You are given a non-empty, zero-indexed array A of n (1 ¬ n ¬ 100 000) integers a0, a1, . . . , an−1 (0 ¬ ai ¬ 1 000). This array represents number of mushrooms growing on the consecutive spots along a road. You are also given integers k and m (0 ¬ k, m < n). A mushroom picker is at spot number k on the road and should perform m moves. In one move she moves to an adjacent spot. She collects all the mushrooms growing on spots she visits. The goal is to calculate the maximum number of mushrooms that the mushroom picker can collect in m moves.

### Solution

```
def prefixSum(A):
n = len(A)
prefix = [0]*(n + 1)
for k in range(1, n+1):
prefix[k] = prefix[k - 1] + A[k - 1]
print(prefix)
return prefix
def maxMushrooms(A, k, m):
prefix = prefixSum(A)
l = len(A)
org_k = k
answer = 0
start = k
# case 1. Move forward
end = min(k + m, l-1)
pdiff = prefix[end+1] - prefix[start]
print(pdiff, prefix[end+1], prefix[start])
answer = max(answer, pdiff)
# case 2 Move left
end = k
start = k - min(k, m)
pdiff = prefix[end+1] - prefix[start]
print(pdiff, prefix[end+1], prefix[start])
answer = max(answer, pdiff)
# case 3: Mix left & right
# At position k you can go back least of both.
# k = 4 m = 2, you can't move more than given moves i.e. 2
# k= 1 m = 10 you can't move more than 1 move.
max_ops = min(m, k)
while max_ops > 0:
start = k - max_ops
#print("start={}".format(start))
print("remaining steps m={} consumes={}".format(m, (2 * max_ops)))
# m - (2 * max_ops) can have negative value.
# m = 6, max_ops = 4 diff = 6 - (2*4) this means
# no operations remain to move right from position k.
# So the end is k itself.
end = min(k + max(0, m - (2 * max_ops)), l-1)
print("end={}".format(end))
pdiff = prefix[end+1] - prefix[start]
print(start, end+1, prefix[start], prefix[end+1])
answer = max(answer, pdiff)
max_ops -= 1
print("answer={}".format(answer))
A = [2,3,1,7,5,1,3,9]
k = 4
m = 6
#maxMushrooms(A, k, m)
A = [9,1,1,1,1,1,9]
k = 3
m = 4
#maxMushrooms(A, k, m)
A = [9,2,1,1,1,1,9]
k = 3
m = 10
print(A)
maxMushrooms(A, k, m)
```

### Reference

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