题目
题目链接：
https://www.nowcoder.com/practice/c754e7a920614cba9b8b692ba9b20b5d
核心
堆，或者叫优先级队列
参考答案Java
java
import java.util.*;
public class Solution {
/**
* 代码中的类名、方法名、参数名已经指定，请勿修改，直接返回方法规定的值即可
*
*
* @param matrix int整型ArrayList<ArrayList<>>
* @param k int整型
* @return int整型
*/
public int KthinMatrix (ArrayList<ArrayList<Integer>> matrix, int k) {
//优先级队列
int n = matrix.size(); //行和列都是n
boolean[][] visited = new boolean[n][n];
PriorityQueue<int[]> pq = new PriorityQueue<>(new Comparator<int[]>() {
public int compare(int[] a,
int[] b) { //int[]:0:横坐标x 1：纵坐标y 2：xy对应的位置值
return matrix.get(a[0]).get(a[1]) - matrix.get(b[0]).get(b[1]);
}
});
int[] root = {0, 0, matrix.get(0).get(0)};
visited[0][0] = true;
pq.add(root);
for (int i = 0; i < k - 1 ; i++) {
int[] cur = pq.poll();
int x = cur[0];
int y = cur[1];
if (x < n && y + 1 < matrix.get(x).size() && !visited[x][y + 1]) {
visited[x][y + 1] = true;
pq.add(new int[] {x, y + 1, matrix.get(x).get(y + 1)});
}
if (x + 1 < n && y < matrix.get(x).size() && !visited[x + 1][y]) {
visited[x + 1][y] = true;
pq.add(new int[] {x + 1, y, matrix.get(x + 1).get(y)});
}
}
return pq.poll()[2];
}
}参考答案Go
go
package main
/**
* 代码中的类名、方法名、参数名已经指定，请勿修改，直接返回方法规定的值即可
*
*
* @param matrix int整型二维数组
* @param k int整型
* @return int整型
*/
func KthinMatrix(matrix [][]int, k int) int {
//优先级队列，堆
n := len(matrix)
visited := make([][]bool, n)
for i := 0; i < n; i++ {
visited[i] = make([]bool, n)
}
pq := &MyPQ{make([]PQNode, 10), 0, 10}
pq.add(0, 0, matrix[0][0])
visited[0][0] = true
for i := 0; i < k-1; i++ {
poll := pq.poll()
x := poll.x
y := poll.y
if x < n && y+1 < n && !visited[x][y+1] { //题目说了矩阵n*n
pq.add(x, y+1, matrix[x][y+1])
visited[x][y+1] = true
}
if x+1 < n && y < n && !visited[x+1][y] {
pq.add(x+1, y, matrix[x+1][y])
visited[x+1][y] = true
}
}
return pq.poll().data
}
// 本答案用小顶堆，从上往下递增
type PQNode struct {
x int //横坐标
y int //纵坐标
data int //坐标值
}
type MyPQ struct {
arr []PQNode
size int
defaultSize int
}
func (pq *MyPQ) ensureCap(cap int) { //堆的扩容
curlen := len(pq.arr)
if curlen >= cap {
return
}
newlen := curlen + curlen>>1
newarr := make([]PQNode, newlen)
for i := 0; i < curlen; i++ {
newarr[i] = pq.arr[i]
}
pq.arr = newarr
}
func (pq *MyPQ) add(x, y, data int) {
pq.ensureCap(pq.size + 1)
node := PQNode{x, y, data}
pq.arr[pq.size] = node
pq.shiftup(pq.size)
pq.size++
}
// 上滤
func (pq *MyPQ) shiftup(idx int) {
root := pq.arr[idx]
for idx > 0 {
pidx := (idx - 1) >> 1
pdata := pq.arr[pidx]
if pdata.data < root.data {
break
}
pq.arr[idx] = pdata
idx = pidx
}
pq.arr[idx] = root
}
// 获取并删除堆顶元素，然后下窜，整理堆
func (pq *MyPQ) poll() PQNode {
root := pq.arr[0]
//fmt.Println("root:", root.data)
