new question added

Author: arorarahul

README.md

@@ -28,6 +28,7 @@ which has to be returned
     - Can maintain a hash Table to solve the algo
     - Can maintain multiple variables to solve the algo
     - Can maintain two pointers to solve the algo
+    - Kabane's algo
 
 ### For Linked Lists: (methods that can be applied)
 - Use multiple variables to not loose track of the linked list and keep moving them ahead in a manner such that various operations can be done on a linked list
@@ -357,7 +358,8 @@ i+given number of times to see if thats true or not.
 - [Find a subset in an array whose sum is w](/dynamic-programming/question5.c)
 - [Travelling salesman problem](/dynamic-programming/question6.c)
 - [All pair shortest path algorithm](/dynamic-programming/question7.c)
-- [Find the maximum sum sub array](/dynamic-programming/question7.c)
+- [Find the maximum sum sub array](/dynamic-programming/question8.c)
+- [Find the maximum sum sub array](/dynamic-programming/question9.c)
 
 ## Some important concepts to solve algos better
 

dynamic-programming/a.exe

@@ -0,0 +1,54 @@
+/*
+Max sum increasing subsequence
+
+In this we need to find a subsequence which is increasing and has the max sum
+
+METHOD:
+We will maintain another array here and for each index this array will have the max sum resulting
+from adding numbers satisfying criteria given in the question by traversing back.
+Each time we keep doing that for all the numbers and then we will have the max sum possible
+
+Time complexity: O(n^2)
+Space complexity: O(n)
+*/
+
+#include <stdio.h>
+#include <stdlib.h>
+
+int getMaxSum(int *arr, int i){
+	int index, sum = 0, maxSum = 0;
+	for(index = i-1; index >=0; index--){
+		if(arr[i] > arr[index]){
+			sum = arr[i]+arr[index];	
+		}
+		if(sum > maxSum){
+			maxSum = sum;
+		}
+	}
+	return maxSum;
+}
+
+void maxIncreaseSubSequence(int *arr, int size){
+	int sum;
+	int cumulative[size];
+	int i, j, index;
+	int maxSum = 0;
+	cumulative[0] = arr[0];
+	for(i=1; i<size;i++){
+		cumulative[i] = getMaxSum(arr,i);
+		if(maxSum < cumulative[i]){
+			maxSum = cumulative[i];
+			index = i;
+		}
+	}	
+	printf("max sum possible in this array is %d at index %d\n", maxSum, index);
+}
+
+int main(){
+	int arr[] = {20,3,1,15,16,2,12,13};
+
+	int size = sizeof(arr)/sizeof(arr[0]);
+
+	maxIncreaseSubSequence(arr, size);
+	return 0;
+}