optimal game strategy

n-queens-all.cpp

@@ -0,0 +1,68 @@
+#include<bits/stdc++.h>
+#include<iostream>
+
+using namespace std;
+
+bool check(vector<vector<int>> &board, int row, int col, int n) {
+	// top left
+	for(int i=row-1, j=col-1;i>=0 && j>=0;i--,j--) {
+		if(board[i][j] == 1)
+			return false;
+	}
+	// left
+	for(int j=col-1;j>=0;j--) {
+		if(board[row][j] == 1)
+			return false;
+	}
+	//down left
+	for(int i=row+1, j=col-1;i<n && j>=0; i++, j--) {
+		if(board[i][j] == 1)
+			return false;
+	}
+	return true;
+}
+
+void place_queens(vector<vector<int>> &board, int col, int n, vector<vector<vector<int>>> &ans) {
+
+	if(col == n) {
+		ans.push_back(board);
+	}
+	int i=0;
+	while(i < n) {
+		board[i][col] = 1;
+		if(check(board, i, col, n)) {
+			place_queens(board, col+1, n, ans);
+		}
+		board[i][col] = 0;
+		i++;
+	}
+}
+
+int main() {
+	int n;
+	cin >> n;
+	vector<vector<int>> board;
+	for(int i=0;i<n;i++) {
+		vector<int> temp(n, 0);
+		board.push_back(temp);
+	}
+	vector<vector<vector<int>>> ans;
+	place_queens(board, 0, n, ans);
+
+	if(ans.size() == 0) {
+		cout << "No solution is possible";
+		return 0;
+	}
+
+	for(int a=0;a<ans.size();a++) {
+		board = ans[a];
+		for(int i=0;i<n;i++) {
+			for(int j=0;j<n;j++) {
+				cout << board[i][j] << " ";
+			}
+			cout << endl;
+		}
+		cout << endl;
+	}
+
+}

optimalgame.cpp

@@ -0,0 +1,47 @@
+#include<bits/stdc++.h>
+using namespace std;
+
+int solve(vector<int>& arr, vector<vector<int>> &ans, int i, int j)
+{
+    // if (i < 0 || j >= arr.size())
+    // {
+    //     return 0;
+    // }
+    // if (ans[i][j] != -1)
+    //     return ans[i][j];
+    if(j == i)
+        return arr[i];
+    if (j == i+1)
+    {
+        ans[i][j] = max(arr[i], arr[j]);
+        return ans[i][j];
+    }
+    int temp = max(arr[i] + min(solve(arr, ans, i+2, j), solve(arr, ans, i+1, j-1)),
+                   arr[j] + min(solve(arr, ans, i+1, j-1), solve(arr, ans, i, j-2)));
+    ans[i][j] = temp;
+    return ans[i][j];
+}
+
+int main()
+{
+    int t; 
+    cin >> t;
+    while (t--)
+    {
+        int n; int temp;
+        cin >> n;
+        vector<int> arr(n);
+        vector<vector<int>> ans(n,vector<int>(n,0));
+        for (int i=0;i<n;i++)
+        {
+            cin >> arr[i];
+        }
+        int res=solve(arr, ans, 0, n-1);
+        cout << res << endl;
+    }
+}
+
+
+
+// F(i, j)  = Max(Vi + min(F(i+2, j), F(i+1, j-1) ), 
+//                    Vj + min(F(i+1, j-1), F(i, j-2) ))