chore(CPlusPlus): add kadane for array (#558)

Co-authored-by: Ming Tsai <37890026+ming-tsai@users.noreply.github.com>

algorithms/CPlusPlus/Arrays/Kadane's-Algorithm.cpp

@@ -0,0 +1,82 @@
+/* Maximum contiguous subarray Sum of array brute to optimized all approaches */
+
+#include <bits/stdc++.h>
+using namespace std;
+//example int arr[3]={-1,3,-2};
+/*subarrays are  
+                 -1 
+                 -1 3 
+                 -1 3 -2 
+                  3 
+                  3 -2 
+                 -2 
+                  3
+
+ans=3
+*/
+int max_subarray_sum_method_1(int arr[],int n)
+{
+    int sum,maxi;//declaring variables
+    maxi=INT_MIN;//initializing maxi by minimum value;
+        for(int i=0;i<n;i++)
+        {
+            for(int j=i;j<n;j++)
+            {   sum=0;
+                for(int k=i;k<=j;k++)
+                {
+                 sum+=arr[k];//taking sum of elements from ith position to jth position
+                }
+                maxi=max(maxi,sum);//taking max of our final answer maxi and sum
+            }
+        }
+        return maxi;
+}
+
+//further optimized version by for two loops 
+
+int max_subarray_sum_method_2(int arr[],int n)
+{
+    int sum,maxi;//declaring variables
+    maxi=INT_MIN;//initializing maxi by minimum value;
+        for(int i=0;i<n;i++)
+        {  sum=0;
+            for(int j=i;j<n;j++)
+            {   
+                sum+=arr[j];//as we are just adding an element in our subarray so we can remove the k loop.
+                maxi=max(maxi,sum);//and taking max of maxi and sum 
+            }
+        }
+        return maxi;
+}
+//most optimized version kadane's algo with one for loop
+int max_subarray_sum_method_3(int arr[],int n)
+{
+      int sum,maxi;//declaring variables
+      sum=0,maxi=arr[0];//initializing sum by 0 and maxi by 0th element;
+        for(int i=0;i<n;i++)
+        { 
+            sum+=arr[i];
+            maxi=max(sum,maxi);
+            if(sum<0) sum=0;
+        }
+        return maxi;
+}
+
+int main()
+{
+ int n;
+ cout<<"Enter the size of array"<<endl;
+ cin>>n;
+ int arr[n];
+ for(int i=0;i<n;i++)
+ {  cout<<"Enter "<<i<<"th elements of array"<<endl;
+    cin>>arr[i];
+ }
+ int ans1=max_subarray_sum_method_1(arr,n);//this is brute force approach time complexity=O(n^3) || space complexity=O(1);
+ int ans2=max_subarray_sum_method_2(arr,n);//this is optimized brute force approach time complexity=O(n^2) || space complexity=O(1);
+ int ans3=max_subarray_sum_method_3(arr,n);//this is further optimized approach called "Kadane's Algorithm" time complexity=O(n)|| space complexity=O(1);
+ cout<<"max_subarray_sum:"<<ans1<<endl;
+ cout<<"max_subarray_sum:"<<ans2<<endl;
+ cout<<"max_subarray_sum:"<<ans3<<endl;//print any ans1,ans2,ans3;
+}
+

algorithms/CPlusPlus/README.md

@@ -1,7 +1,6 @@
 # C++
 
 ## Arrays
-
 - [Counting Inversions](Arrays/counting-inversions.cpp)
 - [Dutch Flag Algorithm](Arrays/dutch-flag-algo.cpp)
 - [Left Rotation](Arrays/left-rotation.cpp)
@@ -20,20 +19,16 @@
 - [Segregate 0s and 1s](Arrays/segregate-0-and-1.cpp)
 - [Search insert position](Arrays/search-insert-position.cpp)
 - [Matrix Multiplication](Arrays/matrix-multiplication.cpp)
-- [Smallest Possible Sum](Arrays/smallest-possible-sum.cpp)
+- [Kadane's Algorithm](Arrays/Kadane's-Algorithm.cpp)
 
