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

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:

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# 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)

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Output:

5 6 0 1 2 3


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