如何修复超过时间限制

Question

Hi the given code is here

int a, b, c, d, e, f;
int fn( int n ) {
    if( n == 0 ) return a;
    if( n == 1 ) return b;
    if( n == 2 ) return c;
    if( n == 3 ) return d;
    if( n == 4 ) return e;
    if( n == 5 ) return f;
    return( fn(n-1) + fn(n-2) + fn(n-3) + fn(n-4) + fn(n-5) + fn(n-6) );
}
int main() {
    int n, caseno = 0, cases;
    scanf("%d", &cases);
    while( cases-- ) {
        scanf("%d %d %d %d %d %d %d", &a, &b, &c, &d, &e, &f, &n);
        printf("Case %d: %d\n", ++caseno, fn(n) % 10000007);
    }
    return 0;
}

It has two problems. One is integer overflow . And another is Time Limit Exceeded . I fixed the integer overflow using long int. But problem is with time. When I submit the code, the online judge shows Time Limit Exceeded . Please help me to fix this problem.

Answer 1

This looks like a pretty standard dynamic programming problem, and the key is memoizing your function. Since this is a problem, I won't provide any code, but I will explain what you have to do. You should maintain an array of values, and before returning from your function you update the value in the array with the return value. At the start of the function, you check if that array has the return value already, and if it does, then you can just return that value.

Read more about memoization here .

Answer 2

Your approach has an exponential time complexity and is far from ideal. The good news is that there is a simple and easy fix.

What you can do is simply create an array whose size is the max possible value of n . I presume it is probably something like 10^5 , as is the standard for such problems.

Let us call this array ans[] . Set the first 6 values of ans[] manually and for the rest, run a loop which does something like this:

ans[i] = (ans[i-1] + ans[i-2] + ans[i-3] + ans[i-4] + ans[i-5] + ans[i-6]) % 1000000007

Now, for each case, you simply need to print ans[n] as your answer. (or ans[n-1] depending upon how you've stored the elements.

On a separate note, you may want to check the number with which you're taking the modulo. It is supposed to be 10^9 + 7 , yours is missing two 0s.