A non-empty array A consisting of N integers is given. Array A represents numbers on a tape.
Any integer P, such that 0 < P < N, splits this tape into two non-empty parts: A[0], A[1], ..., A[P − 1] and A[P], A[P + 1], ..., A[N − 1].
The difference between the two parts is the value of: |(A[0] + A[1] + ... + A[P − 1]) − (A[P] + A[P + 1] + ... + A[N − 1])|
In other words, it is the absolute difference between the sum of the first part and the sum of the second part.
For example, consider array A such that:
A[0] = 3 A[1] = 1 A[2] = 2 A[3] = 4 A[4] = 3We can split this tape in four places:
- P = 1, difference = |3 − 10| = 7
- P = 2, difference = |4 − 9| = 5
- P = 3, difference = |6 − 7| = 1
- P = 4, difference = |10 − 3| = 7
Write a function:
def solution(A)
that, given a non-empty array A of N integers, returns the minimal difference that can be achieved.
For example, given:
A[0] = 3 A[1] = 1 A[2] = 2 A[3] = 4 A[4] = 3the function should return 1, as explained above.
Write an efficient algorithm for the following assumptions:
- N is an integer within the range [2..100,000];
- each element of array A is an integer within the range [−1,000..1,000].
# you can write to stdout for debugging purposes, e.g.
# print "this is a debug message"
def solution(A):
# write your code in Python 2.7
L = len(A)
min = 1000
if L == 1:
min = A[0]
elif L == 2:
min = abs(A[0] - A[1])
else:
rsums = [0] * L
lsum = 0
for i in range(L-2, 0, -1):
sums[i] = A[i] + sums[i + 1]
for i in range(0, L-2):
lsum += A[i]
diff = abs(lsum - rsums[i+1])
if diff < min:
min = diff
return min
[2, 1]
[1]
Traceback (most recent call last): File "user.py", line 109, in <module> main() File "user.py", line 86, in main result = sol.solution ( A ) File "/tmp/solution.py", line 19, in solution sums[i] = A[i] + sums[i + 1] NameError: global name 'sums' is not defined
# you can write to stdout for debugging purposes, e.g.
# print "this is a debug message"
def solution(A):
# write your code in Python 2.7
L = len(A)
min = 1000
if L == 1:
min = A[0]
elif L == 2:
min = abs(A[0] - A[1])
else:
rsums = [0] * L
lsum = 0
for i in range(L-2, 0, -1):
rsums[i] = A[i] + rsums[i + 1]
for i in range(0, L-2):
lsum += A[i]
diff = abs(lsum - rsums[i+1])
if diff < min:
min = diff
return min
[2, 1]
[1]
# you can write to stdout for debugging purposes, e.g.
# print "this is a debug message"
def solution(A):
# write your code in Python 2.7
L = len(A)
min = 1000
if L == 1:
min = A[0]
elif L == 2:
min = abs(A[0] - A[1])
else:
rsums = [0] * L
lsum = 0
rsums[L-1] = A[L-1]
for i in range(L-2, 0, -1):
rsums[i] = A[i] + rsums[i + 1]
for i in range(0, L-2):
lsum += A[i]
diff = abs(lsum - rsums[i+1])
if diff < min:
min = diff
return min
[2, 1]
[1]
# you can write to stdout for debugging purposes, e.g.
# print "this is a debug message"
def solution(A):
# write your code in Python 2.7
L = len(A)
min = 1000
if L == 1:
min = A[0]
elif L == 2:
min = abs(A[0] - A[1])
else:
rsums = [0] * L
lsum = 0
rsums[L-1] = A[L-1]
for i in range(L-2, 0, -1):
rsums[i] = A[i] + rsums[i + 1]
for i in range(0, L-2):
lsum += A[i]
diff = abs(lsum - rsums[i+1])
if diff < min:
min = diff
return min
[-1, 1]
[1]
# you can write to stdout for debugging purposes, e.g.
# print "this is a debug message"
def solution(A):
# write your code in Python 2.7
L = len(A)
min = 1000
if L == 1:
min = A[0]
elif L == 2:
min = abs(A[0] - A[1])
else:
rsums = [0] * L
lsum = 0
rsums[L-1] = A[L-1]
for i in range(L-2, 0, -1):
rsums[i] = A[i] + rsums[i + 1]
for i in range(0, L-2):
lsum += A[i]
diff = abs(lsum - rsums[i+1])
if diff < min:
min = diff
return min
[-1, 1, 5, 3, 10, 21, 435, 5, 2, 7, 1, 1]
[1]
# you can write to stdout for debugging purposes, e.g.
# print "this is a debug message"
def solution(A):
# write your code in Python 2.7
L = len(A)
min = 1000
if L == 1:
min = A[0]
elif L == 2:
min = abs(A[0] - A[1])
else:
rsums = [0] * L
lsum = 0
rsums[L-1] = A[L-1]
for i in range(L-2, 0, -1):
rsums[i] = A[i] + rsums[i + 1]
for i in range(0, L-2):
lsum += A[i]
diff = abs(lsum - rsums[i+1])
if diff < min:
min = diff
return min
[-1, 1, 5, 3, 10, 21, -435, 5, 2, 7, 1, 1]
[1]
# you can write to stdout for debugging purposes, e.g.
# print "this is a debug message"
def solution(A):
# write your code in Python 2.7
L = len(A)
min = 1000
if L == 1:
min = A[0]
elif L == 2:
min = abs(A[0] - A[1])
else:
rsums = [0] * L
lsum = 0
rsums[L-1] = A[L-1]
for i in range(L-2, 0, -1):
rsums[i] = A[i] + rsums[i + 1]
for i in range(0, L-2):
lsum += A[i]
diff = abs(lsum - rsums[i+1])
if diff < min:
min = diff
return min
[-1, 1, 5, 3, 10, 21, -435, 5, 2, 7, 1, 1]
[1]
# you can write to stdout for debugging purposes, e.g.
# print "this is a debug message"
def solution(A):
# write your code in Python 2.7
L = len(A)
min = 1000
if L == 1:
min = A[0]
elif L == 2:
min = abs(A[0] - A[1])
else:
rsums = [0] * L
lsum = 0
rsums[L-1] = A[L-1]
for i in range(L-2, 0, -1):
rsums[i] = A[i] + rsums[i + 1]
for i in range(0, L-2):
lsum += A[i]
diff = abs(lsum - rsums[i+1])
if diff < min:
min = diff
return min
The solution obtained perfect score.