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programming twist


Forum Post 6 Answers programming twist

You have N soldiers numbered from 1 to N. Each of your soldiers is either a liar or a truthful person. You have M sets of information about them.Each line contains 3 integers - A, B and C. This means that in the set of soldiers numbered as {A, A+1, A+2, ..., B}, exactly C of them are liars.
There are M lines like the above.
Let L be the total number of your liar soldiers. Since you can't find the exact value of L, you want to find the minimum and maximum value of L.
The first line of the input contains two integers N and M.
Each of next M lines contains three integers - A, B and C (1 <= Ai <= Bi <= n) and (0 <= Ci <= Bi-Ai). where Ai, B i and C i refers to the values of A, B and C in the ith line respectively
N and M are not more than 101, and it is guaranteed the given informations are satisfiable. You can always find a situation that satisfies the given information .
Print two integers Lmin and Lmax to the output.

 - jayram singh October 09, 2012 | Flag |


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One idea:

Seems like an integer linear program.

x_i = 0 if the ith soldier is truthful, x_i = 1 otherwise.

You get m equations of the form x_A + .. + x_B = C

You have to maximize and minimize \sum x_i.

- Loler October 09, 2012 | Flag Reply
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can u plz elaborate it??

- jayram singh October 10, 2012 | Flag
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@jayram: Search the web for what an integer linear program is. All will be clear :-)

- Loler October 10, 2012 | Flag
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Integer linear programming is NP-complete. You can derive approximation methods from it, but this problem asks for an exact solution. You need to use other techniques here.

- Anonymous October 10, 2012 | Flag
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yeah ! i solved it.

- jayram singh October 11, 2012 | Flag
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@Anonymous: This is just an instance of an integer linear program. There are special cases where it is solvable in polynomial time and this might be one of those.

Of course it was just an idea. Not claiming it is a good solution or anything.

- Loler October 11, 2012 | Flag




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