Print modified array after executing the commands of addition and subtraction

Given an array of size ‘n’ and a given set of commands of size ‘m’. Every command consist of four integers q, l, r, k. These commands are of following types: 

• If q = 0, add ‘k’ to all integers in range ‘a’ to ‘b'(1 <= a <= b <= n). 
• If q = 1, subtract ‘k’ to all integers in range ‘a’ to ‘b'(1 <= a <= b <= n). 

Note: Initially all the array elements are set to ‘0’ and array indexing is from ‘1’. 

Input : n = 5
        commands[] = {{0 1 3 2}, {1 3 5 3}, 
                      {0 2 5 1}}
Output : 0 2 -1 -1 -3
Explanation
First command: Add 2 from index 1 to 3
>=  2 2 2 0 0
Second command: Subtract 3 from index 3 to 5 
>= 2 2 -1 -3 -3
Third command: Add 1 from index 2 to 5
>= 2 3 0 -2 -2

Simple approach is to execute every command by iterating from left index(l) up-to the right index(r) and update every index according to given command. Time complexity of this approach is O(n*m)

Better approach is to use Fenwick tree(BIT) or segment tree. But it will only optimize upto log(n) time i.e., overall complexity would become O(m*log(n))

Efficient approach is to use simple mathematics. Since all commands can be handled as offline so we can store all updates in our temporary array and then execute it at the last. 

• For command ‘0‘, add ‘+k‘ and ‘-k‘ in l^th and (r+1)^th index elements respectively. 
• For command ‘1‘, add ‘-k‘ and ‘+k‘ in the l^th and (r+1)^th index elements respectively. 

After that sum up all the elements for every index ‘i‘ starting from 1^st index i.e., a_i will contain the sum of all elements from 1 to i^th index. This can easily be achieved with the help of dynamic programming. 

Implementation:

Javascript

<script>
// javascript program to find modified array
// after executing m commands/queries

    // Update function for every command
    function updateQuery(arr , n , q , l , r , k) {

        // If q == 0, add 'k' and '-k'
        // to 'l-1' and 'r' index
        if (q == 0) {
            arr[l - 1] += k;
            arr[r] += -k;
        }

        // If q == 1, add '-k' and 'k'
        // to 'l-1' and 'r' index
        else {
            arr[l - 1] += -k;
            arr[r] += k;
        }

        return;
    }

    // Function to generate the final
    // array after executing all
    // commands
    function generateArray(arr, n)
    {

        // Generate final array with the
        // help of DP concept
        for (i = 1; i < n; ++i)
            arr[i] += arr[i - 1];

    }

    // Driver code
        var n = 5;
        var arr = Array(n + 1).fill(0);
        var q = 0, l = 1, r = 3, k = 2;
        updateQuery(arr, n, q, l, r, k);

        q = 1;
        l = 3;
        r = 5;
        k = 3;
        updateQuery(arr, n, q, l, r, k);

        q = 0;
        l = 2;
        r = 5;
        k = 1;
        updateQuery(arr, n, q, l, r, k);

        // Generate final array
        generateArray(arr, n);

        // Printing the final modified array
        for (i = 0; i < n; i++)
            document.write(arr[i] + " ");

// This code is contributed by aashish1995
</script>

Output

2 3 0 -2 -2 

Time complexity: O(Max(m,n))
Auxiliary space: O(n)