Add Sprague Grundy Theorem (TheAlgorithms#550)

Author: Gyan172004

src/math/sprague_grundy_theorem.rs

@@ -0,0 +1,70 @@
+/**
+ * Sprague Grundy Theorem for combinatorial games like Nim
+ *
+ * The Sprague Grundy Theorem is a fundamental concept in combinatorial game theory, commonly used to analyze
+ * games like Nim. It calculates the Grundy number (also known as the nimber) for a position in a game.
+ * The Grundy number represents the game's position, and it helps determine the winning strategy.
+ *
+ * The Grundy number of a terminal state is 0; otherwise, it is recursively defined as the minimum
+ * excludant (mex) of the Grundy values of possible next states.
+ *
+ * For more details on Sprague Grundy Theorem, you can visit:(https://en.wikipedia.org/wiki/Sprague%E2%80%93Grundy_theorem)
+ *
+ * Author : [Gyandeep](https://github.com/Gyan172004)
+ */
+
+ pub fn calculate_grundy_number(
+    position: i64,
+    grundy_numbers: &mut [i64],
+    possible_moves: &[i64],
+) -> i64 {
+    // Check if we've already calculated the Grundy number for this position.
+    if grundy_numbers[position as usize] != -1 {
+        return grundy_numbers[position as usize];
+    }
+
+    // Base case: terminal state
+    if position == 0 {
+        grundy_numbers[0] = 0;
+        return 0;
+    }
+
+    // Calculate Grundy values for possible next states.
+    let mut next_state_grundy_values: Vec<i64> = vec![];
+    for move_size in possible_moves.iter() {
+        if position - move_size >= 0 {
+            next_state_grundy_values.push(calculate_grundy_number(
+                position - move_size,
+                grundy_numbers,
+                possible_moves,
+            ));
+        }
+    }
+
+    // Sort the Grundy values and find the minimum excludant.
+    next_state_grundy_values.sort_unstable();
+    let mut mex: i64 = 0;
+    for grundy_value in next_state_grundy_values.iter() {
+        if *grundy_value != mex {
+            break;
+        }
+        mex += 1;
+    }
+
+    // Store the calculated Grundy number and return it.
+    grundy_numbers[position as usize] = mex;
+    return mex;
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn calculate_grundy_number_test() {
+        let mut grundy_numbers: Vec<i64> = vec![-1; 7];
+        let possible_moves: Vec<i64> = vec![1, 4];
+        calculate_grundy_number(6, &mut grundy_numbers, &possible_moves);
+        assert_eq!(grundy_numbers, [0, 1, 0, 1, 2, 0, 1]);
+    }
+}