Problem:
Score : 300 points

Problem Statement

There is a circular pond with a perimeter of K meters, and N houses around them.

The i-th house is built at a distance of A_i meters from the northmost point of the pond, measured clockwise around the pond.

When traveling between these houses, you can only go around the pond.

Find the minimum distance that needs to be traveled when you start at one of the houses and visit all the N houses.

Constraints

2 \leq K \leq 10^6

2 \leq N \leq 2 \times 10^5

0 \leq A_1 < ... < A_N < K

All values in input are integers.

Input

Input is given from Standard Input in the following format:

K N
A_1 A_2 ... A_N

Output

Print the minimum distance that needs to be traveled when you start at one of the houses and visit all the N houses.

Sample Input 1

20 3
5 10 15

Sample Output 1

10

If you start at the 1-st house and go to the 2-nd and 3-rd houses in this order, the total distance traveled will be 10.

Sample Input 2

20 3
0 5 15

Sample Output 2

10

If you start at the 2-nd house and go to the 1-st and 3-rd houses in this order, the total distance traveled will be 10.

Solution in Python (3.4.3) (judge verdict: Accepted)

# maintain overall min 
# iterate over two loops 
# find the absolute distance and before exiting the first maintain overall min
# also check the distance of last and first house
def findDistBetween(i,j):
    return abs(i - j)

def minDistfindDistBetweenLastAndFirstHouse(i,j):
    dist = findDistBetween(i, j)
    return K - dist 

K, N = input().split()
As = input().split()

K = int(K)
N = int(N)

# print ("As is")
# print (As)
# print (As.split())
A = [0] * len(As)
for i in range(len(As)):
    A[i] = int(As[i])
    
# A = list(map(lambda x: int(x), As))
# print (A)
# overAllMin = float('inf')
# minDist = 0 
# for i in range(N):
#     minDist = 0
#     for j in range(N):
#         # print (i, j)
#         minDist += findDistBetween(A[i], A[j])
#     # find the dist b/w last and first house
#     # minDist2 = minDistfindDistBetweenLastAndFirstHouse(A[0], A[-1])
#     # minDist = min(minDist, minDist2)
#     print ("Min dist", minDist)
#     # print ("min dist2", minDist2)
#     overAllMin = min(overAllMin, minDist)

# print (overAllMin)
overAllMin = float('inf')
Arev = list(reversed(A))
dist1 = 0 
dist2 = 0
prevHouse = -1
for i in range(N):
    # print ("PRev house", prevHouse)
    # print ("Next house", A[i])

    dist1 = max(findDistBetween(A[i], prevHouse), dist1)
    prevHouse = A[i]
    

ma = max(dist1, minDistfindDistBetweenLastAndFirstHouse(A[0], A[-1]))
print (K - ma)
# for i in range(N):
#     count = 0
#     curHouse = A[i]
#     j = i
#     flag0 = 0 
#     flag1 = 0
#     dist1 = 0 
#     dist2 = 0
#     while count < N:
#         if flag0 is 0:
#             dist1 += findDistBetween(curHouse, A[j])
#         curHouse = A[j]
#         j += 1
#         flag0 = 0
#         count += 1

#         if j == N and count < N: 
#             print ("in condition")
#             j = 0
#             dist1 += minDistfindDistBetweenLastAndFirstHouse(A[0], A[-1])
#             flag0 = 1
        
        # count += 1

        # print ("dist1", dist1)

    # count = 0
    # curHouse = A[i]
    # j = i
    # while count < N:
    #     if flag1 is 0:
    #         dist2 += findDistBetween(curHouse, A[j])
    #     curHouse = A[j]
    #     j -= 1
    #     count += 1
    #     flag1 = 0
    #     if j == -1 and count < N: 
    #         j = N - 1 
    #         dist2 += minDistfindDistBetweenLastAndFirstHouse(A[0], A[-1])
    #         flag1 = 1
    #     # count += 1 
# overAllMin = min(dist1, K - findDistBetween(A[0], A[-1]), overAllMin)
# print (dist1,  K - findDistBetween(A[0], A[-1]), overAllMin)
        
# print (overAllMin)