Ram_Negative's blog

COIN CHANGE

By Ram_Negative, history, 7 years ago, In English

hi how to solve the problem change from the spoj (http://www.spoj.com/problems/TPC07/)

i read concrete mathematics chapter 7 about coin change. but i can't able to understand can anybody help me to get idea about solving this problem ?

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7 years ago, # |
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This is a dynamic programming problem. First learn something about it, then approach this problem

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    7 years ago, # ^ |
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    The upper limit of n is quite large, where 1 ≤ n ≤ 1000000000. How to cater for this with DP?

    Probably there is a more general formula?

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    7 years ago, # ^ |
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    Well the idea is for dp, but you need to use matrices to run it fast, in time (50 is the maximal value of a coin).

    I can explain more if you want.

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7 years ago, # |
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It can be solved in O(1).

We want to count the number of solutions of x1 + 5x2 + 10x3 + 25x4 + 50x5 = N.

x1 must be congruent with n%5, so is equivalent to count the number of solutions of x1 + x2 + 2x3 + 5x4 + 10x5 = ⌊ N / 5⌋ = M

Let's suppose (i.e xi = 5ai + ri), for i ≤ 3.

We can brute force all possibilities of ri, now we have to count the solutions of

a1 + a2 + 2a3 + x4 + 2x5 = ⌊ (M - r1 - r2 - 2r3) / 5⌋ = P

Grouping, (a1 + a2 + x4) + 2(a3 + x5) = P which can be solved by

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