Kattis - Generalized Recursive Functions WA - algorithm

Question

I have been desperately stuck on this question on Kattis here. The basic idea is that you are given a general formula for a valid two variable recursive function and then given that formula you are to evaluate the function of this function at various inputs. I have trawled through this question for over an hour and I was wondering if anyone could point me in the right direction (or give a counter-example) of why my answer is wrong. The code I used which got me a Wrong Answer verdict is shown below.
#include<bits/stdc++.h>
using namespace std;
long long dp[105][105];
int a[25];
int b[25];
long long rec(int x_in, int y_in, int coeffs, long long c) {
if(dp[x_in][y_in]!=-1){
return dp[x_in][y_in];
}
else {
long long ans = c;
for(int i=0; i<coeffs; ++i) {
int x_cell = max(0, x_in-a[i]);
int y_cell = max(0, y_in-b[i]);
ans+=rec(x_cell, y_cell, coeffs, c);
}
dp[x_in][y_in] = ans;
return dp[x_in][y_in];
}
}
int main() {
int n;
scanf("%d", &n);
string ex;
getline(cin, ex);
for(int caseno=0; caseno<n; ++caseno) {
memset(dp, -1, sizeof(dp));
if(caseno>0) printf("\n");
string coeffs_list;
getline(cin, coeffs_list);
int pairs = 0;
long long c, d;
char * dup = strdup(coeffs_list.c_str());
char * token = strtok(dup, " ") ;
while(token != NULL){
a[pairs] = atoi(token);
token = strtok(NULL, " ") ;
b[pairs] = atoi(token);
token = strtok(NULL, " ") ;
pairs++;
}
free(dup);
c= (long long) a[pairs-1];
d = (long long) b[pairs-1];
pairs--;
dp[0][0] = d;
for(int i=1; i<105; ++i) {dp[0][i] = d; dp[i][0]=d;}
string inputs;
getline(cin, inputs);
int x_i, y_i;
char * dup2 = strdup(inputs.c_str());
char * token2 = strtok(dup2, " ") ;
while(token2 != NULL){
x_i = atoi(token2);
token2 = strtok(NULL, " ") ;
y_i = atoi(token2);
token2 = strtok(NULL, " ") ;
printf("%lld\n", rec(x_i, y_i, pairs, c));
}
free(dup2);
}
}
As you can see the basic idea of what i did was to construct a dp table and evaluate the function accordingly. Thank you in advance for anyone that could help me over here.

Answer 1

The function can grow very fast, thus overflow a 64bit integer (you can check this by using assert(rec(...) >= 0) (not guaranteed but likely to fail for an overflow)). Use a custom BigInteger implementation or switch to Java/Python.
e.g. for n=20, a_i=1, b_i=0: f(x,y)=20*f(x-1,y)+c = O(20^x*(c+d))
This is also indicated by most solutions under stats using Java: https://open.kattis.com/problems/generalizedrecursivefunctions/statistics https://baylor.kattis.com/problems/generalizedrecursivefunctions/statistics