Problem: 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.

Submission attempts (in order):
# maintain overall min 

# 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 

#     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])





# 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)

#     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)    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
     
    
    




# maintain overall min 

# 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 

#     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])





# print (overAllMin)
overAllMin = float('inf')
Arev = list(reversed(A))
dist1 = 0 
dist2 = 0 
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 
    # print (dist1, dist2, overAllMin)
    overAllMin = min(dist1, dist2, overAllMin)
        
print (overAllMin)    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
     
    
    



# maintain overall min 

# 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 

#     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])





# 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)

#     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)    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
     
    
    




Verdicts: Wrong Answer

Wrong Answer

Accepted