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Given Length and Sum of Digits...
By damn_me, 10 years ago, In English

I was trying solving this problem http://codeforces.me/problemset/problem/489/C. Thinkinh in dp manner, I thought i'll need a table that can tell me the number of i digits that sum to particular j. Then if I want to calculate dp[i][j], then my subproblems will be dp[i-1][sum-j] and so on. However, I am unable to implement this idea.

Please help with this. Also, I coded the brute force way: http://ideone.com/83pdfJ but this gives TLE. Where to optimize in it?

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10 years ago, # |
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Mine code

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    10 years ago, # ^ |
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    Yeah, we can do that but I wanted to go for DP manner. Can you please explain that??

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      10 years ago, # ^ |
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      I think it would be more difficult to solve this problem with DP.

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10 years ago, # |
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You can solve it by using string. Submission: 8731134.

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10 years ago, # |
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It can be solved more easy with greedy algorithm.

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10 years ago, # |
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you can use dp but it is not simple
mindp[i][j] = i digit j sum minimum number witch leading zeros are NOT allowed 
mindp2[i][j] = i digit j sum minimum number witch leading zeros are allowed

now mindp[i][j] can update from mindp2[i-1][j-k] where k = [1,9]
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    10 years ago, # ^ |
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    Why we are thinking about the leading zeroes? What I thought is for k=1, the only digits are 1 to 9. For k>=0, i'll modify dp[k][j] which denotes k digit with j sum. j<=900 i.e. all possible sum. I'll mark dp[i][1...9] as boolean true or 1. Now, inserting one other for loops which iterate from 0 to 9 (as m) , i'll check if dp[k-1][j-m] is true, if it is, i'll make dp[k][j] as true. Similarly filling whole of the table and then iterating it recursively, I'll get the number. However, this is inefficient complexity wise :P

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      10 years ago, # ^ |
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      but i think your approch without considering leading zeroes loos at 100001 because 00001 is false :/

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8 years ago, # |
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You can use dp approach in a tabular form but only till 4 test cases will be passed but in the 5 test case the number given is 100 digit long which by no way can be stored in the table. Anyways this solution csn be used for dp tabular solution-http://codeforces.me/contest/489/submission/23355950

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