FAQ Database Discussion Community

Is my recurrence relation right for subset sum?

Is this recurrence relation correct for the subset sum problem? Statement: Print Yes or No depending on whether there is a subset of the given array a[ ] which sums up to a given number n. dp[i][j] = true, if 0 to j elements in array sum up to i...

Maximum number of distinct inversions in an array

Given an array A of n integers, we say that a pair of indices i<j∈[n] is an inversion in A if A[i]>A[j]. What is the maximum number of distinct inversions that A can have? Is it a) n - 1 b) n c) n(n−1)/2 d) n^2 e) n(n−1)(2n−1)/6 ...

Proving a tricky Recurrence Relation for the k + 1 case

I am absolutely stumped on this one. T(n) = { 3, if n = 2 || T(n - 1) + (n/4), if n > 2 Prove by induction that T(n) = (n^2 + n + 18) / 8 [V n >= 2] I know how to execute a proof by...

Solving recurrence equation without the Master's Theorem

So, on a previous exam, I was asked to solve the following recurrence equation without using the Master Theorem: T(n)= 9T(n/3) + n^2 Unfortunately, I couldn't figure it out on the exam, so I used solved it using the Master's Theorem just so I could know the answer (but, of...

Median of median algorithm recurrence relation

I know that the linear select (median of medians algorithm) recurrence equation is as follows: T(n) <= an + T(n/5) + T(7n/10) But where do these terms come from? I've been trying to understand, but I'm extremely confused. Can anyone please shed some light?...

What is the Difference between T(n) (reccurence relations), Big O and Big Theta

I am wondering about this for my Algorithm class. It seems to be unclear what the difference is between BigO, Big Theta, and Recurrence relations (T(n)) For example: T(n) = 4T(n/3) + O(1)

partition recurrence relation understanding

Determine if there is a subset of S that sums to floor(N/2) floor. Given S = {3,1,1,2,2,1}, a valid solution to the partition problem is the two sets S1 = {1,1,1,2} and S2 = {2,3}. Let: p(i, j) be True if a subset of {x1, ..., xj} sums to i...

Recurrence relation of an algorithm

void doSomething(int *a, int left, int right){ if (left == right){ for (int j = 0; i < right; ++j) cout << a[j]; cout << endl; return; } for (int i = left; i < right; ++i){ std::swap(a[left], a[i]); doSomething(a, left + 1, right); std::swap(a[left], a[i]); } } "Derive the...

Solving a complex recurrence relation for the Traveling Salesman

I need to solve the exact time complexity for the brute force version of the Traveling Salesman using a recurrence relation. I've worked out the recurrence relation to be as follows: T(n)=T(n-1)*(n-1)+1 But I'm having trouble reducing that that to a closed form of the function, and thus get the...

coin change recurrence solution

Given a value N, if we want to make change for N cents, and we have infinite supply of each of S = { S1, S2, .. , Sm} valued coins, how many ways can we make the change? The order of coins doesn’t matter.There is additional restriction though: you...

Resolution easy recurrence equation

I have to find the recurrence equation of following function. public static boolean f(int[] a) { return fr(a, 0); } private static boolean fr(int[] a, int i) { int n = a.length; if(i >= n-1) return true; else if(a[i] > a[i+1]) return false; else return fr(a, i+1); } I think...