HackerRank Find the Path Problem Solution
In this post, we well solve HackerRank Find the Path Problem Solution.
You are given a table, a. with n rows and m columns. The top-left corner of the table has coordinates (0, 0), and the bottom-right corner has coordinates (n-1, m-1). The th cell contains integer aj.
A path in the table is a sequence of cells (r1, 1), (r2, C2),…, (rk, Ck) such that for each {1,…,k-1}, cell (r, c) and cell (ri+1, C++1) share a side.
The weight of the path (r₁, c₁), (r₂, C2),…, (rk, Ck) is defined by 1 ar,,&, where
arc is the weight of the cell (r, c).
You must answer q queries. In each query, you are given the coordinates of two cells, (ri, ci) and (r2, C2). You must find and print the minimum possible weight of a path connecting them.
Note: A cell can share sides with at most 4 other cells. A cell with coordinates (r, c) shares sides with (r-1,c), (r+1,c), (r, c-1) and (r, c + 1).
Input Format
The first line contains 2 space-separated integers, n (the number of rows in a) and m (the number of columns in a), respectively.
Each of n subsequent lines contains m space-separated integers. The th integer in the ¿th
line denotes the value of aij.
The next line contains a single integer, q, denoting the number of queries.
Each of the q subsequent lines describes a query in the form of 4 space-separated integers:
- C1, r2, and c₂, respectively.
Sample Input
3 5
0 0 0 0 0
1 9 9 9 1
0 0 0 0 0
3
0 0 2 4
0 3 2 3
1 1 1 3
Sample Output
1
1
18
Find the Path C Solution
#include <stdio.h>
#include <stdlib.h>
#define INF 1000000000
typedef struct{
int i;
int j;
int w;
} node;
int min(int x,int y);
void build(int v,int l,int r);
void solve(int v,int l,int r);
void DJ(int si,int sj,int l,int r,int **d);
void heap_insert(node *elem,int *size);
void heap_update(node *elem);
void heap_read(int *size,node *ans);
int n,r1,c1,r2,c2,ans,a[7][5000],heap_list[7][5000],****d;
node heap[40000];
int main(){
int m,q,i,j;
scanf("%d%d",&n,&m);
d=(int****)malloc(m*4*sizeof(int***));
for(i=0;i<n;i++)
for(j=0;j<m;j++)
scanf("%d",&a[i][j]);
build(1,0,m-1);
scanf("%d",&q);
while(q--){
scanf("%d%d%d%d",&r1,&c1,&r2,&c2);
ans=INF;
solve(1,0,m-1);
printf("%d\n",ans);
}
return 0;
}
int min(int x,int y){
return (x<y)?x:y;
}
void build(int v,int l,int r){
int tm,i,j;
tm=(l+r)/2;
d[v]=(int***)malloc(n*sizeof(int**));
for(i=0;i<n;i++){
d[v][i]=(int**)malloc(n*sizeof(int*));
for(j=0;j<n;j++)
d[v][i][j]=(int*)malloc((r-l+1)*sizeof(int));
DJ(i,tm-l,l,r,d[v][i]);
}
if(l!=r){
build(2*v,l,tm);
build(2*v+1,tm+1,r);
}
return;
}
void solve(int v,int l,int r){
int tm,i;
tm=(l+r)/2;
for(i=0;i<n;i++)
ans=min(ans,d[v][i][r1][c1-l]+d[v][i][r2][c2-l]+a[i][tm]);
if(c1<tm && c2<tm)
solve(2*v,l,tm);
else if(c1>tm && c2>tm)
solve(2*v+1,tm+1,r);
return;
}
void DJ(int si,int sj,int l,int r,int **d){
int i,j,next_solve_i,next_solve_j,heap_size=0;
node elem;
for(i=0;i<n;i++)
for(j=0;j<r-l+1;j++)
d[i][j]=-1;
d[si][sj]=0;
next_solve_i=si;
next_solve_j=sj;
while(1){
if(next_solve_i){
if(d[next_solve_i-1][next_solve_j]==-1 || d[next_solve_i-1][next_solve_j]>d[next_solve_i][next_solve_j]+a[next_solve_i-1][next_solve_j+l]){
elem.i=next_solve_i-1;
elem.j=next_solve_j;
elem.w=d[next_solve_i][next_solve_j]+a[next_solve_i-1][next_solve_j+l];
if(d[next_solve_i-1][next_solve_j]==-1)
heap_insert(&elem,&heap_size);
else
heap_update(&elem);
d[next_solve_i-1][next_solve_j]=d[next_solve_i][next_solve_j]+a[next_solve_i-1][next_solve_j+l];
}
}
if(next_solve_i+1<n){
if(d[next_solve_i+1][next_solve_j]==-1 || d[next_solve_i+1][next_solve_j]>d[next_solve_i][next_solve_j]+a[next_solve_i+1][next_solve_j+l]){
elem.i=next_solve_i+1;
elem.j=next_solve_j;
