0 and array

Topic:

An array of length n and a sub-array of the nearest 0.

Ideas:

For an array a, its sub-arrays and the nearest 0 will only appear in two cases:

1. Array subscript from 0 to I
2. Array subscript from I to J
   (where i,j are less than the array length)

How to do?

1. For the first case, just ask for the array a from 0 with a.length all the previous I items and then find the smallest.
2. For the second case, we first find all the first I items in 1 and then the order from small to large, and finally subtract the sorted first and 22, the lowest difference
3. Finally, the smallest of the 1 and 22 cases can be returned.

Apply for the same length of space sum[0 ... N-1],sum[i] is the former I of a and.
? Trick: definition sum[-1] = 0
? Obviously there are:
? Algorithm:
? To sum[0 ... N-1], and then calculates the difference between the sum of adjacent elements, and the minimum value is recorded as Min1.
? Min1: Arbitrarily fetching two sets in a, the minimum value of the respective element and the difference
? Because sum[-1]=0,sum[0 ... N-1] The absolute minimum value is recorded as Min2.
? The minimum value of the sum of the first k elements of a min2:a
? The smaller of the min1 and the min2, is the request.

The calculation of the sum itself and the calculation of the adjacent element difference are all O (N), the sort of sum is O (NLOGN), therefore, the total time complexity: O (NLOGN)
Emphasis: In addition to the minimum value for calculating the difference of the sum adjacent elements, do not forget the minimum value of the sum itself. A corresponding A[I...J], a corresponding A[0...J]

1 " "2 0 and array3 " "4 5 6 defsums (a):7n =Len (a)8sums = [0] * (n + 1)9      forIinchRange (0, N):TenSums[i + 1] = Sums[i] +A[i] One     returnSorted ((sums[1:])) A  -  - defdiff (a): then =Len (a) -D = [0] * (n-1) -      forIinchRange (1, N): -D[I-1] = a[i]-a[i-1] +     returnmin (d) -  +  A defMain (a): atA_sums =sums (a) -Min_diff =diff (A_sums) -     returnmin (min_diff, min (a_sums)) -  -Test = [10, 14, 2, 3,-4] - Print(Main (test))

0 and array