What Is The Space Complexity Of The Following Dynamic #2063

What is the space complexity of the following dynamic programming implementation of the matrix chain problem?</p> <pre><code class="language-c"> #include<stdio.h> #include<limits.h> int mat_chain_multiplication(int *mat, int n) { int arr[n][n]; int i,k,row,col,len; for(i=1;i<n;i++) arr[i][i] = 0; for(len = 2; len < n; len++) { for(row = 1; row <= n - len + 1; row++) { col = row + len - 1; arr[row][col] = INT_MAX; for(k = row; k <= col - 1; k++) { int tmp = arr[row][k] + arr[k + 1][col] + mat[row - 1] * mat[k] * mat[col]; if(tmp < arr[row][col]) arr[row][col] = tmp; } } } return arr[1][n - 1]; } int main() { int mat[6] = {20,5,30,10,40}; int ans = mat_chain_multiplication(mat,5); 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 - Matrix-chain Multiplication - Quiz No.1.

 #include<stdio.h> #include<limits.h> int mat_chain_multiplication(int *mat, int n) { int arr[n][n]; int i,k,row,col,len; for(i=1;i<n;i++) arr[i][i] = 0; for(len = 2; len < n; len++) { for(row = 1; row <= n - len + 1; row++) { col = row + len - 1; arr[row][col] = INT_MAX; for(k = row; k <= col - 1; k++) { int tmp = arr[row][k] + arr[k + 1][col] + mat[row - 1] * mat[k] * mat[col]; if(tmp < arr[row][col]) arr[row][col] = tmp; } } } return arr[1][n - 1]; } int main() { int mat[6] = {20,5,30,10,40}; int ans = mat_chain_multiplication(mat,5); printf("%d",ans); return 0; }