elem.w=d[next_solve_i][next_solve_j]+a[next_solve_i+1][next_solve_j+l];
if(d[next_solve_i+1][next_solve_j]==-1)
heap_insert(&elem,&heap_size);
else
heap_update(&elem);
d[next_solve_i+1][next_solve_j]=d[next_solve_i][next_solve_j]+a[next_solve_i+1][next_solve_j+l];
}
}
if(next_solve_j){
if(d[next_solve_i][next_solve_j-1]==-1 || d[next_solve_i][next_solve_j-1]>d[next_solve_i][next_solve_j]+a[next_solve_i][next_solve_j-1+l]){
elem.i=next_solve_i;
elem.j=next_solve_j-1;
elem.w=d[next_solve_i][next_solve_j]+a[next_solve_i][next_solve_j-1+l];
if(d[next_solve_i][next_solve_j-1]==-1)
heap_insert(&elem,&heap_size);
else
heap_update(&elem);
d[next_solve_i][next_solve_j-1]=d[next_solve_i][next_solve_j]+a[next_solve_i][next_solve_j-1+l];
}
}
if(next_solve_j+1+l<=r){
if(d[next_solve_i][next_solve_j+1]==-1 || d[next_solve_i][next_solve_j+1]>d[next_solve_i][next_solve_j]+a[next_solve_i][next_solve_j+1+l]){
elem.i=next_solve_i;
elem.j=next_solve_j+1;
elem.w=d[next_solve_i][next_solve_j]+a[next_solve_i][next_solve_j+1+l];
if(d[next_solve_i][next_solve_j+1]==-1)
heap_insert(&elem,&heap_size);
else
heap_update(&elem);
d[next_solve_i][next_solve_j+1]=d[next_solve_i][next_solve_j]+a[next_solve_i][next_solve_j+1+l];
}
}
if(heap_size==0)
break;
heap_read(&heap_size,&elem);
next_solve_i=elem.i;
next_solve_j=elem.j;
}
return;
}
void heap_insert(node *elem,int *size){
(*size)++;
int index=(*size);
while(index>1 && elem->w<heap[index/2].w){
heap[index]=heap[index/2];
heap_list[heap[index].i][heap[index].j]=index;
index/=2;
}
heap[index]=(*elem);
heap_list[elem->i][elem->j]=index;
return;
}
void heap_update(node *elem){
int index=heap_list[elem->i][elem->j];
while(index>1 && elem->w<heap[index/2].w){
heap[index]=heap[index/2];
heap_list[heap[index].i][heap[index].j]=index;
index/=2;
}
heap[index]=(*elem);
heap_list[elem->i][elem->j]=index;
return;
}
void heap_read(int *size,node *ans){
(*ans)=heap[1];
int index=1;
while(index*2<*size && heap[*size].w>heap[index*2].w || index*2+1<*size && heap[*size].w>heap[index*2+1].w){
index=(heap[index*2].w>heap[index*2+1].w)?index*2+1:index*2;
heap[index/2]=heap[index];
heap_list[heap[index].i][heap[index].j]=index/2;
}
heap[index]=heap[*size];
heap_list[heap[index].i][heap[index].j]=index;
(*size)--;
return;
}Find the Path C++ Solution
#include <bits/stdc++.h>
using namespace std;
int N, M;
vector<vector<int64_t>> G;
const int64_t INF = 1e11;
vector<vector<int64_t>> dijk(int r, int c, int L, int R) {
set<pair<int64_t, pair<int, int>>> Q;
vector<vector<int64_t>> D(N, vector<int64_t>(R-L+1, INF));
Q.insert(make_pair(0, make_pair(r,c)));
vector<vector<int>> dirs = {{1,0},{0,1},{-1,0},{0,-1}};
while (!Q.empty()) {
auto curr = *Q.begin();
Q.erase(Q.begin());
int64_t d = curr.first;
int r = curr.second.first, c = curr.second.second;
if (d > D[r][c-L]) {
continue;
}
D[r][c-L] = d;
for (auto dir : dirs) {
int cr = r+dir[0];
int cc = c+dir[1];
if (cr < 0 || cc < L || cr >= N || cc > R)
continue;
int64_t cd = d + G[cr][cc];
if (cd < D[cr][cc-L]) {
Q.insert(make_pair(cd, make_pair(cr, cc)));
D[cr][cc-L] = cd;
}
}
}
return D;
}
vector<vector<int>> Qs;
vector<int64_t> ans;
vector<unordered_map<int, pair<int, vector<vector<int64_t>>>>> SPs(7);
void div_and_conq(int l, int r, vector<int> Qis) {
if (l > r)
return;
int mid = (r+l)/2;
for (int i = 0; i < N; ++i) {
SPs[i][mid] = make_pair(l, dijk(i, mid, l, r));
}
vector<int> Qls, Qrs;
for (int i : Qis) {
if (Qs[i][1] < mid && Qs[i][3] < mid) {
Qls.push_back(i);
} else if (Qs[i][1] > mid && Qs[i][3] > mid) {
Qrs.push_back(i);
} else {
for (int j = 0; j < N; ++j) {
for (auto& kv : SPs[j]) {
int mid = kv.first;
int upperl = kv.second.first;
