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Rus_ich [418]
3 years ago
12

An edge of a flow network is called critical if decreasing the capacity of this edge results in a decrease in the maximum flow.

On input a flow network G, you ran Ford-Fulkerson and computed a maximum flow f.
i. Give an efficient algorithm that finds a critical edge in G.
ii. Give an efficient algorithm that finds every critical edge in G.
Mathematics
1 answer:
OLEGan [10]3 years ago
3 0

Answer:

  1. Begin
  2. find the residual graph of the graph G(V,E) using ford Fulkerson
  3. For each edge u, v in the residual graph such that u, v is not in the residual graph and also not in G
  4. Apply DFS to see if u has no path to v
  5. then return edge (u,v)
  6. else
  7. nothing
  8. end

Step-by-step explanation:

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40% of 125 is what number?
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Solution for 40 is what percent of 125:

40:125*100 =

( 40*100):125 =

4000:125 = 32

Now we have: 40 is what percent of 125 = 32

Question: 40 is what percent of 125?

Percentage solution with steps:

Step 1: We make the assumption that 125 is 100% since it is our output value.

Step 2: We next represent the value we seek with $x$x​.

Step 3: From step 1, it follows that $100\%=125$100%=125​.

Step 4: In the same vein, $x\%=40$x%=40​.

Step 5: This gives us a pair of simple equations:

$100\%=125(1)$100%=125(1)​.

$x\%=40(2)$x%=40(2)​.

Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS
(left hand side) of both equations have the same unit (%); we have

$\frac{100\%}{x\%}=\frac{125}{40}$
100%
x%​=
125
40​​

Step 7: Taking the inverse (or reciprocal) of both sides yields

$\frac{x\%}{100\%}=\frac{40}{125}$
x%
100%​=
40
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$\Rightarrow x=32\%$⇒x=32%​

Therefore, $40$40​ is $32\%$32%​ of $125$125​.
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