 ## Dynamic-Programming
-
 - [Longest Common Subsequence](Dynamic-Programming/longest-common-subsequence.cpp)
 - [Longest Common Substring](Dynamic-Programming/longest-common-substring.cpp)
 - [0/1-knapsack](Dynamic-Programming/01-knapsack.cpp)
 - [Matrix chain Multiplication](Dynamic-Programming/matrix-chain-multiplication.cpp)
 - [Edit Distance](Dynamic-Programming/edit-distance.cpp)
-- [Maximum sum rectangle](Dynamic-Programming/maximum-sum-rectangle.cpp)
-- [Coin Change](Dynamic-Programming/coin-change-problem.cpp)
 
 ## Graphs
-
 - [Bellman Ford Algorithm](Graphs/bellman-ford.cpp)
 - [kruskal Algorithm](Graphs/kruskal-algorithm.cpp)
 - [Breadth First Search](Graphs/breadth-first-search.cpp)
@@ -43,11 +38,9 @@
 - [Connected Components](Graphs/total-connected-components.cpp)
 
 ## Multiplication
-
 - [Karatsuba](Multiplication/karatsuba.cpp)
 
 ## Linked Lists
-
 - [All possible insertions](Linked-Lists/all-possible-insertion.cpp)
 - [Singly linked lists](Linked-Lists/singly.cpp)
 - [doubley linked lists](Linked-Lists/doubly.cpp)
@@ -62,7 +55,6 @@
 - [Remove Duplicate in Sorted linked list](Linked-Lists/remove-duplicates-in-sorted-linked-list.cpp)
 
 ## Searching
-
 - [Linear Search](Searching/linear-search.cpp)
 - [Jump Search](Searching/jump-search.cpp)
 - [Binary Search](Searching/binary-search.cpp)
@@ -73,14 +65,12 @@
 - [Exponential Search](Searching/exponential-search.cpp)
 
 ## Stacks
-
 - [Balancing Parenthesis](Stacks/balanced-parenthesis.cpp)
 - [Reversing Stack](Stacks/reverse-stack.cpp)
 - [Stack using Array](Stacks/stack-using-array.cpp)
 - [Infix to postfix expression conversion](Stacks/infix-to-postfix.cpp)
 
 ## Sorting
-
 - [Bubble Sort](Sorting/bubble-sort.cpp)
 - [Insertion Sort](Sorting/insertion-sort.cpp)
 - [Quicksort](Sorting/quick-sort.cpp)
@@ -98,7 +88,6 @@
 - [Cycle Sort](Sorting/cycle-sort.cpp)
 
 ## Strings
-
 - [Rabin-Karp pattern search algo](Strings/rabin-karp.cpp)
 - [All subsequence of a string (Recursion) ](Strings/sequence.cpp)
 - [String reversal](Strings/string-reverse.cpp)
@@ -111,7 +100,6 @@
 - [Boyer Moore pattern search](Strings/Boyer_Moore.cpp)
 
 ## Trees
-
 - [Creating Binary Tree](Trees/build-binary-tree.cpp)
 - [Counting and finding sum of all the nodes in BST](Trees/count-and-sum-of-nodes-in-binary-tree.cpp)
 - [Level Order Traversal](Trees/level-order-traversal.cpp)
@@ -125,10 +113,8 @@
 - [Finding the elements of a tree visible from top view](Trees/Top-View-Of-A-Tree.cpp)
 - [Binary Tree Implementation](Trees/binary-tree-implementation.cpp)
 - [Iterative Segment Tree](Trees/IterativeSegmentTree.cpp)
-- [Fenwick Tree](Trees/Fenwick_Tree.cpp)
 
 # Maths
-
 - [Kaprekar Number](Maths/Kaprekar-number.cpp)
 - [Prime Number](Maths/prime-check.cpp)
 - [Prime Sieve](Maths/prime-sieve.cpp)
@@ -143,7 +129,6 @@
 - [Segmented Sieve](Maths/segmented-sieve-range.cpp)
 
 # Recursion
-
 - [Tower of Hanoi](Recursion/towerofHanoi.cpp)
 - [Factorial](Recursion/factorial.cpp)
 - [Permutation](Recursion/permutation.cpp)
@@ -161,3 +146,4 @@
 - [Array sorted or not](Recursion\array-sorted-or-not.cpp)
 - [Product of two numbers](Recursion\product-of-numbers.cpp)
 - [Product of digits in a number](Recursion\product-of-digits.cpp)
+