A more clear explanation on why sum of subarray works.:
Suppose we have original array:
[a0, a1, a2, a3, a4, a5, a6]
what we are given here(or we calculate ourselves) is:
[b0, b1, b2, b3, b4, b5, b6]
where,
b[i] = 0, when i == 0
b[i] = a[i] - a[i - 1], when i != 0
suppose if a2 and a6 are the points that give us the max difference (a2 < a6)
then in our given array, we need to find the sum of sub array from b3 to b6.
b3 = a3 - a2
b4 = a4 - a3
b5 = a5 - a4
b6 = a6 - a5
adding all these, all the middle terms will cancel out except two
i.e.
b3 + b4 + b5 + b6 = a6 - a2
a6 - a2 is the required solution.
so we need to find the largest sub array sum to get the most profit
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