Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 9.3, Problem 2E
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Analysis of Linear search (Worst, Average and Best Cases)#include <stdio.h>// Linearly search x in arr[]. If x is present then return the index,// otherwise return -1int search(int arr[], int n, int x){ int i; for (i=0; i<n; i++) { if (arr[i] == x) return i; } return -1;}
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- What is the runtime complexity of the equilibrating stable matching algorithm? N students apply to M colleges, each of which has S spots, and each college has a rank list, as does each school.arrow_forwardArrange the functions √n (square root of n), 1000log(n), nlog(n), 2n!, 2n, 3n, n2/100000 in increasing order for their Big-O estimate.arrow_forwardT(n)=2T(n-3)+4n T(n)=2T(n/2)+n Find the tightest asymptotic upper bound of T(n)=*** using the recurrence tree method for a and barrow_forward
- Prove the following fact about Huffman codes: If the frequency of symbol i isstrictly larger than the frequency of symbol j, then the length of the codeword for symbol i is less than or equal to the length of the codeword for symbol j.Explain why it is sometimes more efficient to compute the distance from a single source to all other nodes, even if a specific query can only be answered partially.arrow_forwardBacktrack Search Algorithm Using Known Subgroupa group G with the base B=[51, 132,..... k] and a strong generating set S as the input; a subgroup L of G whose members meet the decidable condition P;a powerful generating set with respect to B for the subgroup K = H (P);arrow_forwardRun mergesort for large random arrays, and make an empirical determination of the average length of the other subarray when the first subarray exhausts, as a function of N (the sum of the two subarray sizes for a given merge).arrow_forward
- Suppose that the maximum subarray sum (S) for A[0..k − 1] as well as the maximum sum for a subarray that ends at A[k − 1] (E) are known. Show how to extend S and E to include one more element A[k].arrow_forwardExplain The Rank-Maximal Matching Algorithm .arrow_forwardWhat is the recurrence relation of maximum subarray sum problem by using Divide and Conquer approach CHOOSE ANY ONE OPTION 1.T(n) = 7T(n/2) + n 2.T(n) = 8T(n/2) + n 3.T(n) = 2T(n/2) + n 4.T(n) = T(n/2) + narrow_forward
- The pseudo-code to create the matrix:Procedure AdjacencyMatrix(N): //N represents the number of nodesMatrix[N][N]for i from 1 to N for j from 1 to N Take input -> Matrix[i][j] endforendforWe can also populate the Matrix using this common way: Procedure AdjacencyMatrix(N, E): // N -> number of nodesMatrix[N][E] // E -> number of edgesfor i from 1 to E input -> n1, n2, cost Matrix[n1][n2] = cost Matrix[n2][n1] = costendfor make a Java code implemented using above pseudo-code?arrow_forwardFor σarthm := (0, S, +, ·). Prove PA ⊨ ∀x (x ≠ 0 ⟹ ∃y(x = S(y))). In English, this say that every element other than 0 is a successor.arrow_forwardWrite The Rank-Maximal Matching Algorithm. Let G = (AUP, EU... UE). Initialize G₁ = G₁, and M to any maximum matching in G. For i = 1 tor-1 solve \ the steps, and output.arrow_forward
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