auto& SP = kv.second.second;
int64_t d = SP[Qs[i][0]][Qs[i][1]-upperl]+SP[Qs[i][2]][Qs[i][3]-upperl]+G[j][mid];
ans[i] = min(ans[i], d);
}
}
}
}
div_and_conq(l, mid-1, Qls);
div_and_conq(mid+1, r, Qrs);
for (int i = 0; i < N; ++i) {
SPs[i].erase(mid);
}
}
int main() {
ios::sync_with_stdio(false);
cin >> N >> M;
G.assign(N, vector<int64_t>(M));
for (auto &v : G) {
for (int64_t& i : v) {
cin >> i;
}
}
int Q;
cin >> Q;
Qs.resize(Q);
ans.assign(Q, INF);
vector<int> Qis;
for (int i = 0; i < Q; ++i) {
int a,b,c,d;
cin >> a >> b >> c >> d;
Qs[i] = {a,b,c,d};
Qis.push_back(i);
}
div_and_conq(0, M-1, Qis);
for (int64_t i : ans) {
cout << i << endl;
}
return 0;
}Find the Path C Sharp Solution
using System.CodeDom.Compiler;
using System.Collections.Generic;
using System.Collections;
using System.ComponentModel;
using System.Diagnostics.CodeAnalysis;
using System.Globalization;
using System.IO;
using System.Linq;
using System.Reflection;
using System.Runtime.Serialization;
using System.Text.RegularExpressions;
using System.Text;
using System;
struct Node
{
public int w;
public int r;
public int c;
public Node(int w, int r, int c){
this.w = w;
this.r = r;
this.c = c;
}
}
class Heap
{
public int length = 0;
private Node[] heap;
public Heap(int n, int m){
this.heap = new Node[(int)(n*m*0.67)];
}
public void initialize(){
this.length = 0;
}
public void push (Node node){
this.heap[this.length] = node;
this.length++;
int node_w=node.w, node_i=this.length-1, parent_i;
while (node_i>0){
parent_i = (node_i-1)/2;
if (node_w>=this.heap[parent_i].w){
break;
}
else{
this.heap[node_i] = this.heap[parent_i];
this.heap[parent_i] = node;
node_i = parent_i;
}
}
}
public Node pop(){
Node node=this.heap[this.length-1], node_return=this.heap[0];
this.heap[0] = node;
this.length--;
int node_w=node.w, node_i=0,
child_l_i=node_i*2+1, child_r_i=child_l_i+1, child_s_i;
while (child_l_i<this.length){
if (child_r_i<this.length){
if (this.heap[child_r_i].w<this.heap[child_l_i].w){
child_s_i = child_r_i;
}
else{
child_s_i = child_l_i;
}
}
else{
child_s_i = child_l_i;
}
if (node_w<this.heap[child_s_i].w){
break;
}
else{
this.heap[node_i] = this.heap[child_s_i];
this.heap[child_s_i] = node;
node_i = child_s_i;
child_l_i = node_i*2+1;
child_r_i = child_l_i+1;
}
}
return node_return;
}
}
class Collectively
{
private int n, m, max_w;
private int [] middle_w;
private int [,,] map;
private List<List<int>> a;
private Heap heap;
public Collectively(List<List<int>> a, int n, int m, int max_w){
this.a = a;
this.n = n;
this.m = m;
this.max_w = max_w;
this.middle_w = new int[this.n];
this.map = new int[this.n, this.n, this.m];
this.heap = new Heap(n, m);
}
public float update_map(int left, int middle, int right){
int to_fill=(right-left+1)*this.n, filled=1, filled_all=1, w, r, r_, c, c_;
bool[,] explored;
Node node;
for (int i_n=0; i_n<this.n; i_n++){
this.middle_w[i_n] = this.a[i_n][middle];
explored = new bool[this.n, this.m];
heap.initialize();
heap.push(new Node(this.a[i_n][middle], i_n, middle));
explored[i_n, middle] = true;
this.map[i_n, i_n, middle] = this.a[i_n][middle];
filled = 1;
filled_all = 1;
while (true){
node = heap.pop();
if (filled>=to_fill){
break;
}
w = node.w;
c = node.c;
r = node.r;
c_ = c;
if (r>0){
r_ = r-1;
if (!explored[r_, c_]){
heap.push(new Node(this.a[r_][c_]+w, r_, c_));
explored[r_, c_] = true;
this.map[i_n, r_, c_] = this.a[r_][c_]+w;
filled_all += 1;
if (c_>=left && c_<=right){
filled++;
}
}
}
if (r<this.n-1){
r_ = r+1;
if (!explored[r_, c_]){
heap.push(new Node(this.a[r_][c_]+w, r_, c_));
explored[r_, c_] = true;
this.map[i_n, r_, c_] = this.a[r_][c_]+w;
filled_all += 1;
