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I was trying to solve uva 11137:

People in Cubeland use cubic coins. Not only the unit of currency is called a cube but also the coins are shaped like cubes and their values are cubes. Coins with values of all cubic numbers up to 9261 (= 213), i.e., coins with the denominations of 1, 8, 27, :::, up to 9261 cubes, are available in Cubeland.

Your task is to count the number of ways to pay a given amount using cubic coins of Cubeland. For example, there are 3 ways to pay 21 cubes: twenty one 1 cube coins, or one 8 cube coin and thirteen 1 cube coins, or two 8 cube coin and five 1 cube coins.

Input Input consists of lines each containing an integer amount to be paid. You may assume that all the amounts are positive and less than 10000.

Output For each of the given amounts to be paid output one line containing a single integer representing the number of ways to pay the given amount using the coins available in Cubeland

But I am having some problems. My code is:

#include <stdio.h>
#include <string.h>
#define max_coin 21
#define max_ammount 10000
int coin[max_coin], make;
unsigned long long int dp[max_coin][max_ammount];

unsigned long long int ways(int i, int ammount)
{
    if(ammount <= 0) return 1;
    if(i >= max_coin-1) return 0;
    if(dp[i][ammount] != -1) return dp[i][ammount];

    unsigned long long int return1 = 0, return2 = 0;
    if(ammount - coin[i] >= 0) return1 = ways(i, ammount-coin[i]);
    return2 = ways(i+1, ammount);

    return dp[i][ammount] = return1 + return2;
}

void make_coins()
{
    int i = 0;
    coin[i] = 1;
    for(i++; i < 21; i++) coin[i] = (i+1)*(i+1)*(i+1);
    return ;
}

int main(void)
{
    memset(dp,-1,sizeof(dp));
    make_coins();
    while(scanf("%d",&make) == 1) printf("%llu\n", ways(0, make));

    return 0;
}

It gives the right output for almost all inputs. But for large inputs like 9999 (the largest), its output doesn't match with the sample. What mistake have I done?

For 9999

  • Accepted output : 440022018293

  • My output : 1935335135

My code may have problem with many other inputs, I don't know; I have tried the udebug example given uva though.

Tangent
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    What's that **cast to `int` doing there**? – Antti Haapala -- Слава Україні Nov 12 '17 at 16:28
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    Here's a chance for you to investigate how to debug programs. You don't show how you check that the answers for test case 10, 21, 77 given by UVA work. You've not shown any code that prints out the combinations found, or that validates the combinations. How do you know that the answers you came up with are correct? Have you explored with some numbers in the 3-digit range, for example? Basically, you are expected to do the work, or come up with a much more specific question than "this doesn't give the right answer". – Jonathan Leffler Nov 12 '17 at 16:28
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    If I remove the cast then at least the result, though wrong, is in same neighbourhood. – Antti Haapala -- Слава Україні Nov 12 '17 at 16:28
  • The casts in `return dp[i][a] = (unsigned long long)ret1 + (unsigned long long)ret2;` are pretty peculiar given that `ret1` and `ret2` are both `unsigned long long int` (aka `unsigned long long`) already. `make` should not be a global variable; it should be local to `main()`. You use 23 when it the maximum number of coin types is 21; why the wasted space? – Jonathan Leffler Nov 12 '17 at 16:30
  • I'd suggest that you first change every single number type to (signed) `long long`, remove all casts and then debug – Antti Haapala -- Слава Україні Nov 12 '17 at 16:34
  • I believe you start running into problems from 9261 upwards. It's an off-by-one error. Beware 'magic numbers' in your code, like 20, 21, 23 (and 10002 is another magic number). You have 3 different magic numbers in use for the same quantity — it isn't surprising you get things wrong. Use a name such as `enum { MAX_CUBE = 21 };` and get on with life. – Jonathan Leffler Nov 12 '17 at 16:39
  • @JonathanLeffler Now I modified the code I didn't understand off-by-one error. Sorry for late – Tangent Dec 01 '17 at 16:43
  • You say the actual answer is 440022018293. If you ask Google what log2 of 440022018293 is, it says 38 point something. The `int` type isn’t defined this way be the C standard, but on almost all modern implementations it’s 32 bits. If you take the lower 32 bits, you’ll get 1935335135. Therefore, you probably have a cast to `int` somewhere. – Daniel H Dec 01 '17 at 16:50

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