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Problem. You are given an undirected graph G = (V,E) in which the edge weights are highly restricted.
In particular, each edge has a positive integer weight of either {1, 2, . . . ,W}, where W is a constant (independent of the number of edges or vertices). Show that it is possible to compute the single- source shortest paths in such a graph in O(n + m) time, where n = |V | and m = |E|. (Hint: Because W is a constant, a running time of O(W(n + m)) is as good as O(n + m).)
Requirement: algorithm running time needs to be in DIJKstra's running time or better.
Prove the subsequent Boolean expression: (x∨y) ∧ (x∨~y) ∧ (~x∨z) = x∧z Ans: In the following expression, LHS is equal to: (x∨y)∧(x∨ ~y)∧(~x ∨ z) = [x∧(x∨ ~y)] ∨ [y∧(x∨
The Limit : In the earlier section we looked at some problems & in both problems we had a function (slope in the tangent problem case & average rate of change in the rate of chan
Q. How to Add Mixed Numbers? Ans. If you have to add mixed numbers, you might try this method first: First rewrite the mixed number as a whole number plus a fracti
lim n tends to infintiy ( {x} + {2x} + {3x}..... +{nx}/ n2(to the square) )where {X} denotes the fractional part of x? Ans) all no.s are positive or 0. so limit is either positive
INTRODUCTION : When a child of seven isn't able to solve the sum 23+9, what could the reasons be? When she is asked to subtract 9 from 16, why does she write 9 - 16 = 13 ?
An apartment complex contains 250 apartments to rent. If they rent x apartments then their monthly profit is specified by, in dollars,, P ( x
The base of an isosceles triangle and the altitude drawn from one of the congruent sides are equal to 18cm and 15cm, respectively. Find the lengths of the sides of the triangle.
Exponential and Logarithm Equations : In this section we'll learn solving equations along with exponential functions or logarithms in them. We'll begin with equations which invol
Dividing Whole Numbers: Example: Divide 347 by 5. Solution: Beginning from the left of the dividend, the divisor is divided into the
how to reverse positive digit number using mod function
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