83 lines
2.4 KiB
C++
83 lines
2.4 KiB
C++
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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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