数组的最大与和。
给你一个长度为 n 的整数数组 nums 和一个整数 numSlots ,满足2 * numSlots >= n 。总共有 numSlots 个篮子,编号为 1 到 numSlots 。
你需要把所有 n 个整数分到这些篮子中,且每个篮子 至多 有 2 个整数。一种分配方案的 与和 定义为每个数与它所在篮子编号的 按位与运算 结果之和。
比方说,将数字 [1, 3] 放入篮子 1 中,[4, 6] 放入篮子 2 中,这个方案的与和为 (1 AND 1) + (3 AND 1) + (4 AND 2) + (6 AND 2) = 1 + 1 + 0 + 2 = 4 。
请你返回将 nums 中所有数放入 numSlots 个篮子中的最大与和。
力扣2172。
km算法。
代码用rust编写。代码如下:
fn main() {
let mut nums: Vec<i32> = vec![1, 2, 3, 4, 5, 6];
let ans = maximum_and_sum(&mut nums, 3);
println!("ans = {}", ans);
}
fn maximum_and_sum(arr: &mut Vec<i32>, mut m: i32) -> i32 {
m <<= 1;
let mut graph: Vec<Vec<i32>> = vec![];
for i in 0..m {
graph.push(vec![]);
for _ in 0..m {
graph[i as usize].push(0);
}
}
for i in 0..arr.len() as i32 {
let mut j = 0;
let mut num = 1;
while j < m {
graph[i as usize][j as usize] = arr[i as usize] & num;
graph[i as usize][(j + 1) as usize] = arr[i as usize] & num;
num += 1;
j += 2;
}
}
return km(&mut graph);
}
fn get_max<T: Clone + Copy + std::cmp::PartialOrd>(a: T, b: T) -> T {
if a > b {
a
} else {
b
}
}
fn get_min<T: Clone + Copy + std::cmp::PartialOrd>(a: T, b: T) -> T {
if a < b {
a
} else {
b
}
}
fn km(graph: &mut Vec<Vec<i32>>) -> i32 {
let nn = graph.len() as i32;
let mut match0: Vec<i32> = vec![];
let mut lx: Vec<i32> = vec![];
let mut ly: Vec<i32> = vec![];
// dfs过程中,碰过的点!
let mut x: Vec<bool> = vec![];
let mut y: Vec<bool> = vec![];
// 降低的预期!
// 公主上,打一个,降低预期的值,只维持最小!
let mut slack: Vec<i32> = vec![];
let mut falsev: Vec<bool> = vec![];
for _ in 0..nn {
match0.push(0);
lx.push(0);
ly.push(0);
x.push(false);
y.push(false);
slack.push(0);
falsev.push(false);
}
let invalid = 2147483647;
for i in 0..nn {
match0[i as usize] = -1;
lx[i as usize] = -invalid;
for j in 0..nn {
lx[i as usize] = get_max(lx[i as usize], graph[i as usize][j as usize]);
}
ly[i as usize] = 0;
}
for from in 0..nn {
for i in 0..nn {
slack[i as usize] = invalid;
}
x = falsev.clone();
y = falsev.clone();
// dfs() : from王子,能不能不降预期,匹配成功!
// 能:dfs返回true!
// 不能:dfs返回false!
while !dfs(
from,
&mut x,
&mut y,
&mut lx,
&mut ly,
&mut match0,
&mut slack,
graph,
) {
// 刚才的dfs,失败了!
// 需要拿到,公主的slack里面,预期下降幅度的最小值!
let mut d = invalid;
for i in 0..nn {
if !y[i as usize] && slack[i as usize] < d {
d = slack[i as usize];
}
}
// 按照最小预期来调整预期
for i in 0..nn {
if x[i as usize] {
lx[i as usize] = lx[i as usize] - d;
}
if y[i as usize] {
ly[i as usize] = ly[i as usize] + d;
}
}
x = falsev.clone();
y = falsev.clone();
// 然后回到while里,再次尝试
}
}
let mut ans = 0;
for i in 0..nn {
ans += lx[i as usize] + ly[i as usize];
}
return ans;
}
// from, 当前的王子
// x,王子碰没碰过
// y, 公主碰没碰过
// lx,所有王子的预期
// ly, 所有公主的预期
// match,所有公主,之前的分配,之前的爷们!
// slack,连过,但没允许的公主,最小下降的幅度
// map,报价,所有王子对公主的报价
// 返回,from号王子,不降预期能不能配成!
fn dfs(
from: i32,
x: &mut Vec<bool>,
y: &mut Vec<bool>,
lx: &mut Vec<i32>,
ly: &mut Vec<i32>,
match0: &mut Vec<i32>,
slack: &mut Vec<i32>,
map: &mut Vec<Vec<i32>>,
) -> bool {
let nn = map.len() as i32;
x[from as usize] = true;
for to in 0..nn {
if !y[to as usize] {
// 只有没dfs过的公主,才会去尝试
let d = lx[from as usize] + ly[to as usize] - map[from as usize][to as usize];
if d != 0 {
// 如果当前的路不符合预期,更新公主的slack值
slack[to as usize] = get_min(slack[to as usize], d);
} else {
// 如果当前的路符合预期,尝试直接拿下,或者抢夺让之前的安排倒腾去
y[to as usize] = true;
if match0[to as usize] == -1
|| dfs(match0[to as usize], x, y, lx, ly, match0, slack, map)
{
match0[to as usize] = from;
return true;
}
}
}
}
return false;
}
执行结果如下: