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Greedy Algorithm--Algorithms

Largest Number:

  Find max digit
  Append it to the number
  Remove it from the list of digits

  Repeat while there are digits in the list 

car fueling:

  Refill at the the closest gas station

  Refill at the farthest reachable gas station

  Go until there is no fuel 

MinRefills(x

,n,L)

numRefills 0,currentRefill0

while currentRefilln:

  lastRe ll currentRe ll

  while (currentRefillnand x[currentRefill+1]x[lastRefill]L):

      currentRefill currentRefill+1

  if currentRefill==lastRefill:

        return IMPOSSIBLE

  if currentRefilln:

        numRefills numRefills

+1

return numRefills

O(n)

For unsorted data, Sort in O(n log n) + greedy in O(n) 

Greedy Algorithm

While knapsack is not fullChoose item i with maximumvi/wi

If item fits into knapsack, take all of it

Otherwise take so much as to fill the knapsack

Return total value and amounts taken 

Knapsack(W,w1,v1,...,wn,vn)

A [0,0,...,0],V0

repeat ntimes:

  if W= 0:

    return (V,A)

  select iwith wi>0and maxvi/Wj

  a min(wi,W)

  V V +a vi/wi

  wiwia,A[i]A[i]+a,WWa

return (V,A)


Better:

Knapsack(W,w1,v1,...,wn,vn)

A [0,0,...,0],V0

for ifrom 1to n:

  if W= 0:

    return (V,A)

  a min(wi,W)

  V V +a vi/wi

  wiwia,A[i]A[i]+a,WWa

return (V,A)