Construct sum-array with sum of elements in given range

You are given an array of n-elements and an odd-integer m. You have to construct a new sum_array from given array such that sum_array[i] = Σarr[j] for (i-(m/2)) < j (i+(m/2)).
note : for 0 > j or j >= n take arr[j] = 0.

Examples:

```Input : arr[] = {1, 2, 3, 4, 5},
m = 3
Output : sum_array = {3, 6, 9, 12, 9}
Explanation : sum_array[0] = arr[0] + arr[1]
sum_array[1] = arr[0] + arr[1] + arr[2]
sum_array[2] = arr[1] + arr[2] + arr[3]
sum_array[3] = arr[2] + arr[3] + arr[4]
sum_array[4] = arr[3] + arr[4]

Input : arr[] = {2, 4, 3, 4, 2},
m = 1
Output : sum_array = {2, 4, 3, 4, 2}
Explanation : sum_array[0] = arr[0]
sum_array[1] = arr[1]
sum_array[2] = arr[2]
sum_array[3] = arr[3]
sum_array[4] = arr[4]
```

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Basic Approach : As per problem statement, we calculate sum_array[i] by iterating over i-(m/2) to i+(m/2). According to this approach, we have a nested loop which will result into time complexity of O(n*m).

Efficient Approach : For calculating sum_array is to use sliding window concept and thus can easily save our time. For Sliding window, the time complexity is O(n).
Algorithm

```
calculate sum of first (m/2)+1 elementssum_array[0] = sumfor i=1 to i<nif( (i-(m/2)-1) >= 0 )
sum -= arr[(i-(m/2)-1)]if( (i+m/2) < n)
sum += arr[(i+m/2)]sum_array[i] = sumprint sum_array
```

C++

 `// CPP Program to find sum array for a given ` `// array. ` `#include ` `using` `namespace` `std; ` ` `  `// function to calc sum_array and print ` `void` `calcSum_array(``int` `arr[], ``int` `n, ``int` `m) ` `{ ` `    ``int` `sum = 0; ` `    ``int` `sum_array[n]; ` ` `  `    ``// calc 1st m/2 + 1 element for 1st window ` `    ``for` `(``int` `i = 0; i < m / 2 + 1; i++) ` `        ``sum += arr[i]; ` `    ``sum_array[0] = sum; ` ` `  `    ``// use sliding window to ` `    ``// calculate rest of sum_array ` `    ``for` `(``int` `i = 1; i < n; i++) { ` `        ``if` `(i - (m / 2) - 1 >= 0) ` `            ``sum -= arr[i - (m / 2) - 1]; ` `        ``if` `(i + (m / 2) < n) ` `            ``sum += arr[i + (m / 2)]; ` `        ``sum_array[i] = sum; ` `    ``} ` ` `  `    ``// print sum_array ` `    ``for` `(``int` `i = 0; i < n; i++) ` `        ``cout << sum_array[i] << ``" "``; ` `} ` ` `  `// driver program ` `int` `main() ` `{ ` `    ``int` `arr[] = { 3, 6, 2, 7, 3, 8, 4,  ` `                      ``9, 1, 5, 0, 4 }; ` `    ``int` `m = 5; ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(``int``); ` `    ``calcSum_array(arr, n, m); ` `    ``return` `0; ` `} `

Java

 `// Java Program to find sum array  ` `// for a given array. ` `class` `GFG  ` `{ ` `    ``// function to calc sum_array and print ` `    ``static` `void` `calcSum_array(``int` `arr[], ``int` `n, ``int` `m) ` `    ``{ ` `        ``int` `sum = ``0``; ` `        ``int` `sum_array[] = ``new` `int``[n]; ` `     `  `        ``// calc 1st m/2 + 1 element ` `        ``// for 1st window ` `        ``for` `(``int` `i = ``0``; i < m / ``2` `+ ``1``; i++) ` `            ``sum += arr[i]; ` `        ``sum_array[``0``] = sum; ` `     `  `        ``// use sliding window to ` `        ``// calculate rest of sum_array ` `        ``for` `(``int` `i = ``1``; i < n; i++)  ` `        ``{ ` `            ``if` `(i - (m / ``2``) - ``1` `>= ``0``) ` `                ``sum -= arr[i - (m / ``2``) - ``1``]; ` `            ``if` `(i + (m / ``2``) < n) ` `                ``sum += arr[i + (m / ``2``)]; ` `            ``sum_array[i] = sum; ` `        ``} ` `     `  `        ``// print sum_array ` `        ``for` `(``int` `i = ``0``; i < n; i++) ` `            ``System.out.print(sum_array[i] + ``" "``); ` `    ``} ` `     `  `    ``// Driver program ` `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` `        ``int` `arr[] = { ``3``, ``6``, ``2``, ``7``, ``3``, ``8``, ``4``, ``9``, ``1``, ``5``, ``0``, ``4` `}; ` `        ``int` `m = ``5``; ` `        ``int` `n = arr.length; ` `        ``calcSum_array(arr, n, m); ` `    ``} ` `} ` ` `  `// This code is contributed by prerna saini. `