if (c_>=left && c_<=right){
filled++;
}
}
}
r_ = r;
if (c>0){
c_ = c-1;
if (!explored[r_, c_]){
heap.push(new Node(this.a[r_][c_]+w, r_, c_));
explored[r_, c_] = true;
this.map[i_n, r_, c_] = this.a[r_][c_]+w;
filled_all += 1;
if (c_>=left && c_<=right){
filled++;
}
}
}
if (c<this.m-1){
c_ = c+1;
if (!explored[r_, c_]){
heap.push(new Node(this.a[r_][c_]+w, r_, c_));
explored[r_, c_] = true;
this.map[i_n, r_, c_] = this.a[r_][c_]+w;
filled_all += 1;
if (c_>=left && c_<=right){
filled++;
}
}
}
}
}
return (float)(filled_all) / (float)(filled);
}
public int get_min_w(List<int> query){
int min_w = this.max_w, w;
for (int i_n=0; i_n<this.n; i_n++){
w = this.map[i_n, query[0], query[1]] +
this.map[i_n, query[2], query[3]] -
this.middle_w[i_n];
if (w<min_w){
min_w = w;
}
}
return min_w;
}
}
class Individually
{
private int n, m;
private List<List<int>> a;
private Heap heap;
public Individually(List<List<int>> a, int n, int m){
this.a = a;
this.n = n;
this.m = m;
this.heap = new Heap(n, m);
}
public int get_min_w(List<int> query){
int w, distance, r, r_, c, c_,
r_1 = query[0], c_1 = query[1], r_2 = query[2], c_2 = query[3];
bool[,] explored = new bool[this.n, this.m];
Node node;
heap.initialize();
explored[r_1, c_1] = true;
heap.push(new Node(this.a[r_1][c_1], r_1, c_1));
while (true){
node = heap.pop();
w = node.w;
c = node.c;
r = node.r;
distance = Math.Abs(r-r_2)+Math.Abs(c-c_2);
if (distance<=1){
if (distance==1){
return w+a[r_2][c_2];
}
else{
return w;
}
}
c_ = c;
if (r>0){
r_ = r-1;
if (!explored[r_, c_]){
heap.push(new Node(a[r_][c_]+w, r_, c_));
explored[r_, c_] = true;
}
}
if (r<n-1){
r_ = r+1;
if (!explored[r_, c_]){
heap.push(new Node(a[r_][c_]+w, r_, c_));
explored[r_, c_] = true;
}
}
r_ = r;
if (c>0){
c_ = c-1;
if (!explored[r_, c_]){
heap.push(new Node(a[r_][c_]+w, r_, c_));
explored[r_, c_] = true;
}
}
if (c<m-1){
c_ = c+1;
if (!explored[r_, c_]){
heap.push(new Node(a[r_][c_]+w, r_, c_));
explored[r_, c_] = true;
}
}
}
}
}
class WorkSpace
{
private int n, m;
public int[] result;
private List<List<int>> a, queries, index_remained;
private bool[] index_solved;
private Collectively collectively;
private Individually individually;
public WorkSpace(List<List<int>> a, List<List<int>> queries){
this.n = a.Count();
this.m = a[0].Count();
this.result = new int[queries.Count()];
this.a = a;
this.queries = queries;
// this.index_remained = new List<List<int>>();
this.index_solved = new bool[queries.Count()];
this.collectively = new Collectively(a, n, m, 3000*n*m+1);
this.individually = null;
}
public void solve(List<int> index_to_solve, int left, int right){
int middle = (int)((left + right) / 2);
List<int> index_solving = new List<int>();
List<int> index_unsolved_left = new List<int>();
List<int> index_unsolved_right = new List<int>();
foreach (int index in index_to_solve){
int dc_1 = this.queries[index][1] - middle,
dc_2 = this.queries[index][3] - middle;
if (dc_1*dc_2<=0){
index_solving.Add(index);
}
else if (dc_1<0){
index_unsolved_left.Add(index);
}
else if (dc_1>0){
index_unsolved_right.Add(index);
}
}
if (index_solving.Count()>this.n){
float ratio = this.collectively.update_map(left, middle, right);
foreach (int index in index_solving){
this.result[index] = this.collectively.get_min_w(this.queries[index]);
this.index_solved[index] = true;
}
if (ratio<6.0){
this.solve(index_unsolved_left, left, middle-1);
this.solve(index_unsolved_right, middle+1, right);
}
}
}
public void solve_remained(){
this.collectively = null;
this.individually = new Individually(a, n, m);
for (int index=0; index<this.index_solved.Count(); index++){
if (!index_solved[index]){
this.result[index] = this.individually.get_min_w(this.queries[index]);
