Breadth-First Search + Dynamic Programming + Bit Manipulation + Bitmask
Intuition\n Describe your first thoughts on how to solve this problem. \n- Use BFS to preprocess the minimum number of moves to reach one pawn from the other pa
# Intuition\n<!-- Describe your first thoughts on how to solve this problem. -->\n- Use BFS to preprocess the minimum number of moves to reach one pawn from the other pawns.\n- Consider the knight\u2019s original position as another pawn.\n- Use DP with a bitmask to store current pawns that have not been captured.\n\n# Approach\n<!-- Describe your approach to solving the problem. -->\nBreadth-First Search + Dynamic Programming + Bit Manipulation + Bitmask\n\n# Complexity\n- Time complexity: $O(n^3 + 2^n \\cdot n^2)$\n<!-- Add your time complexity here, e.g. $$O(n)$$ -->\n\n- Space complexity: $O(2^n \\cdot n^2)$\n<!-- Add your space complexity here, e.g. $$O(n)$$ -->\nwhere $n$ is the length of the $positions$ array\n\n# Code\n```rust []\nuse std::collections::{VecDeque, HashMap};\n\nimpl Solution {\n    pub fn max_moves(kx: i32, ky: i32, mut positions: Vec<Vec<i32>>) -> i32 {\n        let n = positions.len();\n\n        let kx = kx as usize;\n        let ky = ky as usize;\n\n        let m = [[1, -2], [2, -1], [2, 1], [1, 2], [-1, 2], [-2, 1], [-2, -1], [-1, -2]];\n        let h: HashMap<[i32; 2], usize> = positions.iter().enumerate().map(|t| ([t.1[0], t.1[1]], t.0)).collect();\n        \n        let mut d = vec![vec![0; n+1]; n+1];\n        \n        Self::calc(0, kx, ky, &m, &h, &mut d);\n\n        for k in 1..n {\n            Self::calc(k, positions[k-1][0] as usize, positions[k-1][1] as usize, &m, &h, &mut d);\n        }\n\n        let mut dp = vec![vec![vec![0; n + 1]; 1 << n]; n];                \n\n        Self::dfs(0, 0, 0, &m, &d, &mut dp)\n    }\n\n    pub fn dfs(\n        i: usize, j: usize, k: usize, \n        m: &[[i32; 2]; 8], d: &Vec<Vec<i32>>, \n        dp: &mut Vec<Vec<Vec<i32>>>\n    ) -> i32 {\n        if dp[i][j][k] > 0 {\n            return dp[i][j][k];\n        }\n\n        let mut r = if i % 2 == 0 {0} else {i32::MAX};\n\n        for l in 0..d.len() - 1 {\n            if j & (1 << l) == 0 {\n                let w = if i == d.len() - 2 {0} else {Self::dfs(i + 1, j | (1 << l), l + 1, m, d, dp)};\n\n                if i % 2 == 0 {\n                    r = r.max(d[k][l+1] + w);\n                } else {\n                    r = r.min(d[k][l+1] + w);\n                }            \n            }\n        }\n\n        dp[i][j][k] = r;\n\n        dp[i][j][k]\n    }\n\n    pub fn calc(\n        k: usize, kx: usize, ky: usize, \n        m: &[[i32; 2]; 8], h: &HashMap<[i32; 2], usize>,\n        d: &mut Vec<Vec<i32>>\n    ) {\n        let mut v = [[false; 50]; 50];\n        let mut q = VecDeque::from([([kx, ky], 0)]);\n\n        let mut s = k;     \n        let mut f = false;   \n\n        v[kx][ky] = true;\n\n        while !q.is_empty() {\n            let t = q.pop_front().unwrap();\n\n            let c = [t.0[0] as i32, t.0[1] as i32];\n\n            for i in 0..m.len() {\n                let n = [c[0] + m[i][0], c[1] + m[i][1]];\n\n                if n[0] >= 0 && n[0] < 50 && n[1] >= 0 && n[1] < 50 {\n                    let jx = n[0] as usize;\n                    let jy = n[1] as usize;\n\n                    if !v[jx][jy] {\n                        v[jx][jy] = true;\n\n                        q.push_back(([jx, jy], t.1 + 1));\n\n                        if h.contains_key(&n) {                            \n                            let l = h[&n] + 1;\n\n                            if l > k {\n                                s += 1;\n\n                                d[k][l] = t.1 + 1;\n                                d[l][k] = t.1 + 1;\n\n                                if s == h.len() + 1 {\n                                    f = true;\n\n                                    break;\n                                }\n                            }\n                        }\n                    }\n                }\n            }  \n\n            if f {\n                break;\n            }                            \n        }        \n    }     \n}\n```
['Dynamic Programming', 'Bit Manipulation', 'Breadth-First Search', 'Bitmask', 'Rust']