7406

Find the length of the longest increasing subsequence using only one auxiliary recursion function

Question:

I need to find the length of the longest monotonically increasing subsequence using only a single recursion function. For example given an arr={45 1 21 3 33 6 53 9 18} it need to give back 5. I have started to write the code but i'm stuck, and i don't know how to find out which of the calls gives the maximum length.

The function longestSet is my auxiliary function i can use any variables i want but it have to be called from the function max_set.

void question3(int question) { int *arr, size; printf("enter the array size\n"); scanf("%d", &size); arr=(int*)malloc(size*sizeof(int)); fillArr(arr, size-1); max_set(arr, size); free(arr); } void max_set(int arr[], int size) { int i=0, finelmax=0, count=0,longrising; longrising=longestSet(arr,size,i,finelmax,count); printf("the length of the longest risind set is: %d", longrising); } int longestSet(int arr[], int size, int i, int finelmax, int count) { if(i==size) return count; if(arr[i]>=finelmax) { finelmax=arr[i]; return longestSet(arr,size,i+1,finelmax,count+1); } return longestSet(arr,size,i+1,finelmax,count); }

Answer1:

Something like this:

int longestSet(int arr[], int size, int i, int finelmax, int count) { if(i==size) return count; int length1 = longestSet(arr, size, i + 1, finelmax, count); if(arr[i] > finelmax) { int length2 = longestSet(arr, size, i + 1, arr[i], count + 1); if(length2 > length1) length1 = length2; } return length1; }

What this basically does is at each point compare if it would be better to include the current number or skip it. Also will be pretty slow - you can for example add memoization to it to improve, but I'm guessing that's not part of the homework?

Answer2:

I'm giving here the full code with a single recursion function you asked. Unfortunately it's in java but your purpose would be solved as the function used for recursion is almost same.

import java.util.StringTokenizer; import java.io.BufferedReader; import java.io.IOException; import java.io.InputStreamReader; class longestSubSequence{ public static void main (String [] args)throws IOException{ new longestSubSequence().run(); } int max = -1; int index = 1; int [] array; private void run() throws IOException{ array = new int [50]; BufferedReader br = new BufferedReader(new InputStreamReader(System.in)); // Input your array StringTokenizer st = new StringTokenizer (br.readLine()); array[0] = -1; while (st.hasMoreTokens()){ array[index++] = Integer.parseInt(st.nextToken()); } index--; dfs (0, 0); System.out.println(max);// Prints the maximum length } private void dfs (int curr, int length){ if (length > max )max = length; if (curr >= index) return ; for (int I=curr+1;I <= index; I++){ if (array[I] >= array[curr]){ dfs (I, length+1); } } } }

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