}
}
}
}
class Result
{
public static List<int> shortestPath(List<List<int>> a, List<List<int>> queries)
{
int m=a[0].Count();
WorkSpace work_space = new WorkSpace(a, queries);
work_space.solve(Enumerable.Range(0, queries.Count()).ToList(), 0, m-1);
work_space.solve_remained();
return new List<int>(work_space.result);
}
}
class Solution
{
public static void Main(string[] args)
{
TextWriter textWriter = new StreamWriter(@System.Environment.GetEnvironmentVariable("OUTPUT_PATH"), true);
string[] firstMultipleInput = Console.ReadLine().TrimEnd().Split(' ');
int n = Convert.ToInt32(firstMultipleInput[0]);
int m = Convert.ToInt32(firstMultipleInput[1]);
List<List<int>> a = new List<List<int>>();
for (int i = 0; i < n; i++)
{
a.Add(Console.ReadLine().TrimEnd().Split(' ').ToList().Select(aTemp => Convert.ToInt32(aTemp)).ToList());
}
int q = Convert.ToInt32(Console.ReadLine().Trim());
List<List<int>> queries = new List<List<int>>();
for (int i = 0; i < q; i++)
{
queries.Add(Console.ReadLine().TrimEnd().Split(' ').ToList().Select(queriesTemp => Convert.ToInt32(queriesTemp)).ToList());
}
List<int> result = Result.shortestPath(a, queries);
textWriter.WriteLine(String.Join("\n", result));
textWriter.Flush();
textWriter.Close();
}
}
Find the Path Java Solution
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;
public class C {
InputStream is;
PrintWriter out;
String INPUT = "";
void solve()
{
int n = ni(), m = ni();
int[][] a = new int[m][n];
for(int i = 0;i < n;i++){
for(int j = 0;j < m;j++){
a[j][i] = ni();
}
}
d = new long[m][n][][];
build(0, m, a);
int Q = ni();
for(int q = 0;q < Q;q++){
int sc = ni(), sr = ni();
int tc = ni(), tr = ni();
if(sr > tr){
{int du = tr; tr = sr; sr = du;}
{int du = tc; tc = sc; sc = du;}
}
out.println(go(0, m, sr, sc, tr, tc, a));
}
}
static long go(int L, int R, int sr, int sc, int tr, int tc, int[][] a)
{
int M = L+R>>>1;
int m = a[0].length;
long ret = Long.MAX_VALUE;
for(int i = 0;i < m;i++){
ret = Math.min(ret, d[M][i][sr-L][sc] + d[M][i][tr-L][tc] - a[M][i]);
}
if(sr <= M && M <= tr){
return ret;
}
if(R-L <= 1)return ret;
if(tr < M){
return Math.min(ret, go(L, M, sr, sc, tr, tc, a));
}else{
return Math.min(ret, go(M, R, sr, sc, tr, tc, a));
}
}
static long[][][][] d;
static void build(int L, int R, int[][] a)
{
int m = a[0].length;
int M = L+R>>>1;
if(d[M][0] != null)return;
for(int i = 0;i < m;i++){
d[M][i] = dijk(a, M, i, L, R);
}
if(R-L <= 1)return;
build(L, M, a);
build(M, R, a);
}
public static long[][] dijk(int[][] a, int sr, int sc, int L, int R)
{
int m = a[0].length;
long[][] td = new long[R-L][m];
for(int i = 0;i < R-L;i++){
Arrays.fill(td[i], Long.MAX_VALUE / 3);
}
td[sr-L][sc] = 0;
MinHeapL q = new MinHeapL((R-L)*m);
q.add((sr-L)*m+sc, 0L);
td[sr-L][sc] = a[sr][sc];
int[] dr = { 1, 0, -1, 0 };
int[] dc = { 0, 1, 0, -1 };
while(q.size() > 0){
int cur = q.argmin();
q.remove(cur);
int r = cur / m, c = cur % m;
for(int k = 0;k < 4;k++){
int nr = r + dr[k], nc = c + dc[k];
if(nr >= L-L && nr < R-L && nc >= 0 && nc < m){
long nd = td[r][c] + a[nr+L][nc];
if(nd < td[nr][nc]){
td[nr][nc] = nd;
q.update(nr*m+nc, nd);
}
}
}
}
return td;
}
public static class MinHeapL {
public long[] a;
public int[] map;
public int[] imap;
public int n;
public int pos;
public static long INF = Long.MAX_VALUE;
public MinHeapL(int m)
{
n = Integer.highestOneBit((m+1)<<1);
a = new long[n];
map = new int[n];
imap = new int[n];
Arrays.fill(a, INF);
Arrays.fill(map, -1);
Arrays.fill(imap, -1);
pos = 1;
}
public long add(int ind, long x)
{
int ret = imap[ind];
if(imap[ind] < 0){
a[pos] = x; map[pos] = ind; imap[ind] = pos;
pos++;
up(pos-1);
}
