chore(CPlusPlus): add kadane for array (#558)
Co-authored-by: Ming Tsai <37890026+ming-tsai@users.noreply.github.com>pull/592/head
MONIKA CHAUHAN
GitHub
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/* Maximum contiguous subarray Sum of array brute to optimized all approaches */
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#include <bits/stdc++.h>
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using namespace std;
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//example int arr[3]={-1,3,-2};
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/*subarrays are
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-1
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-1 3
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-1 3 -2
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3
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3 -2
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-2
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3
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ans=3
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*/
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int max_subarray_sum_method_1(int arr[],int n)
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{
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int sum,maxi;//declaring variables
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maxi=INT_MIN;//initializing maxi by minimum value;
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for(int i=0;i<n;i++)
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{
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for(int j=i;j<n;j++)
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{ sum=0;
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for(int k=i;k<=j;k++)
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{
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sum+=arr[k];//taking sum of elements from ith position to jth position
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}
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maxi=max(maxi,sum);//taking max of our final answer maxi and sum
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}
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}
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return maxi;
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}
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//further optimized version by for two loops
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int max_subarray_sum_method_2(int arr[],int n)
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{
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int sum,maxi;//declaring variables
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maxi=INT_MIN;//initializing maxi by minimum value;
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for(int i=0;i<n;i++)
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{ sum=0;
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for(int j=i;j<n;j++)
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{
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sum+=arr[j];//as we are just adding an element in our subarray so we can remove the k loop.
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maxi=max(maxi,sum);//and taking max of maxi and sum
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}
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}
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return maxi;
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}
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//most optimized version kadane's algo with one for loop
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int max_subarray_sum_method_3(int arr[],int n)
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{
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int sum,maxi;//declaring variables
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sum=0,maxi=arr[0];//initializing sum by 0 and maxi by 0th element;
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for(int i=0;i<n;i++)
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{
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sum+=arr[i];
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maxi=max(sum,maxi);
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if(sum<0) sum=0;
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}
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return maxi;
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}
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int main()
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{
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int n;
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cout<<"Enter the size of array"<<endl;
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cin>>n;
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int arr[n];
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for(int i=0;i<n;i++)
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{ cout<<"Enter "<<i<<"th elements of array"<<endl;
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cin>>arr[i];
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}
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int ans1=max_subarray_sum_method_1(arr,n);//this is brute force approach time complexity=O(n^3) || space complexity=O(1);
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int ans2=max_subarray_sum_method_2(arr,n);//this is optimized brute force approach time complexity=O(n^2) || space complexity=O(1);
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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);
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cout<<"max_subarray_sum:"<<ans1<<endl;
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cout<<"max_subarray_sum:"<<ans2<<endl;
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cout<<"max_subarray_sum:"<<ans3<<endl;//print any ans1,ans2,ans3;
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}
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@ -1,7 +1,6 @@
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# C++
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## Arrays
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- [Counting Inversions](Arrays/counting-inversions.cpp)
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- [Dutch Flag Algorithm](Arrays/dutch-flag-algo.cpp)
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- [Left Rotation](Arrays/left-rotation.cpp)
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@ -20,20 +19,16 @@
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- [Segregate 0s and 1s](Arrays/segregate-0-and-1.cpp)
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- [Search insert position](Arrays/search-insert-position.cpp)
