Added Number Spiral problem (CSES 1071) with explanation and test cases

Author: Aditya12604

CPP/patterns/Pattern/NumberSpiral_CSES1071.cpp

@@ -0,0 +1,66 @@
+/*
+Problem: Number Spiral (CSES Problem Set)
+Link: https://cses.fi/problemset/task/1071/
+Topic: Math / Pattern Recognition
+
+Description:
+Given coordinates (y, x) in an infinite number spiral, find the value at that position.
+The spiral grows outwards starting from 1 at (1,1).
+
+Example spiral pattern:
+  1   2   9  10 25
+  4   3   8  11 24
+  5   6   7  12 23
+ 16  15  14  13 22
+ 17  18  19  20 21
+
+Approach:
+- The maximum of (x, y) determines which square layer the cell belongs to.
+- The last number of each layer (n) is always n^2.
+- Depending on whether n is even or odd, the numbering direction differs:
+  - Even layers fill top-to-bottom.
+  - Odd layers fill left-to-right.
+- Use this pattern to directly calculate the value at (x, y) in O(1) time.
+
+Time Complexity: O(1)
+Space Complexity: O(1)
+*/
+
+#include <bits/stdc++.h>
+using namespace std;
+
+long long numberSpiralValue(long long x, long long y) {
+    if (x == 1 && y == 1) return 1;
+
+    long long layer = max(x, y);
+    long long base = (layer - 1) * (layer - 1);
+
+    if (layer % 2 == 0) {  // even layer
+        if (y == layer) 
+            return base + x;
+        else 
+            return base + layer + (layer - y);
+    } 
+    else {  // odd layer
+        if (x == layer)
+            return base + y;
+        else
+            return base + layer + (layer - x);
+    }
+}
+
+int main() {
+    vector<pair<long long, long long>> tests = {
+        {2, 3}, // Expected output: 8
+        {1, 1}, // Expected output: 1
+        {4, 2}, // Expected output: 15
+        {3, 5}  // Expected output: 27
+    };
+
+    for (auto [y, x] : tests) {
+        cout << "Input (y=" << y << ", x=" << x << ") -> Output: " 
+             << numberSpiralValue(x, y) << endl;
+    }
+
+    return 0;
+}