Greedy Consider the generalization of the rickety bridge crossing puzzle in which we have n > 1 people whose bridge crossing times are t₁, t2, tn. You may assume that t₁ ≤ t₂ ≤... tn. All the other conditions of the problem remain the same: all begin on the same side of the bridge, at most two people at the time can cross the bridge (and they move with the speed of the slower of the two) and they must carry with them the only flashlight the group has. Design a greedy algorithm for this problem and find how long it will take to cross the bridge by using this algorithm. Find an instance with the smallest number of people for which your greedy algorithm does not yield a minimum crossing time.

Greedy Consider the generalization of the rickety bridge crossing puzzle in which we have n > 1 people whose bridge crossing times are t₁, t2, tn. You may assume that t₁ ≤ t₂ ≤... tn. All the other conditions of the problem remain the same: all begin on the same side of the bridge, at most two people at the time can cross the bridge (and they move with the speed of the slower of the two) and they must carry with them the only flashlight the group has. Design a greedy algorithm for this problem and find how long it will take to cross the bridge by using this algorithm. Find an instance with the smallest number of people for which your greedy algorithm does not yield a minimum crossing time.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Consider the problem of making change for n cents using the fewest number of coins. Assume that we live in a country where coins come in k dierent denominations c1, c2, . . . , ck, such that the coin values are positive integers, k ≥ 1, and c1 = 1, i.e., there are pennies, so there is a solution for every value of n. For example, in case of the US coins, k = 4, c1 = 1, c2 = 5, c3 = 10, c4 = 25, i.e., there are pennies, nickels, dimes, and quarters. To give optimal change in the US for n cents, it is sufficient to pick as many quarters as possible, then as many dimes as possible, then as many nickels as possible, and nally give the rest in pennies. Design a bottom-up (non-recursive) O(nk)-time algorithm that makes change for any set of k different coin denominations. Write down the pseudocode and analyze its running time. Argue why your choice of the array and the order in which you fill in the values is the correct one. Notice how it is a lot easier to analyze the running time of…
Consider the problem of making change for n cents using the fewest number of coins. Assume that we live in a country where coins come in k dierent denominations c1, c2, . . . , ck, such that the coin values are positive integers, k ≥ 1, and c1 = 1, i.e., there are pennies, so there is a solution for every value of n. For example, in case of the US coins, k = 4, c1 = 1, c2 = 5, c3 = 10, c4 = 25, i.e., there are pennies, nickels, dimes, and quarters. To give optimal change in the US for n cents, it is sufficient to pick as many quarters as possible, then as many dimes as possible, then as many nickels as possible, and nally give the rest in pennies. Design a bottom-up (non-recursive) O(nk)-time algorithm that makes change for any set of k different coin denominations. Write down the pseudocode and analyze its running time. Argue why your choice of the array and the order in which you ll in the values is the correct one.
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Subject : calculas Show that: ¬q 1) p→¬q 2) (p∧r)∨s 3) s→(t∨u) 4) ¬t∧¬u where ¬ is denied.
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