Python3

 `# Python3 Program to find Sum array  ` `# for a given array. ` `import` `math as mt ` ` `  `# function to calc Sum_array and print ` `def` `calcSum_array(arr, n, m): ` ` `  `    ``Sum` `=` `0` `    ``Sum_array ``=` `[``0` `for` `i ``in` `range``(n)] ` ` `  `    ``# calc 1st m/2 + 1 element for 1st window ` `    ``for` `i ``in` `range``(m ``/``/` `2` `+` `1``): ` `        ``Sum` `+``=` `arr[i] ` `    ``Sum_array[``0``] ``=` `Sum` ` `  `    ``# use sliding window to ` `    ``# calculate rest of Sum_array ` `    ``for` `i ``in` `range``(``1``, n): ` `        ``if` `(i ``-` `(m ``/``/` `2``) ``-` `1` `>``=` `0``): ` `            ``Sum` `-``=` `arr[i ``-` `(m ``/``/` `2``) ``-` `1``] ` `        ``if` `(i ``+` `(m ``/` `2``) < n): ` `            ``Sum` `+``=` `arr[i ``+` `(m ``/``/``2``)] ` `        ``Sum_array[i] ``=` `Sum` `     `  `    ``# prSum_array ` `    ``for` `i ``in` `range``(n): ` `        ``print``(Sum_array[i], end ``=` `" "``) ` ` `  `# Driver Code ` `arr ``=` `[ ``3``, ``6``, ``2``, ``7``, ``3``, ``8``, ``4``, ``9``, ``1``, ``5``, ``0``, ``4` `] ` `m ``=` `5` `n ``=` `len``(arr) ` `calcSum_array(arr, n, m) ` ` `  `# This code is contributed by mohit kumar 29 `

C#

 `// C# Program to find sum array  ` `// for a given array. ` `using` `System; ` ` `  `class` `GFG  ` `{ ` `    ``// function to calc sum_array and print ` `    ``static` `void` `calcSum_array(``int` `[]arr, ``int` `n, ``int` `m) ` `    ``{ ` `        ``int` `sum = 0; ` `        ``int` `[]sum_array = ``new` `int``[n]; ` `     `  `        ``// calc 1st m/2 + 1 element ` `        ``// for 1st window ` `        ``for` `(``int` `i = 0; i < m / 2 + 1; i++) ` `            ``sum += arr[i]; ` `        ``sum_array[0] = sum; ` `     `  `        ``// use sliding window to ` `        ``// calculate rest of sum_array ` `        ``for` `(``int` `i = 1; i < n; i++)  ` `        ``{ ` `            ``if` `(i - (m / 2) - 1 >= 0) ` `                ``sum -= arr[i - (m / 2) - 1]; ` `            ``if` `(i + (m / 2) < n) ` `                ``sum += arr[i + (m / 2)]; ` `            ``sum_array[i] = sum; ` `        ``} ` `     `  `        ``// print sum_array ` `        ``for` `(``int` `i = 0; i < n; i++) ` `        ``Console.Write(sum_array[i] + ``" "``); ` `    ``} ` `     `  `    ``// Driver program ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``int` `[]arr = { 3, 6, 2, 7, 3, 8, 4, 9, 1, 5, 0, 4 }; ` `        ``int` `m = 5; ` `        ``int` `n = arr.Length; ` `        ``calcSum_array(arr, n, m); ` `    ``} ` `} ` ` `  `// This code is contributed by vt_m. `

PHP

 `= 0) ` `            ``\$sum` `= ``\$sum` `- ``\$arr``[``\$i` `-  ` `                    ``(int)(``\$m` `/ 2) - 1]; ` `        ``if` `(``\$i` `+ (int)(``\$m` `/ 2) < ``\$n``) ` `            ``\$sum` `= ``\$sum` `+ ``\$arr``[``\$i` `+  ` `                    ``(int)(``\$m` `/ 2)]; ` `        ``\$sum_array``[``\$i``] = ``\$sum``; ` `    ``} ` ` `  `    ``// print sum_array ` `    ``for` `(``\$i` `= 0; ``\$i` `< ``\$n``; ``\$i``++) ` `        ``echo` `\$sum_array``[``\$i``] . ``" "``; ` `} ` ` `  `// Driver Code ` `\$arr` `= ``array``(3, 6, 2, 7, 3, 8,  ` `             ``4, 9, 1, 5, 0, 4 ); ` `\$m` `= 5; ` `\$n` `= sizeof(``\$arr``); ` `calcSum_array(``\$arr``, ``\$n``, ``\$m``); ` ` `  `// This code is contributed by Mukul Singh ` `?> `

Output:

```11 18 21 26 24 31 25 27 19 19 10 9
```

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Improved By : mohit kumar 29, Code_Mech

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