return ret != -1 ? a[ret] : x;
}
public long update(int ind, long x)
{
int ret = imap[ind];
if(imap[ind] < 0){
a[pos] = x; map[pos] = ind; imap[ind] = pos;
pos++;
up(pos-1);
}else{
a[ret] = x;
up(ret);
down(ret);
}
return x;
}
public long remove(int ind)
{
if(pos == 1)return INF;
if(imap[ind] == -1)return INF;
pos--;
int rem = imap[ind];
long ret = a[rem];
map[rem] = map[pos];
imap[map[pos]] = rem;
imap[ind] = -1;
a[rem] = a[pos];
a[pos] = INF;
map[pos] = -1;
up(rem);
down(rem);
return ret;
}
public long min() { return a[1]; }
public int argmin() { return map[1]; }
public int size() { return pos-1; }
private void up(int cur)
{
for(int c = cur, p = c>>>1;p >= 1 && a[p] > a[c];c>>>=1, p>>>=1){
long d = a[p]; a[p] = a[c]; a[c] = d;
int e = imap[map[p]]; imap[map[p]] = imap[map[c]]; imap[map[c]] = e;
e = map[p]; map[p] = map[c]; map[c] = e;
}
}
private void down(int cur)
{
for(int c = cur;2*c < pos;){
int b = a[2*c] < a[2*c+1] ? 2*c : 2*c+1;
if(a[b] < a[c]){
long d = a[c]; a[c] = a[b]; a[b] = d;
int e = imap[map[c]]; imap[map[c]] = imap[map[b]]; imap[map[b]] = e;
e = map[c]; map[c] = map[b]; map[b] = e;
c = b;
}else{
break;
}
}
}
}
void run() throws Exception
{
is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
out = new PrintWriter(System.out);
long s = System.currentTimeMillis();
solve();
out.flush();
if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
}
public static void main(String[] args) throws Exception { new C().run(); }
private byte[] inbuf = new byte[1024];
private int lenbuf = 0, ptrbuf = 0;
private int readByte()
{
if(lenbuf == -1)throw new InputMismatchException();
if(ptrbuf >= lenbuf){
ptrbuf = 0;
try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
if(lenbuf <= 0)return -1;
}
return inbuf[ptrbuf++];
}
private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
private double nd() { return Double.parseDouble(ns()); }
private char nc() { return (char)skip(); }
private String ns()
{
int b = skip();
StringBuilder sb = new StringBuilder();
while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
sb.appendCodePoint(b);
b = readByte();
}
return sb.toString();
}
private char[] ns(int n)
{
char[] buf = new char[n];
int b = skip(), p = 0;
while(p < n && !(isSpaceChar(b))){
buf[p++] = (char)b;
b = readByte();
}
return n == p ? buf : Arrays.copyOf(buf, p);
}
private char[][] nm(int n, int m)
{
char[][] map = new char[n][];
for(int i = 0;i < n;i++)map[i] = ns(m);
return map;
}
private int[] na(int n)
{
int[] a = new int[n];
for(int i = 0;i < n;i++)a[i] = ni();
return a;
}
private int ni()
{
int num = 0, b;
boolean minus = false;
while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
if(b == '-'){
minus = true;
b = readByte();
}
while(true){
if(b >= '0' && b <= '9'){
num = num * 10 + (b - '0');
}else{
return minus ? -num : num;
}
b = readByte();
}
}
private long nl()
{
long num = 0;
int b;
boolean minus = false;
while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
if(b == '-'){
minus = true;
b = readByte();
}
while(true){
if(b >= '0' && b <= '9'){
num = num * 10 + (b - '0');
}else{
return minus ? -num : num;
}
b = readByte();
}
}
private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); }
}Find the Path JavaScript Solution
'use strict';
const fs = require('fs');
process.stdin.resume();
process.stdin.setEncoding('utf-8');
let inputString = '';
let currentLine = 0;
process.stdin.on('data', inputStdin => {
inputString += inputStdin;
});
process.stdin.on('end', _ => {
inputString = inputString.trim().split('\n').map(str => str.trim());
main();
});
function readLine() {
return inputString[currentLine++];
}
/*
* Complete the shortestPath function below.
