Amazon Interview Report
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/*- xankar May 12, 2016 in United States
Prison cell question
In a kingdom there are prison cells (numbered 1 to P) built to form a straight line segment. Cells number i and i+1 are adjacent, and prisoners in adjacent cells are called "neighbors." A wall with a window separates adjacent cells, and neighbors can communicate through that window.
All prisoners live in peace until a prisoner is released. When that happens, the released prisoner's neighbors find out, and each communicates this to his other neighbor. That prisoner passes it on to his other neighbor, and so on until they reach a prisoner with no other neighbor (because he is in cell 1, or in cell P, or the other adjacent cell is empty). A prisoner who discovers that another prisoner has been released will angrily break everything in his cell, unless he is bribed with a gold coin. So, after releasing a prisoner in cell A, all prisoners housed on either side of cell A - until cell 1, cell P or an empty cell - need to be bribed.
Assume that each prison cell is initially occupied by exactly one prisoner, and that only one prisoner can be released per day. Given the list of Q prisoners to be released in Q days, find the minimum total number of gold coins needed as bribes if the prisoners may be released in any order.
Note that each bribe only has an effect for one day. If a prisoner who was bribed yesterday hears about another released prisoner today, then he needs to be bribed again.
Task: find the minimum amount of gold we need to bribe the prisoners so that the chosen prisoners can be released without causing cell destruction.
8 cells, 1 prisoner has to be released. The prisoner to be released is the 3rd one.
7 gold coins
20 cells, 3 prisoners to be released: 3, 6 and 14
|1|2| |4|5| |7|8|9|10|11|12|13| |15|16|17|18|19|20|
release prisoner 3: 19 gold coins
release prisoner 6: 16 gold coins
release prisoner 14: 13 gold coins
release 14: 19 gold coins
release 6: 12 gold coins
release 3: 4 gold coins
number of cells
prisoners that need to be released
least number of gold coins we need to give
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