What Is The Space Complexity Of The Following Dynamic #2017

What is the space complexity of the following dynamic programming implementation used to find the length of the longest increasing subsequence?</p> <pre><code class="language-c"> #include<stdio.h> int longest_inc_sub(int *arr, int len) { int i, j, tmp_max; int LIS[len]; // array to store the lengths of the longest increasing subsequence LIS[0]=1; for(i = 1; i < len; i++) { tmp_max = 0; for(j = 0; j < i; j++) { if(arr[j] < arr[i]) { if(LIS[j] > tmp_max) tmp_max = LIS[j]; } } LIS[i] = tmp_max + 1; } int max = LIS[0]; for(i = 0; i < len; i++) if(LIS[i] > max) max = LIS[i]; return max; } int main() { int arr[] = {10,22,9,33,21,50,41,60,80}, len = 9; int ans = longest_inc_sub(arr, len); 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 - Longest Increasing Subsequence - Quiz No.1.

 #include<stdio.h> int longest_inc_sub(int *arr, int len) { int i, j, tmp_max; int LIS[len];  // array to store the lengths of the longest increasing subsequence LIS[0]=1; for(i = 1; i < len; i++) { tmp_max = 0; for(j = 0; j < i; j++) { if(arr[j] < arr[i]) { if(LIS[j] > tmp_max) tmp_max = LIS[j]; } } LIS[i] = tmp_max + 1; } int max = LIS[0]; for(i = 0; i < len; i++) if(LIS[i] > max) max = LIS[i]; return max; } int main() { int arr[] = {10,22,9,33,21,50,41,60,80}, len = 9; int ans = longest_inc_sub(arr, len); printf("%d",ans); return 0; }