# Recent questions tagged algorithm-design

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Hi Experts, I have been practicing Master Theorem since Yesterday as I am recently involved in algorithm course. I have found a hard the following problem whether the Master Theorem is applicable or it violates rules. if yes then kindly elaborate for better understanding…. Apology for English grammar T(n) = 2^1.534T( n 2 ) + 2^ 2n
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Define $R_n$ to be the maximum amount earned by cutting a rod of length $n$ meters into one or more pieces of integer length and selling them. For $i>0$, let $p[i]$ denote the selling price of a rod whose length is $i$ meters. Consider the array of prices: ... $R_7$? $R_7=18$ $R_7=19$ $R_7$ is achieved by three different solutions $R_7$ cannot be achieved by a solution consisting of three pieces
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Given two arrays of numbers $a_{1},...,a_{n}$ and $b_{1},...,b_{n}$ where each number is $0$ or $1$, the fastest algorithm to find the largest span $(i, j)$ such that $a_{i}+a_{i+1}+\dots+a_{j}=b_{i}+b_{i+1}+\dots+b_{j}$ or report that there is ... $\Theta (n)$ time and space Takes $O(\sqrt n)$ time only if the sum of the $2n$ elements is an even number
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Consider a sequence of $14$ elements: $A=[-5, -10, 6, 3, -1, -2, 13, 4, -9, -1, 4, 12, -3, 0]$. The sequence sum $S(i,j) = \Sigma_{k=i}^j A[k]$. Determine the maximum of $S(i,j)$, where $0 \leq i \leq j <14$. (Divide and conquer approach may be used.) Answer: ___________
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An element in an array $X$ is called a leader if it is greater than all elements to the right of it in $X$. The best algorithm to find all leaders in an array solves it in linear time using a left to right pass of the array solves it in linear time using a right to left pass of the array solves it using divide and conquer in time $\Theta (n\log n)$ solves it in time $\Theta( n^2)$
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There are $5$ bags labeled $1$ to $5$. All the coins in a given bag have the same weight. Some bags have coins of weight $10$ gm, others have coins of weight $11$ gm. I pick $1, 2, 4, 8, 16$ coins respectively from bags $1$ to $5$ Their total weight comes out to $323$ gm. Then the product of the labels of the bags having $11$ gm coins is ___.
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Let $T$ be a Depth First Tree of a undirected graph $G$. An array $P$ indexed by the vertices of $G$ is given. $P[V]$ is the parent of vertex $V$, in $T$. Parent of the root is the root itself. Give a method for finding and printing the ... be proportional to the length of the cycle. Describe the algorithm in a PASCAL $(C)$ - like language. Assume that the variables have been suitably declared.
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An array $A$ contains $n$ integers in locations $A, A, \dots A[n-1]$. It is required to shift the elements of the array cyclically to the left by $K$ places, where $1\leq K \leq n-1$. An incomplete algorithm for doing this in linear time, without using another array is given below. Complete ... A[j]:=____; j:=(j+K) mod n; if j<min then min:=j; end; A[(n+i-K)mod n]:=____; i:=______; end;
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