new question added

Author: arorarahul

README.md

@@ -359,7 +359,8 @@ i+given number of times to see if thats true or not.
 - [Travelling salesman problem](/dynamic-programming/question6.c)
 - [All pair shortest path algorithm](/dynamic-programming/question7.c)
 - [Find the maximum sum sub array](/dynamic-programming/question8.c)
-- [Find the maximum sum sub array](/dynamic-programming/question9.c)
+- [Find the max sum increasing sub sequence](/dynamic-programming/question9.c)
+- [Find the longest subsequence in an array such that elements are consecutive](/dynamic-programming/question10.c)
 
 ## Some important concepts to solve algos better
 

dynamic-programming/a.exe

@@ -0,0 +1,71 @@
+/*
+Find the longest subsequence in an array such that elements are consecutive
+
+Eg picking 10 from 2nd index 11 from 10th index and 12 from 15th index
+but 10 11 12 are consecutive as natural numbers
+
+
+METHOD1:
+Sort the array, then traverse it once to find the longest subsequence which contains consecutive 
+elements
+
+Time complexity: O(nlogn)
+Space complexity: O(1)
+
+METHOD2:
+Maintain a hash table with elements that are present marked as 1. Now scan the array again and
+for the first number see all the consecutive numbers lesser than that to find the starting value
+of the sequence. Once found, see numbers greater than that, that are consecutive to find out
+end of sub sequence. Once numbers are visited or made part of a subsequence, mark them as processed
+by maintaining a flag. Repeat this for all numbers and output a longest subsequence.
+
+Time complexity: O(n)
+//as in worst case all elements will be examined twice in the second traversal.
+
+Space complexity: O(n)
+*/
+//METHOD1
+#include <stdio.h>
+#include <stdlib.h>
+
+int cmpfunc(const void *a, const void *b){
+	return (*(int *)a - *(int *)b);
+}
+
+void longestSubSeq(int *arr, int size){
+	int i;
+	int start,end=0,length=1;
+	int maxLength = 0;
+	for(i=0;i<size-1;i++){
+		if(arr[i+1] - arr[i] == 1){
+			length++;
+			if(length > maxLength){
+				maxLength = length;
+				end = i;
+			}
+		}else{
+			length = 1;
+		}
+	}
+	end = end + 1;
+	start = end-maxLength+1;
+	printf("max length is %d\n", maxLength);
+	printf("start value is %d\n", start);
+	printf("end value is %d\n", end);
+	//print the subsequence
+	for(i=start;i<=end;i++){
+		printf("%d\n", arr[i]);
+	}
+
+}
+
+int main(){
+	int arr[] = {15,14,10,4,3,11,13,5,6,12,7};
+
+	int size = sizeof(arr)/sizeof(arr[0]);
+
+	qsort(arr,size,sizeof(int),cmpfunc);
+
+	longestSubSeq(arr, size);
+	return 0;
+}