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2022-10-25:在一个 2 * 3 的板上(board)有 5 块砖瓦,用数字 1~5 来表示, 以及一块空缺用 0 来表示。一次 移动 定义为选择 0 与一个相邻的数字(上下左右)进行交换.
作者:福大大架构师每日一题
- 2022-10-25 北京
本文字数:2383 字
阅读完需:约 8 分钟

2022-10-25:在一个 2 * 3 的板上(board)有 5 块砖瓦,用数字 1~5 来表示,以及一块空缺用 0 来表示。一次 移动 定义为选择 0 与一个相邻的数字(上下左右)进行交换.最终当板 board 的结果是 [[1,2,3],[4,5,0]] 谜板被解开。给出一个谜板的初始状态 board ,返回最少可以通过多少次移动解开谜板,如果不能解开谜板,则返回 -1 。输入:board = [[1,2,3],[4,0,5]]。输出:1。
答案 2022-10-25:
力扣 773。A*算法,曼哈顿距离。经过测试,rust 的运行速度和内存占用都是最优的,go 次之,java 再次之。c++运行速度比 java 还慢了。这道题可以用穷举打表法。
代码用 rust 编写。代码如下:
use std::collections::HashSet;impl Solution { pub fn sliding_puzzle(m: Vec<Vec<i32>>) -> i32 { unsafe { nexts = vec![0, 0, 0]; let mut set: HashSet<i32> = HashSet::new(); let from = m[0][0] * b6 + m[0][1] * b5 + m[0][2] * b4 + m[1][0] * b3 + m[1][1] * b2 + m[1][2]; let mut heap = Vec::new(); // [ // 从from出发到达当前状态,已经走了几步, // 从当前状态到最终状态的估计距离 // 当前状态是什么,用数字代表 // ] heap.push(vec![0, Solution::distance(from), from]); let mut ans = -1; while heap.len() > 0 { heap.sort_by(|a, b| (b[0] + b[1]).cmp(&(a[0] + a[1]))); let arr = heap.pop().unwrap(); let distance = arr[0]; let cur = arr[2]; if set.contains(&cur) { continue; } if cur == 123450 { ans = distance; break; } set.insert(cur); let next_size = Solution::nexts(cur); for i in 0..next_size { let next = nexts[i as usize]; if !set.contains(&next) { heap.push(vec![distance + 1, Solution::distance(next), next]); } } } return ans; } }
unsafe fn nexts(from: i32) -> i32 { // 301245 // 10000 // a = 3 let a = from / b6; // b = 0 let b = (from / b5) % 10; // c = 1 let c = (from / b4) % 10; // d = 2 let d = (from / b3) % 10; // e = 4 let e = (from / b2) % 10; // f = 5 let f = from % 10; if a == 0 { nexts[0] = from + (b - a) * b6 + (a - b) * b5; nexts[1] = from + (d - a) * b6 + (a - d) * b3; return 2; } else if b == 0 { nexts[0] = from + (a - b) * b5 + (b - a) * b6; nexts[1] = from + (c - b) * b5 + (b - c) * b4; nexts[2] = from + (e - b) * b5 + (b - e) * b2; return 3; } else if c == 0 { nexts[0] = from + (b - c) * b4 + (c - b) * b5; nexts[1] = from + (f - c) * b4 + (c - f); return 2; } else if d == 0 { nexts[0] = from + (a - d) * b3 + (d - a) * b6; nexts[1] = from + (e - d) * b3 + (d - e) * b2; return 2; } else if e == 0 { nexts[0] = from + (b - e) * b2 + (e - b) * b5; nexts[1] = from + (d - e) * b2 + (e - d) * b3; nexts[2] = from + (f - e) * b2 + (e - f); return 3; } else { nexts[0] = from + (e - f) + (f - e) * b2; nexts[1] = from + (c - f) + (f - c) * b4; return 2; } }
// 当前的数,num // 最终要去的数,123450 // 返回num -> 123450 曼哈顿距离! fn distance(num: i32) -> i32 { let a = -1; let b = i32::abs(a); let mut ans = end[(num / b6) as usize][0] + end[(num / b6) as usize][1]; ans += end[((num / b5) % 10) as usize][0] + i32::abs(end[((num / b5) % 10) as usize][1] - 1); ans += end[((num / b4) % 10) as usize][0] + i32::abs(end[((num / b4) % 10) as usize][1] - 2); ans += i32::abs(end[((num / b3) % 10) as usize][0] - 1) + end[((num / b3) % 10) as usize][1]; ans += i32::abs(end[((num / b2) % 10) as usize][0] - 1) + i32::abs(end[((num / b2) % 10) as usize][1] - 1); ans += i32::abs(end[(num % 10) as usize][0] - 1) + i32::abs(end[(num % 10) as usize][1] - 2); return ans; }}
const b6: i32 = 100000;
const b5: i32 = 10000;
const b4: i32 = 1000;
const b3: i32 = 100;
const b2: i32 = 10;
static mut nexts: Vec<i32> = vec![];
const end: [[i32; 2]; 6] = [[1, 2], [0, 0], [0, 1], [0, 2], [1, 0], [1, 1]];
fn main() { let nums = vec![vec![1, 2, 3], vec![4, 0, 5]]; let ans = Solution::sliding_puzzle(nums); println!("ans = {:?}", ans);}
struct Solution {}
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