I am finding with some formulas for my web application. I need a formula that counts the number of values between two number, e.g. there are four numbers (3,4,5,6) between 2 and 7
Count number of values between two numbers
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4this problem just might be NP-complete. i hope you have enough computing power to tackle it. – 2010-12-08
4 Answers
larger - smaller - 1. If you don't count the larger and the smaller (like your example).
If the numbers are $n, n+1, \dots, n+k , n+k+1$, the numbers you want are $n+1, n+2, \dots, n+k$, which are $k$ in number = $n+k+1 - n - 1$ = larger - smaller - 1.
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0@Arturo: Agree with that :-) – 2010-12-08
The number between $a,b$ is $(a
- Including $a,b$ them self: $b-a+1$
- Excluding $a,b$ :$b-a-1$
HINT $\ $ The problem admits an obvious shift symmetry, e.g. considering the example that you gave, a shift of $-2\:$ to $[3, 6]$ yields $[1,4]$, which clearly has $4$ integers. Innate symmetries should always be investigated since they may play a key role in simplifying the search for a solution. Moreover, it's best to learn these symmetry-based problem solving techniques for simple problems like this, since you may not be able to see the forest for the trees in much more complex problems.
The bigger number minus the smaller number minus 1. Or if $b$ is the bigger number, $s$ the smaller. We have: $b - s - 1$