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2022-12-20:二狗买了一些小兵玩具,和大胖一起玩, 一共有 n 个小兵,这 n 个小兵拍成一列, 第 i 个小兵战斗力为 hi,然后他们两个开始对小兵进行排列, 一共进行 m 次操作,二狗每次操作选择一个数 k,
作者:福大大架构师每日一题
- 2022-12-20 北京
本文字数:2863 字
阅读完需:约 9 分钟

2022-12-20:二狗买了一些小兵玩具,和大胖一起玩,一共有 n 个小兵,这 n 个小兵拍成一列,第 i 个小兵战斗力为 hi,然后他们两个开始对小兵进行排列,一共进行 m 次操作,二狗每次操作选择一个数 k,将前 k 个小兵战斗力从小到大排列,大胖每次操作选择一个数 k,将前 k 个小兵战斗力从大到小排列,问所有操作结束后,排列顺序什么样,给定一个长度为 n 的数组 arr,表示每个小兵的战斗力,给定一个长度为 m 的数组 op,op[i] = { k , 0 }, 表示对前 k 个士兵执行从小到大的操作,op[i] = { k , 1 }, 表示对前 k 个士兵执行从大到小的操作。返回数组 ans,表示最终的排列。1 <= n, m <= 2 * 10^5,-10 ^ 9<= arr[i] <= + 10^9。来自百度。
答案 2022-12-20:
单调栈+有序表。rust 语言里结构体的有序表需要实现 Ord 的 trait。时间复杂度 O(M) + O(N*logN)。
rust 代码如下:
use rand::Rng;use std::cmp::Ordering;use std::collections::BTreeSet;use std::iter::repeat;fn main() { let mut arr = vec![3, 2, 6, 7, 5, 1]; let mut op = vec![vec![3, 0], vec![4, 1], vec![2, 0]]; let ans2 = game2(&mut arr, &mut op); println!("ans2 = {:?}", ans2); let nn: i32 = 200; let mm: i32 = 100; let vv: i32 = 200; let test_time: i32 = 5000; println!("测试开始"); for i in 0..test_time { let n: i32 = rand::thread_rng().gen_range(0, nn) + 1; let m: i32 = rand::thread_rng().gen_range(0, mm) + 1; let mut arr = random_array(n, vv); let mut op = random_op(m, n); let ans1 = game1(&mut arr, &mut op); let ans2 = game2(&mut arr, &mut op); if ans1 != ans2 { println!("出错了!"); println!("i = {}", i); println!("ans1 = {:?}", ans1); println!("ans2 = {:?}", ans2); break; } } println!("测试结束");}
// 暴力方法// 为了验证fn game1(arr: &mut Vec<i32>, op: &mut Vec<Vec<i32>>) -> Vec<i32> { let n = arr.len() as i32; let mut help: Vec<i32> = repeat(0).take(n as usize).collect(); for i in 0..n { help[i as usize] = arr[i as usize]; } for o in op.iter() { if o[1] == 0 { help[0..o[0] as usize].sort_by(|a, b| a.cmp(b)); } else { help[0..o[0] as usize].sort_by(|a, b| b.cmp(a)); } } let mut ans: Vec<i32> = repeat(0).take(n as usize).collect(); for i in 0..n { ans[i as usize] = help[i as usize]; } return ans;}
// 正式方法// 时间复杂度O(M) + O(N*logN)fn game2(arr: &mut Vec<i32>, op: &mut Vec<Vec<i32>>) -> Vec<i32> { let n = arr.len() as i32; let m = op.len() as i32; let mut stack: Vec<i32> = repeat(0).take(m as usize).collect(); let mut r = 0; for i in 0..m { while r != 0 && op[stack[(r - 1) as usize] as usize][0] <= op[i as usize][0] { r -= 1; } stack[r as usize] = i; r += 1; } let mut ans: Vec<i32> = repeat(0).take(n as usize).collect(); let mut ansi = n - 1; let mut l = 0; while ansi >= op[stack[l as usize] as usize][0] { ans[ansi as usize] = arr[ansi as usize]; ansi -= 1; } let mut sorted: BTreeSet<Number> = BTreeSet::new(); for i in 0..op[stack[l as usize] as usize][0] { sorted.insert(Number::new(arr[i as usize], i)); } while l != r { // 当前处理的指令 let cur = &op[stack[l as usize] as usize]; l += 1; if l != r { let mut next = &op[stack[l as usize] as usize]; let num = cur[0] - next[0]; if cur[1] == 0 { for i in 0..num { ans[ansi as usize] = sorted.pop_last().unwrap().value; ansi -= 1; } } else { for i in 0..num { ans[ansi as usize] = sorted.pop_first().unwrap().value; ansi -= 1; } } } else { if cur[1] == 0 { while sorted.len() > 0 { ans[ansi as usize] = sorted.pop_last().unwrap().value; ansi -= 1; } } else { while sorted.len() > 0 { ans[ansi as usize] = sorted.pop_first().unwrap().value; ansi -= 1; } } } } return ans;}
struct Number { value: i32, index: i32,}
impl Number { fn new(v: i32, i: i32) -> Self { Self { value: v, index: i } }}
impl Ord for Number { fn cmp(&self, other: &Self) -> Ordering { if self.value != other.value { self.value.cmp(&other.value) } else { self.index.cmp(&other.index) } }}
impl PartialOrd for Number { fn partial_cmp(&self, other: &Self) -> Option<Ordering> { Some(self.cmp(other)) }}
impl PartialEq for Number { fn eq(&self, other: &Self) -> bool { (self.value, &self.index) == (other.value, &other.index) }}
impl Eq for Number {}
// 为了测试fn random_array(n: i32, v: i32) -> Vec<i32> { let mut ans: Vec<i32> = repeat(0).take(n as usize).collect(); for i in 0..n { ans[i as usize] = rand::thread_rng().gen_range(0, v) + 1; } return ans;}
// 为了测试fn random_op(m: i32, n: i32) -> Vec<Vec<i32>> { let mut ans: Vec<Vec<i32>> = repeat(repeat(0).take(2).collect()) .take(m as usize) .collect(); for i in 0..m { ans[i as usize][0] = rand::thread_rng().gen_range(0, n + 1); ans[i as usize][1] = rand::thread_rng().gen_range(0, 2); } return ans;}
// 为了测试fn is_equal(arr1: &mut Vec<i32>, arr2: &mut Vec<i32>) -> bool { if arr1.len() != arr2.len() { return false; } for i in 0..arr1.len() { if arr1[i as usize] != arr2[i as usize] { return false; } } return true;}
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