*/
class MinHeap {
constructor() {
this._arr = [];
}
insert(value, data) {
let i = this._arr.length;
let j = (i - 1) >> 1;
while (j >= 0 && value < this._arr[j][0]) {
this._arr[i] = this._arr[j];
i = j;
j = (i - 1) >> 1;
}
this._arr[i] = [value, data];
}
extract() {
const result = this._arr[0];
const [value, data] = this._arr.pop();
if (this._arr.length) {
let i = 0;
let j = 1;
while (true) {
if (j + 1 < this._arr.length && this._arr[j][0] >= this._arr[j + 1][0]) j++; // Get child with least value
if (j >= this._arr.length || value <= this._arr[j][0]) break;
this._arr[i] = this._arr[j];
i = j;
j = j * 2 + 1;
}
this._arr[i] = [value, data];
}
return result;
}
}
function shortestPath(a, queries) {
const chunk = Math.floor(2500 / a.length);
// Create graph
const width = a[0].length;
const nodes = [].concat(...a.map((row, y) => row.map((weight, x) => ({ weight, x, y, distTo: new Map, gates: [] }))));
const gates = Array.from({ length: (Math.floor((width - 1) / chunk) + 1) }, (_, x) =>
a.map((_, y) => nodes[y * width + x * chunk])
);
nodes.forEach((node, i) => {
node.neighbors = [-1, 1, -width, width]
.map(d => i + d)
.map((j, k) => (k > 1 || j % width - i % width === j - i) && nodes[j])
.filter(Boolean);
node.gates = gates.slice(Math.floor(node.x / chunk));
});
gates.forEach((gate, x) => {
const min = Math.max(0, (x - 1) * chunk);
const max = Math.min(width, (x + 1) * chunk);
gate.forEach((centre, y) => {
flood(centre, min, max);
// Make jumps between more distant gates
if (!x) return;
gates.slice(0, x - 1).forEach((gate, j) => {
for (const start of gate) {
start.distTo.set(centre, Math.min(...gates[x - 1].map(mid => distanceVia(start, mid, centre))));
}
});
});
});
function distanceVia(a, b, c) {
if (a === b) return b.distTo.get(c);
if (b === c) return a.distTo.get(b);
return a.distTo.get(b) + b.distTo.get(c) - b.weight;
}
function flood(centre, min, max) {
const heap = new MinHeap();
heap.insert(centre.weight, centre);
const visited = new Set;
for (let count = (max - min) * a.length; count;) {
const [dist, node] = heap.extract();
if (visited.has(node)) continue;
visited.add(node);
if (node.x >= min && node.x < max) {
node.distTo.set(centre, dist);
count--;
}
for (const neighbor of node.neighbors) {
if (!visited.has(neighbor)) heap.insert(dist + neighbor.weight, neighbor);
}
}
}
function distance(a, b) {
if (a === b) return a.weight;
if (a.x > b.x) [a, b] = [b, a];
const i = Math.floor(a.x / chunk);
const j = Math.floor(b.x / chunk);
const heap = new MinHeap();
const visited = new Set;
if (j - i > 1) { // Separated by multiple gates
return Math.min(...a.gates[1].map(start =>
a.distTo.get(start) - start.weight +
Math.min(...b.gates[0].map(end =>
start.distTo.get(end) + b.distTo.get(end) - end.weight
))
));
}
if (j > i) { // Separated by one gate
return Math.min(...a.gates[1].map(mid =>
a.distTo.get(mid) + b.distTo.get(mid) - mid.weight
));
}
// Within same pair of gates:
// Get distance via one of both surrounding gates:
const dist = Math.min(
...a.gates[0].concat(a.gates[1] || []).map(centre => a.distTo.get(centre) + b.distTo.get(centre) - centre.weight),
);
// ... That way we don't have to search beyond the nearby gates.
heap.insert(a.weight, a);
heap.insert(dist, b);
while (true) {
const [dist, node] = heap.extract();
if (visited.has(node)) continue;
if (node === b) return dist;
visited.add(node);
// If node is in a gate, do not include neighbors on the other side of it, but
// instead add the gate-nodes, with their relative distances
for (const neighbor of node.neighbors) {
if (!visited.has(neighbor) && Math.floor(neighbor.x / chunk) === i) {
heap.insert(dist + neighbor.weight, neighbor);
}
}
}
}
return queries.map(([ai, aj, bi, bj]) => distance(nodes[ai * width + aj], nodes[bi * width + bj]));
}
function main() {
const ws = fs.createWriteStream(process.env.OUTPUT_PATH);
const nm = readLine().split(' ');
const n = parseInt(nm[0], 10);
const m = parseInt(nm[1], 10);
let a = Array(n);
for (let aRowItr = 0; aRowItr < n; aRowItr++) {
a[aRowItr] = readLine().split(' ').map(aTemp => parseInt(aTemp, 10));
}
const q = parseInt(readLine(), 10);
let queries = Array(q);
for (let queriesRowItr = 0; queriesRowItr < q; queriesRowItr++) {
queries[queriesRowItr] = readLine().split(' ').map(queriesTemp => parseInt(queriesTemp, 10));
}
let result = shortestPath(a, queries);
ws.write(result.join("\n") + "\n");
ws.end();
}Find the Path Python Solution
# Enter your code here. Read input from STDIN. Print output to STDOUT
import sys
from heapq import *
