Math is magic.

891. Sum of Subsequence Widths

https://leetcode.com/contest/weekly-contest-98/problems/sum-of-subsequence-widths/

C++ solution, O(N log N) sort + O(N) calculate - LeetCode Discuss

#solution 1
class Solution:
    def sumSubseqWidths(self, A: List[int]) -> int:
        A.sort(reverse=True)
        geo_seq_sum, xs = 0, [0]
        for i in range(len(A)-1):
            geo_seq_sum += 1<<i
            xs.append((xs[-1]<<1) + (A[i]-A[i+1])*geo_seq_sum)
           
        return sum(xs) % (10**9+7)
# solution 2
class Solution:
    def sumSubseqWidths(self, A: List[int]) -> int:
        A.sort()
        res=0
        for i in range(len(A)):
            res <<= 1
            res += A[~i] - A[i]
            res %= (10**9+7)
        return res

858. Mirror Reflection

Java solution with an easy-to-understand explanation - LeetCode Discuss

829. Consecutive Numbers Sum

https://leetcode.com/problems/consecutive-numbers-sum/

Simple python - LeetCode Discuss

class Solution:
    def consecutiveNumbersSum(self, N: int) -> int:
        if N==1:return 1
        res = 1
        """
        x+0 = n
        x+0+x+1 = n
        x+0+x+1+x+2 = n
        """
        cusum = 0
        for i in range(1, N):
            cusum += i
            quo, remainder = divmod(N-cusum, i+1)
            if not quo:break
            if not remainder:
                res += 1
            
        return res