arcsoftech / binary-search-5

Binary-Search-5

Problem1: Find Function Arguments

Given a number z ∈ N and a function f(x, y) ∈ N, where x ∈ N and y ∈ N.

Function f(x, y) is black box and unknown but we can pass any x and y to function and get f(x, y) value. f(x, y) is strictly increasing: f(x, y) < f(x + 1, y) f(x, y) < f(x, y + 1)

Find all pairs of x and y, where f(x, y) = z.

Example 1:

Input:

f(x, y) = x + y

z = 5

Output:

[[1, 4], [2, 3], [3, 2], [4, 1]] Example 2:

Input:

f(x, y) = x^2 + y

z = 50

Output:

[[1, 49], [2, 46], [3, 41], [4, 34], [5, 25], [6, 14], [7, 1]]

Problem2: Find object in a grid

Given a char grid (o represents an empty cell and x represents a target object) and an API getResponse which would give you a response w.r.t. to your previous position. Write a program to find the object. You can move to any position.

enum Response { HOTTER, // Moving closer to target COLDER, // Moving farther from target SAME, // Same distance from the target as your previous guess EXACT; // Reached destination }

// Throws an error if 'row' or 'col' is out of bounds public Response getResponse(int row, int col) { // black box } Example 1:

Input: [['o', 'o', 'o'], ['o', 'o', 'o'], ['x', 'o', 'o']]

Output: [2, 0] Example 2:

Input: [['o', 'o', 'o', 'o', 'o'], ['o', 'o', 'o', 'o', 'o'], ['o', 'o', 'o', 'o', 'o'], ['o', 'o', 'o', 'o', 'o'], ['o', 'o', 'o', 'x', 'o'], ['o', 'o', 'o', 'o', 'o']]

Output: [4, 3] Assumptions:

There is always one and only one object. If it's not the target object the 1st call would always give HOTTER as result, ortherwise EXACT.