2022-10-27：设计一个数据结构，有效地找到给定子数组的 多数元素 。
子数组的 多数元素 是在子数组中出现 threshold 次数或次数以上的元素。
实现 MajorityChecker 类:
MajorityChecker(int[] arr)
会用给定的数组 arr 对 MajorityChecker 初始化。
int query(int left, int right, int threshold)
返回子数组中的元素 arr[left...right] 至少出现 threshold 次数，
如果不存在这样的元素则返回 -1。
答案2022-10-27：
线段树。
力扣1157，rust测试见图。
代码用rust编写。代码如下：
代码语言：javascript复制use std::iter::repeat;
struct MajorityChecker {
st: SegmentTree,
cq: CountQuicker,
}
struct SegmentTree {
n: i32,
candidate: Vec<i32>,
hp: Vec<i32>,
}
impl SegmentTree {
pub fn new(arr: &mut Vec<i32>) -> Self {
let n = arr.len() as i32;
let candidate: Vec<i32> = repeat(0).take(((n 1) << 2) as usize).collect();
let hp: Vec<i32> = repeat(0).take(((n 1) << 2) as usize).collect();
let mut ans = SegmentTree { n, candidate, hp };
ans.build(arr, 1, n, 1);
return ans;
}
fn build(&mut self, arr: &mut Vec<i32>, l: i32, r: i32, rt: i32) {
if l == r {
self.candidate[rt as usize] = arr[(l - 1) as usize];
self.hp[rt as usize] = 1;
} else {
let m = (l r) >> 1;
self.build(arr, l, m, rt << 1);
self.build(arr, m 1, r, rt << 1 | 1);
let lc = self.candidate[(rt << 1) as usize];
let rc = self.candidate[(rt << 1 | 1) as usize];
let lh = self.hp[(rt << 1) as usize];
let rh = self.hp[(rt << 1 | 1) as usize];
if lc == rc {
self.candidate[rt as usize] = lc;
self.hp[rt as usize] = lh rh;
} else {
self.candidate[rt as usize] = if lh >= rh { lc } else { rc };
self.hp[rt as usize] = i32::abs(lh - rh);
}
}
}
pub fn query(&mut self, left: i32, right: i32) -> i32 {
return self.query0(left 1, right 1, 1, self.n, 1)[0];
}
fn query0(&mut self, ll: i32, rr: i32, l: i32, r: i32, rt: i32) -> Vec<i32> {
if ll <= l && r <= rr {
return vec![self.candidate[rt as usize], self.hp[rt as usize]];
}
let m = (l r) >> 1;
if rr <= m {
return self.query0(ll, rr, l, m, rt << 1);
} else if ll > m {
return self.query0(ll, rr, m 1, r, rt << 1 | 1);
} else {
let mut ansl = self.query0(ll, rr, l, m, rt << 1);
let mut ansr = self.query0(ll, rr, m 1, r, rt << 1 | 1);
if ansl[0] == ansr[0] {
ansl[1] = ansr[1];
return ansl;
} else {
if ansl[1] >= ansr[1] {
ansl[1] -= ansr[1];
return ansl;
} else {
ansr[1] -= ansl[1];
return ansr;
}
}
}
}
}
struct CountQuicker {
cnt: Vec<Vec<i32>>,
}
impl CountQuicker {
pub fn new(arr: &mut Vec<i32>) -> Self {
let mut cnt: Vec<Vec<i32>> = vec![];
let max = *arr.iter().max().unwrap_or(&0);
for _i in 0..=max {
cnt.push(vec![]);
}
for i in 0..arr.len() as i32 {
cnt[arr[i as usize] as usize].push(i);
}
return Self { cnt };
}
pub fn real_times(&mut self, left: i32, right: i32, num: i32) -> i32 {
self.size(num, right) - self.size(num, left - 1)
}
fn size(&mut self, indies_index: i32, index: i32) -> i32 {
let mut l = 0;
let mut r = self.cnt[indies_index as usize].len() as i32 - 1;
let mut m: i32;
let mut ans = -1;
while l <= r {
m = (l r) / 2;
if self.cnt[indies_index as usize][m as usize] <= index {
ans = m;
l = m 1;
} else {
r = m - 1;
}
}
return ans 1;
}
}
impl MajorityChecker {
fn new(arr: Vec<i32>) -> Self {
let mut arr = arr;
let st = SegmentTree::new(&mut arr);
let cq = CountQuicker::new(&mut arr);
Self { st, cq }
}
fn query(&mut self, left: i32, right: i32, threshold: i32) -> i32 {
let candidate = self.st.query(left, right);
return if self.cq.real_times(left, right, candidate) >= threshold {
candidate
} else {
-1
};
}
}
fn main() {
let arr = vec![1, 1, 2, 2, 1, 1];
let mut majority_checker = MajorityChecker::new(arr);
let ans = majority_checker.query(0, 5, 4); // 返回 1
println!("ans = {:?}", ans);
let ans = majority_checker.query(0, 3, 3); // 返回 -1
println!("ans = {:?}", ans);
let ans = majority_checker.query(2, 3, 2); // 返回 2
println!("ans = {:?}", ans);
}
执行结果如下：
***
[左神java代码](https://github.com/algorithmzuo/weekly-problems/blob/main/src/class_2022_08_1_week/Code03_OnlineMajorityElementInSubarray.java)
