Given a range L-R, find the sum of all numbers divisible by 6 in range L-R
L and R are very large.
Input : 1 20 Output : 36 Explanation: 6 + 12 + 18 = 36 Input : 5 7 Output : 6 Explanation: 6 is the only divisible number in range 5-7
A naive approach is be to run a loop from L to R and sum up all the numbers divisible by 6.
An efficient approach is to sum all the numbers divisible by 6 up to R in sum, and sum all numbers divisible by 6 up to L-1. And then there subtraction will be the answer.
sum = 6 + 12 + 8 + …….(R/6)terms.
sum = 6(1 + 2 + 3……R/6 terms)
sumR = 3 * (R/6) * (R/6+1)
similarly we get
sumL as 3 * ((L-1)/6) * ((L-1/6)+1)
and the final answer as sumR – sumL.
Time Complexity: O(1)
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