new question added

README.md

@@ -166,7 +166,7 @@ sometimes, multiple variables can be used.
 is known.
 - For problems involving subsequences, we can break them down to smaller problems. Specifically for 
 linear array, array of length 1 less than total can be taken and a pattern can be found for dynamic programming to make recursive equations. 
-
+- Sometimes results of two DP solutions can be merged using some algo to find the final result.
 
 # Topic0: Programming Questions
 
@@ -377,6 +377,7 @@ linear array, array of length 1 less than total can be taken and a pattern can b
 - [Find kth ugly number](/dynamic-programming/question12.c)
 - [Find the longest increasing subsequence](/dynamic-programming/question13.c)
 - [Find the longest decreasing subsequence](/dynamic-programming/question14.c)
+- [Perfect hill longest subsequence](/dynamic-programming/question15.c)
 
 
 ## Some important concepts to solve algos better

dynamic-programming/question15.c

@@ -0,0 +1,93 @@
+/*
+Perfect hill longest subsequence
+
+Longest subsequence of length 2k+1 where the first k+1 are strictly increasing, and last k+1 are strictly 
+decreasing.
+
+METHOD:
+Here we need to find the longest increasing sub sequence for the given array as did earlier.
+We will store it in an array. In a separate array we will find longest decreasing sub sequence.
+
+Then we will traverse both of these arrays to find the longest perfect hill sequence.
+If for a number longest increasing sequence (from left) is 3 and longest decreasing sequence 
+towards right is 5. that means for a perfect hill sequence numbers need to be balanced on both the sides.
+There we take the min of the two and subtract 1. Multiply the number with 2 and add 1. That will be the
+size of perfect hill sequence. The maximum one will be the answer
+
+Time complexity: O(n^2) + O(n)  == O(n^2) only
+//to compute LIS and LDS, then its just traversing once
+
+Space complexity: O(n) //to store the arrays
+*/
+#include <stdio.h>
+#include <stdlib.h>
+
+int findMin(int a, int b){
+	return (a<b)?a:b;
+}
+
+void findLis(int *arr, int *lis, int size){
+	int i,j;
+	lis[0] = 1;
+	for(i=1;i<size;i++){
+		int max = 1;
+		for(j=i-1;j>=0;j--){
+			int key = 1;
+			if(arr[i] > arr[j]){
+				key = key + lis[j];
+				if(max < key){
+					max = key;
+				}
+			}
+		}
+		lis[i] = max;
+	}
+}
+
+void findLds(int *arr, int *lds, int size){
+	int i,j;
+	lds[size-1] = 1;
+	for(i=size-2;i>=0;i--){
+		int max = 1;
+		for(j=i+1;j<size;j++){
+			int key = 1;
+			if(arr[i] > arr[j]){
+				key = key + lds[j];
+				if(max < key){
+					max = key;
+				}
+			}
+		}
+		lds[i] = max;
+	}
+}
+
+int computePHS(int *arr, int *lis, int *lds, int size){
+
+	findLis(arr,lis,size);
+	findLds(arr,lds,size);
+
+	int i;
+	int max = 1;
+	for(i=0;i<size;i++){
+		int len = (findMin(lis[i],lds[i])-1)*2 + 1;
+		if(max < len){
+			max = len;
+		}
+	}
+	return max;
+}
+
+int main(){
+	int arr[] = {10,15,16,9,4,3,11,1};
+	int size = sizeof(arr)/sizeof(arr[0]);
+
+	int *lis = (int *)malloc(sizeof(int)*size);
+	int *lds = (int *)malloc(sizeof(int)*size);
+
+	int max = computePHS(arr,lis, lds,size);
+
+	printf("max length of perfect hill sequence is %d\n", max);
+
+	return 0;
+}

nextquestions.md

@@ -82,4 +82,5 @@ TODO:
 - DP question6 to be done
 - DP question7 to be done
 - DP question11 (method1 naive) to be done
-- DP question13 and 14(printing the subsequence to be done)
+- DP question13 and 14(printing the subsequence to be done)
+- https://gsamaras.wordpress.com/code/caution-when-reading-char-with-scanf-c/