Python,
pasted
on Feb 22:

def find_single_missing_integer( ArrayWithOneMissingItem ):
# Returns the missing integer in 1..n given an array of size (n1) containing all but one of those integers.
n = len(ArrayWithOneMissingItem) + 1;
running_sum = 0
# ALGORITHM:
# We will iterate through array, keeping a running sum.
# While we iterate we will subtract one number at a time from this sum from the list 1..n. In this way we end up
# having subtracted every number 1..n and will end up with the opposite (negative) of whatever number is missing.
# In order to ensure that the running_sum does not overflow in the positive or negative direction as we do this,
# we will take from the head (1,2,3...) of numbers to subtract if the running_sum is < 0 (to further reduce it as little as possible
# so upcoming sums can make it positive again)
# and from the tail (n, n1, n2...) if the running sum is positive, to reduce it as much as possible. This can be thought of as trying,
# within our algorithm, to stay as close to 0 as possible.
# This will ensure we do not overflow at any point.
#our head and tail "pointers" within every integer 1..n:
all_ints_head=1
all_ints_tail=n
for element in ArrayWithOneMissingItem:
if running_sum > 0:
# When the running sum is positive, we try to decrease it to be negative again.
# logically,
# Add the current item to the running_sum,
# then you subtract the current tail of all numbers
# But we combine these two into adding the difference:
running_sum += (element  all_ints_tail);
all_ints_tail = 1; #decrement tail
else:
running_sum += (element  all_ints_head);
all_ints_head += 1; #increment head
#sanity check  these need to match after all this:
assert(all_ints_head == all_ints_tail)
#but we did not get a chance to subtract this last part from our list of all numbers.
running_sum = all_ints_head;
#now we return the opposite (negative) of this running sum, which will be the single missing integer.
return (running_sum);
# This should be in a tester class, but this whole algorithm is so brittle, who cares.
myList=[1,2,3,5,6]
print "From ", myList, " the missing number is: ", find_single_missing_integer( myList )
myList=[2,3,4,5,6]
print "From ", myList, " the missing number is: ", find_single_missing_integer( myList )
myList=[1,2,3,4,5]
print "From ", myList, " the missing number is: ", find_single_missing_integer( myList )
myList=[6,5,4,3,1]
print "From ", myList, " the missing number is: ", find_single_missing_integer( myList )
myList=[1,2]
print "From ", myList, " the missing number is: ", find_single_missing_integer( myList )
myList=[2,1]
print "From ", myList, " the missing number is: ", find_single_missing_integer( myList )
myList=[1,3]
print "From ", myList, " the missing number is: ", find_single_missing_integer( myList )
myList=[2,3]
print "From ", myList, " the missing number is: ", find_single_missing_integer( myList )
myList=[1]
print "From ", myList, " the missing number is: ", find_single_missing_integer( myList )
myList=[2]
print "From ", myList, " the missing number is: ", find_single_missing_integer( myList )
myList=[1,2,4,5]
print "From ", myList, " the missing number is: ", find_single_missing_integer( myList )
myList=[2,3,4,5]
print "From ", myList, " the missing number is: ", find_single_missing_integer( myList )
myList=[1,2,3,4]
print "From ", myList, " the missing number is: ", find_single_missing_integer( myList )
myList=[5,4,3,2]
print "From ", myList, " the missing number is: ", find_single_missing_integer( myList )
myList=[5,4,3,1]
print "From ", myList, " the missing number is: ", find_single_missing_integer( myList )

Output:

From [1, 2, 3, 5, 6] the missing number is: 4
From [2, 3, 4, 5, 6] the missing number is: 1
From [1, 2, 3, 4, 5] the missing number is: 6
From [6, 5, 4, 3, 1] the missing number is: 2
From [1, 2] the missing number is: 3
From [2, 1] the missing number is: 3
From [1, 3] the missing number is: 2
From [2, 3] the missing number is: 1
From [1] the missing number is: 2
From [2] the missing number is: 1
From [1, 2, 4, 5] the missing number is: 3
From [2, 3, 4, 5] the missing number is: 1
From [1, 2, 3, 4] the missing number is: 5
From [5, 4, 3, 2] the missing number is: 1
From [5, 4, 3, 1] the missing number is: 2

