Merge pull request #291 from dwivediprashant/code/day-3-que-2

Code : solved que-2 of day-3

Author: zonedoutdg

Problems/Mathematics/Day-03/soln/prashant_kumar_dwivedi/Solution2.java

@@ -0,0 +1,96 @@
+/*
+Problem Statement:
+Mike has an unlimited number of unit resistors (each with resistance = 1).
+
+Using these resistors, he can create new elements in two ways:
+1. Series connection:
+   - New resistance = current resistance + 1
+2. Parallel connection:
+   - New resistance = current resistance / (current resistance + 1)
+
+Given a target resistance as a reduced fraction a / b,
+the task is to find the minimum number of unit resistors
+needed to build exactly this resistance.
+
+It is guaranteed that a solution always exists.
+
+---------------------------------------
+Observation:
+Instead of actually building resistor networks, we can
+work directly with the fraction a / b.
+
+At every step:
+- If a > b, we reduce a using b.
+- If b > a, we reduce b using a.
+
+Each reduction corresponds to adding one unit resistor.
+
+---------------------------------------
+Important Insight:
+When a > b:
+- a can be reduced by subtracting b multiple times at once.
+- This is equivalent to using (a / b) resistors.
+
+Similarly, when b > a:
+- b can be reduced using a.
+- This uses (b / a) resistors.
+
+This process continues until one value becomes zero.
+
+---------------------------------------
+Approach:
+1. Read integers a and b.
+2. Initialize a counter for resistors used.
+3. While both a and b are non-zero:
+   - If a > b:
+       - Add a / b to the counter.
+       - Set a = a % b.
+   - Else:
+       - Add b / a to the counter.
+       - Set b = b % a.
+4. Output the counter.
+
+---------------------------------------
+Time Complexity:
+O(log(min(a, b)))
+
+---------------------------------------
+Space Complexity:
+O(1)
+
+---------------------------------------
+Constraints:
+1 ≤ a, b ≤ 10^18
+---------------------------------------
+*/
+
+/*--- submission link
+https://codeforces.com/contest/343/submission/355464586
+*/
+
+import java.util.*;
+
+public class Solution2 {
+    public static void main(String[] args) {
+
+        Scanner sc = new Scanner(System.in);
+
+        long a = sc.nextLong();
+        long b = sc.nextLong();
+
+        long used = 0;
+
+        // keep reducing until one value becomes zero
+        while (a != 0 && b != 0) {
+            if (a > b) {
+                used += a / b;
+                a = a % b;
+            } else {
+                used += b / a;
+                b = b % a;
+            }
+        }
+
+        System.out.println(used);
+    }
+}