Merge pull request #45 from SauravGitte/main

Solve CF 1560B using math logic

Author: ScorchedPearl

Problems/Mathematics/Day-01/sol/Saurav_Gitte/.vscode/settings.json

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+{
+    "files.associations": {
+        "iostream": "cpp"
+    }
+}

Problems/Mathematics/Day-01/sol/Saurav_Gitte/Solution1.cpp

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+/*
+Problem Statement:
+There are n people standing in a circle (n is even). Each person looks at the person
+standing exactly opposite them. Given that person a looks at person b, determine
+the person that person c is looking at.
+
+---------------------------------------
+Approach:
+If 'a' looks at 'b', then the distance between a and b must be exactly n/2.
+Let dist = |a - b|. Then n = 2 * dist.
+Once n is known, the person opposite to c is:
+- c + dist, if it does not exceed n
+- otherwise, c - dist
+
+If c is greater than n, then the configuration is invalid.
+
+----------------------------------------
+
+Time Complexity: O(1)
+
+Space Complexity: O(1)
+
+----------------------------------------
+Example:
+Input:
+a = 1, b = 3, c = 2
+
+Process : 
+1. Calculate dist = |1 - 3| = 2
+2. Calculate n = 2 * dist = 4  
+3. Since c = 2, calculate opposite:
+   - c + dist = 2 + 2 = 4 (which is <= n)
+   - So, the person opposite to c is 4.
+
+Output:
+4
+
+--------------------------------
+*/
+
+#include <bits/stdc++.h>
+using namespace std;
+
+int main() {
+    int t;
+    cin >> t;
+    while (t--) {
+        int a, b, c;
+        cin >> a >> b >> c;
+
+
+        int d = abs(a - b);
+        int n = 2 * d;
+        // 2*10^8 fits in int.
+
+        // Invalid configuration, Answer does not exist
+        if (d == 0 || c > n) {
+            cout << -1 << "\n";
+            continue;
+        }
+
+        int ans;
+        if (c + d <= n)
+            ans = c + d;
+        else
+            ans = c - d;
+
+        cout << ans << "\n";
+    }
+    return 0;
+}