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1. a) Given a digraph G = (V,E), prove that if we add a constant k to the length of every arc coming out from the root node r, the shortest path tree remains the same. Do this by using potentials:
i) Show there is a potential y* for the new costs for which the paths in the tree to each node v have cost y*v, and
ii) explain why this proves it. What is the relationship between the shortest path distances of the modified problem and those of the original problem?
b) Can adding a constant k to the length of every arc coming out from a non-root node produce a change in the shortest path tree? Justify your answer.
tens digit of a 2-digit number is twice its unit digit. If the sum of the digit is 12, find the number.
f(x)= 2e^5x+6 find the domain of f and find x-intercept.
Example 1 Add 4x 4 + 3x 3 - x 2 + x + 6 and -7x 4 - 3x 3 + 8x 2 + 8x - 4 We write them one below the other as shown below.
pi to the ten-thousandths
Sample of Timing and Cost
a cheeseburger cost $6.39 more than a burger of $2.29, what is the difference?
all properties, formulas of infinite series
what is the answer
Which expression below is equal to 5? The correct order of operations must be used here. PEMDAS tells you in which you should do the operations in the subsequent order: Pare
If a pair of dice is thrown and X denotes the sum of the numbers on them. Find the probability distribution of X.Also find the expectation of X. SOLUTION: In a singl
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