Index Mapping (or Trivial Hashing) with negatives allowed
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 the 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][2]
Algorithm:
Assign all the values of the hash matrix as 0.
Traverse the given array:
If the element ele is non negative assign
hash[ele][0] as 1.
Else take the absolute value of ele and
assign hash[ele][1] as 1.
To search any element x in the array.
- If X is non-negative check if hash[X][0] is 1 or not. If hash[X][0] is one then the number is present else not present.
- If X is negative take absolute value of X and then check if hash[X][1] is 1 or not. If hash[X][1] is one then the number is present
Below is the implementation of the above idea.
C++
// CPP program to implement direct index mapping // with negative values allowed. #include <bits/stdc++.h> using namespace std; #define MAX 1000 // Since array is global, it is initialized as 0. bool has[MAX + 1][2]; // searching if X is Present in the given array // or not. bool search(int X) { if (X >= 0) { if (has[X][0] == 1) return true; else return false; } // if X is negative take the absolute // value of X. X = abs(X); if (has[X][1] == 1) return true; return false; } void insert(int a[], int n) { for (int i = 0; i < n; i++) { if (a[i] >= 0) has[a[i]][0] = 1; else has[abs(a[i])][1] = 1; } } // Driver code int main() { int a[] = { -1, 9, -5, -8, -5, -2 }; int n = sizeof(a)/sizeof(a[0]); insert(a, n); int X = -5; if (search(X) == true) cout << "Present"; else cout << "Not Present"; return 0; } |
Java
// Java program to implement direct index // mapping with negative values allowed. class GFG { final static int MAX = 1000; // Since array is global, it // is initialized as 0. static boolean[][] has = new boolean[MAX + 1][2]; // searching if X is Present in // the given array or not. static boolean search(int X) { if (X >= 0) { if (has[X][0] == true) { return true; } else { return false; } } // if X is negative take the // absolute value of X. X = Math.abs(X); if (has[X][1] == true) { return true; } return false; } static void insert(int a[], int n) { for (int i = 0; i < n; i++) { if (a[i] >= 0) { has[a[i]][0] = true; } else { int abs_i = Math.Abs(a[i]); has[abs_i][1] = true; } } } // Driver code public static void main(String args[]) { int a[] = {-1, 9, -5, -8, -5, -2}; int n = a.length; insert(a, n); int X = -5; if (search(X) == true) { System.out.println("Present"); } else { System.out.println("Not Present"); } } } // This code is contributed // by 29AjayKumar |
Python3
# Python3 program to implement direct index # mapping with negative values allowed. # Searching if X is Present in the # given array or not. def search(X): if X >= 0: return has[X][0] == 1 # if X is negative take the absolute # value of X. X = abs(X) return has[X][1] == 1 def insert(a, n): for i in range(0, n): if a[i] >= 0: has[a[i]][0] = 1 else: has[abs(a[i])][1] = 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)] insert(a, n) X = -5 if search(X) == True: print("Present") else: print("Not Present") # This code is contributed by Rituraj Jain |
C#
// C# program to implement direct index // mapping with negative values allowed. using System; class GFG { static int MAX = 1000; // Since array is global, it // is initialized as 0. static bool[,] has = new bool[MAX + 1, 2]; // searching if X is Present in // the given array or not. static bool search(int X) { if (X >= 0) { if (has[X, 0] == true) { return true; } else { return false; } } // if X is negative take the // absolute value of X. X = Math.Abs(X); if (has[X, 1] == true) { return true; } return false; } static void insert(int[] a, int n) { for (int i = 0; i < n; i++) { if (a[i] >= 0) { has[a[i], 0] = true; } else { int abs_i = Math.Abs(a[i]); has[abs_i, 1] = true; } } } // Driver code public static void Main() { int[] a = {-1, 9, -5, -8, -5, -2}; int n = a.Length; insert(a, n); int X = -5; if (search(X) == true) { Console.WriteLine("Present"); } else { Console.WriteLine("Not Present"); } } } // This code is contributed // by Akanksha Rai |
Javascript
<script> // JavaScript program to implement direct index // mapping with negative values allowed. let MAX = 1000; // Since array is global, it // is initialized as 0. let has = new Array(MAX+1); for(let i=0;i<MAX+1;i++) { has[i]=new Array(2); for(let j=0;j<2;j++) has[i][j]=0; } // searching if X is Present in // the given array or not. function search(X) { if (X >= 0) { if (has[X][0] == true) { return true; } else { return false; } } // if X is negative take the // absolute value of X. X = Math.abs(X); if (has[X][1] == true) { return true; } return false; } function insert(a,n) { for (let i = 0; i < n; i++) { if (a[i] >= 0) { has[a[i]][0] = true; } else { int abs_i = Math.abs(a[i]); has[abs_i][1] = true; } } } // Driver code let a=[-1, 9, -5, -8, -5, -2]; let n = a.length; insert(a, n); let X = -5; if (search(X) == true) { document.write("Present"); } else { document.write("Not Present"); } // This code is contributed by rag2127 </script> |
Output:
Present
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