You are given a sequence a1,a2,...,an, and a number b. Your task is to find algorithm which counts all pairs (l,r) such that median of sequence a(l),a(l+1),..,a(r) is bigger than b. My solution on exam was O(n^2logn) which used order statistics tree. Other solutions ...
The Twin Primes Conjecture is Π2: for all n, there exists a p > n such that p and p + 2 are prime. To make this a Π1-sentence, we'd need to strengthen the conjecture by including an explicit lower bound—say, that there are at least log log log n twin primes less than n...
What do you mean by " An algorithm taking Theta(n log n) is far preferential since it takes at least n log n (Omega n log n) and no more than n log n (Big O n log n). ", as in, is it the exact complexity of a algorithm as you wrote said at least Omega(nlogn) and at...
The Twin Primes Conjecture is Π2: for all n, there exists a p > n such that p and p + 2 are prime. To make this a Π1-sentence, we'd need to strengthen the conjecture by including an explicit lower bound—say, that there are at least log log log n twin primes less than n...
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As we only had two indicators of family SES, we used a manifest composite variable rather than a latent factor in the model. Use of a manifest variable representing family SES likely underestimated the association with microbiome, as it included measurement error. Using maternal and paternal ...