A rational is represented as p/qb, for example 2/3. Given a sorted array of rational numbers, how to search an element using Binary Search. Use of floating point arithmetic is not allowed.

Example:

Input: arr[] = {1/5, 2/3, 3/2, 13/2} x = 3/2 Output: Found at index 2

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To compare two rational numbers p/q and r/s, we can compare p*s with q*r.

// C program for Binary Search for Rationalnal Numbers // without using floating point arithmetic #include <stdio.h> struct Rational { int p; int q; }; // Utility function to compare two Rationalnal numbers // 'a' and 'b'. It returns // 0 --> When 'a' and 'b' are same // 1 --> When 'a' is greater //-1 --> When 'b' is greate int compare(struct Rational a, struct Rational b) { // If a/b == c/d then a*d = b*c: // method to ignore division if (a.p * b.q == a.q * b.p) return 0; if (a.p * b.q > a.q * b.p) return 1; return -1; } // Returns index of x in arr[l..r] if it is present, else // returns -1. It mainly uses Binary Search. int binarySearch(struct Rational arr[], int l, int r, struct Rational x) { if (r >= l) { int mid = l + (r - l)/2; // If the element is present at the middle itself if (compare(arr[mid], x) == 0) return mid; // If element is smaller than mid, then it can // only be present in left subarray if (compare(arr[mid], x) > 0) return binarySearch(arr, l, mid-1, x); // Else the element can only be present in right // subarray return binarySearch(arr, mid+1, r, x); } return -1; } // Driver method int main() { Rational arr[] = {{1, 5}, {2, 3}, {3, 2}, {13, 2}}; Rational x = {3, 2}; int n = sizeof(arr)/sizeof(arr[0]); printf("Element found at index %d", binarySearch(arr, 0, n-1, x)); }

Output:

Element found at index 2

Thanks to Utkarsh Trivedi for suggesting above solution.

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