Merge pull request #312 from amansharma264/day-1-sol-1.1

Day 1 sol 1.1

Author: Dheeraj-06

Problems/Mathematics/Day-01/sol/amansharma264/solution1.cpp

@@ -0,0 +1,109 @@
+/*
+====================================================
+PROBLEM STATEMENT:
+====================================================
+There are n people standing in a circle (n is even).
+Each person looks at the person exactly opposite to them.
+
+You are given three distinct integers a, b, and c.
+It is known that person 'a' is looking at person 'b'.
+
+Determine the person that 'c' is looking at.
+If multiple answers exist, print any.
+If no valid answer exists, print -1.
+
+----------------------------------------------------
+PROBLEM LINK:
+https://codeforces.com/problemset/problem/1560/B
+====================================================
+*/
+
+/*
+====================================================
+APPROACH:
+====================================================
+If person 'a' is looking at person 'b', then:
+- The distance between them is |a - b|
+- Since they are opposite, total number of people:
+      n = 2 * |a - b|
+
+Steps:
+1. Compute dist = |a - b|
+2. Compute n = 2 * dist
+3. If a, b, or c is greater than n → invalid → print -1
+4. Otherwise, the person opposite to c is:
+   - c + dist (if within n)
+   - else c - dist
+
+----------------------------------------------------
+WHY THIS WORKS:
+- In a circular arrangement, opposite positions differ
+  by exactly n/2 positions.
+====================================================
+*/
+
+/*
+====================================================
+TIME & SPACE COMPLEXITY:
+====================================================
+Time Complexity:  O(1) per test case
+Space Complexity: O(1)
+====================================================
+*/
+
+/*
+====================================================
+EXAMPLE:
+====================================================
+Input:
+1
+1 3 2
+
+Output:
+4
+
+Explanation:
+|1 - 3| = 2 → n = 4
+Opposite of 2 is 2 + 2 = 4
+====================================================
+*/
+
+/*
+====================================================
+SUBMISSION LINK:
+====================================================
+https://codeforces.com/contest/1560/submission/345095137
+====================================================
+*/
+
+#include <bits/stdc++.h>
+using namespace std;
+
+#define fastio() ios::sync_with_stdio(false); cin.tie(nullptr);
+
+int main() {
+    fastio();
+
+    int t;
+    cin >> t;
+
+    while (t--) {
+        long long a, b, c;
+        cin >> a >> b >> c;
+
+        long long dist = llabs(a - b);
+        long long n = 2 * dist;
+
+        if (a > n || b > n || c > n) {
+            cout << -1 << '\n';
+            continue;
+        }
+
+        if (c + dist <= n)
+            cout << c + dist << '\n';
+        else
+            cout << c - dist << '\n';
+    }
+
+    return 0;
+}