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- [Matrix Multiplication](Arrays/matrix-multiplication.cpp)
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- [Smallest Possible Sum](Arrays/smallest-possible-sum.cpp)
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- [Kadane's Algorithm](Arrays/Kadane's-Algorithm.cpp)
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## Dynamic-Programming
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- [Longest Common Subsequence](Dynamic-Programming/longest-common-subsequence.cpp)
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- [Longest Common Substring](Dynamic-Programming/longest-common-substring.cpp)
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- [0/1-knapsack](Dynamic-Programming/01-knapsack.cpp)
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- [Matrix chain Multiplication](Dynamic-Programming/matrix-chain-multiplication.cpp)
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- [Edit Distance](Dynamic-Programming/edit-distance.cpp)
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- [Maximum sum rectangle](Dynamic-Programming/maximum-sum-rectangle.cpp)
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- [Coin Change](Dynamic-Programming/coin-change-problem.cpp)
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## Graphs
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- [Bellman Ford Algorithm](Graphs/bellman-ford.cpp)
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- [kruskal Algorithm](Graphs/kruskal-algorithm.cpp)
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- [Breadth First Search](Graphs/breadth-first-search.cpp)
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@ -43,11 +38,9 @@
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- [Connected Components](Graphs/total-connected-components.cpp)
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## Multiplication
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- [Karatsuba](Multiplication/karatsuba.cpp)
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## Linked Lists
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- [All possible insertions](Linked-Lists/all-possible-insertion.cpp)
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- [Singly linked lists](Linked-Lists/singly.cpp)
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- [doubley linked lists](Linked-Lists/doubly.cpp)
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@ -62,7 +55,6 @@
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- [Remove Duplicate in Sorted linked list](Linked-Lists/remove-duplicates-in-sorted-linked-list.cpp)
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## Searching
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- [Linear Search](Searching/linear-search.cpp)
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- [Jump Search](Searching/jump-search.cpp)
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- [Binary Search](Searching/binary-search.cpp)
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@ -73,14 +65,12 @@
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- [Exponential Search](Searching/exponential-search.cpp)
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## Stacks
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- [Balancing Parenthesis](Stacks/balanced-parenthesis.cpp)
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- [Reversing Stack](Stacks/reverse-stack.cpp)
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- [Stack using Array](Stacks/stack-using-array.cpp)
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- [Infix to postfix expression conversion](Stacks/infix-to-postfix.cpp)
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## Sorting
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- [Bubble Sort](Sorting/bubble-sort.cpp)
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- [Insertion Sort](Sorting/insertion-sort.cpp)
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- [Quicksort](Sorting/quick-sort.cpp)
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@ -98,7 +88,6 @@
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- [Cycle Sort](Sorting/cycle-sort.cpp)
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## Strings
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- [Rabin-Karp pattern search algo](Strings/rabin-karp.cpp)
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- [All subsequence of a string (Recursion) ](Strings/sequence.cpp)
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- [String reversal](Strings/string-reverse.cpp)
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@ -111,7 +100,6 @@
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- [Boyer Moore pattern search](Strings/Boyer_Moore.cpp)
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## Trees
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- [Creating Binary Tree](Trees/build-binary-tree.cpp)
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- [Counting and finding sum of all the nodes in BST](Trees/count-and-sum-of-nodes-in-binary-tree.cpp)
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- [Level Order Traversal](Trees/level-order-traversal.cpp)
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@ -125,10 +113,8 @@
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- [Finding the elements of a tree visible from top view](Trees/Top-View-Of-A-Tree.cpp)
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- [Binary Tree Implementation](Trees/binary-tree-implementation.cpp)
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- [Iterative Segment Tree](Trees/IterativeSegmentTree.cpp)
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- [Fenwick Tree](Trees/Fenwick_Tree.cpp)
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# Maths
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- [Kaprekar Number](Maths/Kaprekar-number.cpp)
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- [Prime Number](Maths/prime-check.cpp)
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- [Prime Sieve](Maths/prime-sieve.cpp)
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- [Segmented Sieve](Maths/segmented-sieve-range.cpp)
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# Recursion
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- [Tower of Hanoi](Recursion/towerofHanoi.cpp)
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- [Factorial](Recursion/factorial.cpp)
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- [Permutation](Recursion/permutation.cpp)
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- [Array sorted or not](Recursion\array-sorted-or-not.cpp)
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- [Product of two numbers](Recursion\product-of-numbers.cpp)
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- [Product of digits in a number](Recursion\product-of-digits.cpp)
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