Reconstruct the array by replacing arr[i] with (arr[i-1]+1) % M

Given an array of N elements and an integer M. Now, the array is modified by replacing some of the array elements with -1. The task is to print the original array.

The elements in the orginal array are related as, for every index i, a[i] = (a[i-1]+1)% M.

It is guaranteed that there is one non zero value in the array.

Examples:

Input: arr[] = {5, -1, -1, 1, 2, 3}, M = 7
Output: 5 6 0 1 2 3
M = 7, so value at index 2 should be (5+1) % 7 = 6
value at index 3 should be (6+1) % 7 = 0

Input: arr[] = {5, -1, 7, -1, 9, 0}, M = 10
Output: 5 6 7 8 9 0

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

Approach: First find the index of the non negative value index i. Then simply go in two directions i.e. From i-1 to 0 and i+1 to n.

• For index i-1 the value can be calculated by (a[i+1]-1+m)%m because (a – b) mod p = ((a mod p – b mod p) + p) mod p.
• For indexes i+1 the values can be calculated by (a[i-1]+1)%m.

Below is the implementation of the above approach:

 # Python implementation of the above approach def construct(n, m, a):     ind = 0        # Finding the index which is not -1     for i in range(n):         if (a[i]!=-1):             ind = i             break        # Calculating the values of the indexes ind-1 to 0     for i in range(ind-1, -1, -1):         if (a[i]==-1):             a[i]=(a[i + 1]-1 + m)% m        # Calculating the values of the indexes ind + 1 to n     for i in range(ind + 1, n):         if(a[i]==-1):             a[i]=(a[i-1]+1)% m     print(*a)    # Driver code n, m = 6, 7 a =[5, -1, -1, 1, 2, 3] construct(n, m, a)

Output:

5 6 0 1 2 3

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