What Is Space Complexity Of The Following Dynamic Programming #2186

What is space complexity of the following dynamic programming implementation of the dice throw problem where f is the number of faces, n is the number of dice and s is the sum to be found?</p> <pre><code class="language-c"> #include<stdio.h> int get_ways(int num_of_dice, int num_of_faces, int S) { int arr[num_of_dice + 1][S + 1]; int dice, face, sm; for(dice = 0; dice <= num_of_dice; dice++) for(sm = 0; sm <= S; sm++) arr[dice][sm] = 0; for(sm = 1; sm <= S; sm++) arr[1][sm] = 1; for(dice = 2; dice <= num_of_dice; dice++) { for(sm = 1; sm <= S; sm++) { for(face = 1; face <= num_of_faces && face < sm; face++) arr[dice][sm] += arr[dice - 1][sm - face]; } } return arr[num_of_dice][S]; } int main() { int num_of_dice = 3, num_of_faces = 4, sum = 6; int ans = get_ways(num_of_dice, num_of_faces, sum); printf("%d",ans); return 0; }</code></pre>

This multiple choice question (MCQ) is related to the book/course gs gs122 Data Communication and Computer Network. It can also be found in gs gs122 Dynamic Programming - Dice Throw Problem - Quiz No.1.

 #include<stdio.h> int get_ways(int num_of_dice, int num_of_faces, int S) { int arr[num_of_dice + 1][S + 1]; int dice, face, sm; for(dice = 0; dice <= num_of_dice; dice++) for(sm = 0; sm <= S; sm++) arr[dice][sm] = 0; for(sm = 1; sm <= S; sm++) arr[1][sm] = 1; for(dice = 2; dice <= num_of_dice; dice++) { for(sm = 1; sm <= S; sm++) { for(face = 1; face <= num_of_faces && face < sm; face++) arr[dice][sm] += arr[dice - 1][sm - face]; } } return arr[num_of_dice][S]; } int main() { int num_of_dice = 3, num_of_faces = 4, sum = 6; int ans = get_ways(num_of_dice, num_of_faces, sum); printf("%d",ans); return 0; }