new question added

Author: arorarahul

README.md

@@ -376,6 +376,8 @@ linear array, array of length 1 less than total can be taken and a pattern can b
 - [Given a binary matrix, find the largest square sub matrix with all 1's](/dynamic-programming/question11.c)
 - [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)
+
 
 ## Some important concepts to solve algos better
 

dynamic-programming/a.exe

@@ -0,0 +1,55 @@
+/*
+Find the longest decreasing sub sequence in a given array
+
+METHOD:
+It remains the same as that of increasing sub sequence (question13), here either we can reverse
+the array and apply that or reverse the loop
+
+Time complexity: O(n^2)
+Space complexity: O(n)
+*/
+#include <stdio.h>
+#include <stdlib.h>
+
+int lonDecreasingSub(int *arr, int size){
+	int *sol = (int *)malloc(sizeof(int)*size);
+	int i,j;
+	int maxLength = 1;
+	sol[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 + sol[j];
+				// printf("key value for i =  %d and j= %d is %d\n",i,j,key);
+				if(key > max){
+					// printf("updating max to %d\n", key);
+					max = key;
+				}
+			}	
+		}
+		// printf("sol of i =  %d is now %d\n", i, max);
+		// printf("==================================\n");
+		sol[i] = max;
+		if(maxLength < sol[i]){
+			maxLength = sol[i];
+		}
+	}
+	return maxLength;
+}
+
+int main(){
+	int *arr, size = 8;
+	arr = (int *)malloc(sizeof(int)*size);
+
+	int i;
+	for(i=0;i<size;i++){
+		printf("Enter the %d element\n", i);
+		scanf("%d",&arr[i]);
+	}
+
+	int len = lonDecreasingSub(arr,size);
+	printf("length of longest decreasing subsequence is %d\n", len);
+	return 0;
+}

dynamic-programming/question14.c

@@ -82,4 +82,4 @@ TODO:
 - DP question6 to be done
 - DP question7 to be done
 - DP question11 (method1 naive) to be done
-- DP question13 (printing the subsequence to be done)
+- DP question13 and 14(printing the subsequence to be done)