codepad
[
create a new paste
]
login
|
about
Language:
C
C++
D
Haskell
Lua
OCaml
PHP
Perl
Plain Text
Python
Ruby
Scheme
Tcl
def find_single_missing_integer( ArrayWithOneMissingItem ): # Returns the missing integer in 1..n given an array of size (n-1) 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, n-1, n-2...) 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 )
Private
[
?
]
Run code
Submit