pq.arr[0] = pq.arr[pq.size-1]
pq.size -= 1
pq.shiftdown(0)
return root
}
func (pq *MyPQ) shiftdown(idx int) {
root := pq.arr[idx]
half := pq.size >> 1 //核心1: 用位移，别用除法
for idx < half {
childidx := (idx << 1) + 1 //核心2: 用位移，别用乘法
rightidx := childidx + 1
child := pq.arr[childidx]
//小顶堆，哪个子节点更小，哪边就上去
if rightidx < pq.size && pq.arr[childidx].data > pq.arr[rightidx].data {
childidx = rightidx
child = pq.arr[rightidx]
}
if child.data >= root.data {
break
}
pq.arr[idx] = child
idx = childidx
}
pq.arr[idx] = root
}参考答案PHP
php
<?php
/**
* 代码中的类名、方法名、参数名已经指定，请勿修改，直接返回方法规定的值即可
*
*
* @param matrix int整型二维数组
* @param k int整型
* @return int整型
*/
function KthinMatrix( $matrix , $k )
{
// 堆，优先级队列
$pq = new PQ();
$n =count($matrix);
$visited = [];
for($i=0;$i<$n;$i++){
for($j=0;$j<$n;$j++){
$visited[$i][$j] =false;
}
}
$pq->add(0,0,$matrix[0][0]);
$visited[0][0]= true;
for($i=0;$i<$k-1;$i++){
$poll = $pq->poll();
$x = $poll[0];
$y = $poll[1];
if($x <$n && $y+1<$n && !$visited[$x][$y+1]){
$pq->add($x,$y+1,$matrix[$x][$y+1]);
$visited[$x][$y+1]=true;
}
if($x+1<$n&&$y<$n && !$visited[$x+1][$y]){
$pq->add($x+1,$y,$matrix[$x+1][$y]);
$visited[$x+1][$y]=true;
}
}
return $pq->poll()[2];
}
//本答案用对，小顶对，也就是从上往下是递增的
class PQ{
public $arr=[]; //二维数组，0：横坐标 1：纵坐标 2：坐标值
public $defaultsize =10;
public $size;
public function __construct()
{
$this->size =0;
for($i=0;$i<$this->defaultsize;$i++){
$this->arr[$i] =[];
}
}
public function ensurecap($cap){
$curlen =count($this->arr);
if($curlen >= $cap){
return;
}
$newlen = $curlen+$curlen>>1;
$newarr = [];
for($i=0;$i<$newlen;$i++){
if($i<$curlen){
$newarr[$i] = $this->arr[$i];
}else{
$newarr[$i] =[];
}
}
$this->arr = $newarr;
}
public function add($x,$y,$data){
$this->ensurecap($this->size+1);
$this->arr[$this->size] = [$x,$y,$data];
$this->shiftup($this->size);
$this->size++;
}
//上滤
public function shiftup($idx){
$root = $this->arr[$idx];
while ($idx>0){
$pidx = ($idx-1) >>1;
$parent= $this->arr[$pidx];
if($parent[2] <=$root[2]){ //当前节点比父节点大，退出
break;
}
$this->arr[$idx] = $parent;
$idx = $pidx;
}
$this->arr[$idx] = $root;
}
public function poll() {
$root = $this->arr[0];
$this->arr[0] = $this->arr[$this->size-1];
$this->size-=1;
$this->shiftdown(0);
return $root;
}
//下窜
public function shiftdown($idx){
$root = $this->arr[$idx];
$half = $this->size >>1;
while ($idx<$half){
$childidx = ($idx << 1)+1;
$rightidx = $childidx+1;
$child = $this->arr[$childidx];
if($rightidx<$this->size && $child[2] > $this->arr[$rightidx][2]){
$childidx = $rightidx;
$child = $this->arr[$rightidx];
}
if($child[2] >=$root[2]){
break;
}
$this->arr[$idx] = $child;
$idx =$childidx;
}
$this->arr[$idx] = $root;
}
}