Row_Count = 0
Col_Count = 0
Query_Count = 0
Table = []
Query_Dict = {}
Query_Results = []
Shortest_Paths = []
Visited = []
def readInput():
global Row_Count, Col_Count, Query_Count, Table, Query_Dict, Query_Results, Shortest_Paths, Visited
Row_Count, Col_Count = map(int, raw_input().split())
for i in xrange(Row_Count):
row = []
entry_list = raw_input().split()
for j in xrange(Col_Count):
row.append(int(entry_list[j]))
Table.append(row)
Shortest_Paths = [ [ sys.maxint for j in range(Col_Count) ] for i in range(Row_Count) ]
Visited = [ [ False for j in range(Col_Count) ] for i in range(Row_Count) ]
Query_Count = int(raw_input())
for i in xrange(Query_Count):
Query_Results.append(sys.maxint)
query = map(int, raw_input().split())
if query[1] > query[3]:
query = (query[2], query[3], query[0], query[1])
else:
query = (query[0], query[1], query[2], query[3])
if not Query_Dict.has_key(query):
Query_Dict[query] = []
Query_Dict[query].append(i)
def isValidSquare(row, col, left_bound, right_bound):
return row >= 0 and row < Row_Count and col >= left_bound and col <= right_bound
def processSingleSquare(start_row, start_col, left_bound, right_bound):
global Shortest_Paths, Visited
for i in range(Row_Count):
for j in range(left_bound, right_bound + 1):
Shortest_Paths[i][j] = sys.maxint
Visited[i][j] = False
bfs_heap = []
Shortest_Paths[start_row][start_col] = Table[start_row][start_col]
heappush(bfs_heap, (Table[start_row][start_col], start_row, start_col))
while bfs_heap:
weight, row, col = heappop(bfs_heap)
if Visited[row][col]:
continue
Visited[row][col] = True
if isValidSquare(row - 1, col, left_bound, right_bound) and not Visited[row - 1][col] :
if weight + Table[row - 1][col] < Shortest_Paths[row - 1][col]:
Shortest_Paths[row - 1][col] = weight + Table[row - 1][col]
heappush(bfs_heap, (weight + Table[row - 1][col], row - 1, col))
if isValidSquare(row + 1, col, left_bound, right_bound) and not Visited[row + 1][col]:
if weight + Table[row + 1][col] < Shortest_Paths[row + 1][col]:
Shortest_Paths[row + 1][col] = weight + Table[row + 1][col]
heappush(bfs_heap, (weight + Table[row + 1][col], row + 1, col))
if isValidSquare(row, col - 1, left_bound, right_bound) and not Visited[row][col - 1]:
if weight + Table[row][col - 1] < Shortest_Paths[row][col - 1]:
Shortest_Paths[row][col - 1] = weight + Table[row][col - 1]
heappush(bfs_heap, (weight + Table[row][col - 1], row, col - 1))
if isValidSquare(row, col + 1, left_bound, right_bound) and not Visited[row][col + 1]:
if weight + Table[row][col + 1] < Shortest_Paths[row][col + 1]:
Shortest_Paths[row][col + 1] = weight + Table[row][col + 1]
heappush(bfs_heap, (weight + Table[row][col + 1], row, col + 1))
def processOnlyOneColumn(start_row, col_index):
shortest_paths = [ sys.maxint for i in range(Row_Count) ]
shortest_paths[start_row] = Table[start_row][col_index]
weight = Table[start_row][col_index]
for i in reversed(range(0, start_row)):
weight = weight + Table[i][col_index]
shortest_paths[i] = weight
weight = Table[start_row][col_index]
for i in range(start_row + 1, Row_Count):
weight = weight + Table[i][col_index]
shortest_paths[i] = weight
return shortest_paths
def processQueriesByColumn(left_col, right_col, whole_queries):
global Query_Results
if not whole_queries:
return
if left_col >= right_col:
for query in whole_queries:
query_indexes = whole_queries[query]
paths = processOnlyOneColumn(query[0], left_col)
new_min = min(Query_Results[query_indexes[0]], paths[query[2]])
for q_index in query_indexes:
Query_Results[q_index] = new_min
return
paths = []
middle_col = (left_col + right_col) / 2
for i in xrange(Row_Count):
processSingleSquare(i, middle_col, left_col, right_col)
for query in whole_queries:
query_indexes = whole_queries[query]
tmp_w = Shortest_Paths[query[0]][query[1]] + Shortest_Paths[query[2]][query[3]] - Table[i][middle_col]
if tmp_w < Query_Results[query_indexes[0]]:
for q_index in query_indexes:
Query_Results[q_index] = tmp_w
queries_on_left = {}
queries_on_right = {}
for query in whole_queries:
query_indexes = whole_queries[query]
if query[3] < middle_col:
queries_on_left[query] = query_indexes
if query[1] > middle_col:
queries_on_right[query] = query_indexes
processQueriesByColumn(left_col, middle_col - 1, queries_on_left)
processQueriesByColumn(middle_col + 1, right_col, queries_on_right)
def printQueryResults():
for q_result in Query_Results:
print q_result
if __name__ == '__main__':
readInput()
processQueriesByColumn(0, Col_Count - 1, Query_Dict)
printQueryResults()
