etc...
## while loops are controled by boolean expressions, more complex conditions...

## function to return the smallest number in an array:
def smallest(A):
    ax = A[0]
    i = 1
    while i< len(A):
        if (A[i]<ax): ax = A[i]
        i += 1
    #while
    return ax

# return index of smallest element
def smallesti(A):
    axi = 0
    i = 1
    while i<len(A):
        if A[axi] > A[i]:  # why not axi > i?
            axi = i
        i = i+1
    # while
    return axi
# smallesti

# return index of smallest element, -1 if there's a tie for smallest:
def winneri(A):
    axi = 0
    tie = False
    i = 1
    while i<len(A):  # don't stop as soon as tie is found
        if A[axi] > A[i]:  # why not axi > i?
            axi = i
            tie = False
        else: #### what's wrong if there's no else here?
            if A[axi] == A[i]: tie = True
        # if-else
        i = i+1
    # while
    if (tie): return -1
    else: return axi
# winneri

print winneri([4,5,2,7,9,1,4])
print winneri([6,3,2,4,5,2,10])


### Boolean functions: functions that return True or False

# function to determine if all numbers in a list are positive:
def positive(A):  # predicate true if all elements of A are positive
    answer = True
    i = 0
    while i<len(A) and answer:
        if A[i]<0 : answer = False
        i += 1
    # while
    return answer
#positive

# what if A is []???  vacuously true  
# there are no non-positive numbers in [], so all numbers in [] are positive!