[Python] Very short and simple binary search, 99.5%+


  • 0

    As discussed in other solutions, we want to find all P[j] with j > i (Condition 1) and P[i]+lower <= P[j] <= P[i]+upper (Condition 2), where P[x] = sum(A[:x]).

    Put P[N-1], P[N-2], ...P[0] etc. in sorted order into B. When we put a P[i] into B, B only contained P[j]'s with j > i, which takes care of the first condition. We use binary search to find the number of P[j]'s in the valid range for the second condition.

    class Solution(object):
        def countRangeSum(self, A, lower, upper):
            su = sum(A)
            B = [su]
            ans = 0
            for x in A[::-1]:
                su -= x
                ix = bisect.bisect_left(B, lower+su)
                jx = bisect.bisect_right(B, upper+su)
                ans += max(0, jx-ix)
                bisect.insort(B, su)
            return ans
    

    Keep in mind bisect.insort has the list insertion which is O(N), but in practice this is fast.


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