Given a limited range array contains both positive and non-positive numbers, i.e., elements are in the range from -MAX to +MAX. Our task is to search if some number is present in the array or not in O(1) time.
Since range is limited, we can use index mapping (or trivial hashing). We use values as index in a big array. Therefore we can search and insert elements in O(1) time.
How to handle negative numbers?
The idea is to use a 2D array of size hash[MAX+1]
Assign all the values of the hash matrix as 0. Traverse the given array: If the element ele is non negative assign hash[ele] as 1. Else take the absolute value of ele and assign hash[ele] as 1.
To search any element x in the array.
- If X is non-negative check if hash[X] is 1 or not. If hash[X] is one then the number is present else not present.
- If X is negative take absolute vale of X and then check if hash[X] is 1 or not. If hash[X] is one then the number is present
Below is the implementation of the above idea.
# Python3 program to implement direct index
# mapping with negative values allowed.
# Searching if X is Present in the
# given array or not.
if X >= 0:
if has[X] == 1:
# if X is negative take the absolute
# value of X.
X = abs(X)
if has[X] == 1:
def insert(a, n):
for i in range(0, n):
if a[i] >= 0:
has[a[i]] = 1
has[abs(a[i])] = 1
# Driver code
if __name__ == “__main__”:
a = [-1, 9, -5, -8, -5, -2]
n = len(a)
MAX = 1000
# Since array is global, it is
# initialized as 0.
has = [[0 for i in range(2)]
for j in range(MAX + 1)]
X = -5
if search(X) == True:
# This code is contributed by Rituraj Jain
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