In this HackerRank Matrix Interview preparation kit problem a Heap there is Given a list of edges and times, determine the minimum time to stop the attack.
Problem solution in Python programming.
class Edge(object):
def __init__(self, city1: int, city2: int, weight: int):
self.cities = [city1, city2]
self.weight = weight
[N, K] = [int(i) for i in input().split(' ')]
edges = list()
for i in range(N - 1):
line = input()
#print(line)
[city1, city2, weight] = [int(j) for j in line.split(' ')]
edges.append(Edge(city1, city2, weight))
edges.sort(key = lambda x: x.weight, reverse = True)
cityToGroup = dict()
machineCities = dict()
for i in range(K):
mc = int(input())
machineCities[mc] = True
cityToGroup[mc] = mc
result = 0
groups = dict()
for i in range(N):
groups[i] = [i]
cityToGroup[i] = i
for e in edges:
city1 = e.cities[0]
city2 = e.cities[1]
g1 = cityToGroup[city1]
g2 = cityToGroup[city2]
if g1 == g2:
continue
if machineCities.get(g1, None) is not None: # in this group we have a machine
if machineCities.get(g2, None) is not None: # do not add this edge, as it connects the machines
result += e.weight
else:
for c in groups[g2]:
cityToGroup[c] = g1
groups[g1].append(c)
del groups[g2]
else: # Either the second group has a machine or not, we add all g1 cities to it and delete the first g1
for c in groups[g1]:
groups[g2].append(c)
cityToGroup[c] = g2
del groups[g1]
print(result)Problem solution in Java Programming.
import java.io.*;
import java.math.*;
import java.security.*;
import java.text.*;
import java.util.*;
import java.util.concurrent.*;
import java.util.regex.*;
public class Solution {
// Complete the minTime function below.
static int minTime(int[][] roads, int[] machines) {
int n = roads.length + 1;
int[] sum_edge = new int[n];
int[] max_edge = new int[n];
int[] processed_connections = java.util.stream.IntStream.generate(() -> 2).limit(n).toArray();
boolean[] is_visited = new boolean[n];
boolean[] is_machine = new boolean[n];
Arrays.stream(machines).forEach(m -> is_machine[m]=true);
List<int[]>[] edge_list = java.util.stream.Stream.generate(ArrayList::new).limit(n).toArray(List[]::new);
for(int[] road: roads) {
edge_list[road[0]].add(road);
edge_list[road[1]].add(road);
}
int result = 0;
for(int i = 0; i < n; i++) {
if(edge_list[i].size()!=1 || is_visited[i]) continue;
is_visited[i] = true;
boolean found = is_machine[i];
int curr_node = i;
int[] next_edge = edge_list[curr_node].get(0);
int min_edge_time = next_edge[2];
for(boolean finished = false; !finished;) {
curr_node = (curr_node==next_edge[0]? next_edge[1] : next_edge[0]);
int size = edge_list[curr_node].size();
if(size == 1) {
if(found && is_machine[curr_node]) result+=min_edge_time;
is_visited[curr_node] = true;
finished = true;
} else if(size > 2) {
if(is_machine[curr_node]) {
if(found) result+=min_edge_time;
found = true;
} else if(found) {
sum_edge[curr_node] += min_edge_time;
max_edge[curr_node] = Math.max(max_edge[curr_node], min_edge_time);
}
next_edge[2] = 0;
if(++processed_connections[curr_node]<=size) finished=true;
else {
boolean has_more = false;
for(int[] edge : edge_list[curr_node]) {
if(edge[2] != 0) {
next_edge = edge;
has_more = true;
break;
}
}
if(has_more) {
if(is_machine[curr_node]) min_edge_time=next_edge[2];
else {
result += sum_edge[curr_node] - max_edge[curr_node];
found = true;
min_edge_time = Math.min(max_edge[curr_node], next_edge[2]);
}
} else finished = true;
}
} else {
next_edge = (next_edge==edge_list[curr_node].get(0)? edge_list[curr_node].get(1) : edge_list[curr_node].get(0));
if(!is_machine[curr_node]) min_edge_time=Math.min(min_edge_time, next_edge[2]);
else {
if(found) result+=min_edge_time;
found = true;
min_edge_time = next_edge[2];
}
}
}
}
return result;
}
private static final Scanner scanner = new Scanner(System.in);
public static void main(String[] args) throws IOException {
BufferedWriter bufferedWriter = new BufferedWriter(new FileWriter(System.getenv("OUTPUT_PATH")));
String[] nk = scanner.nextLine().split(" ");
int n = Integer.parseInt(nk[0]);
int k = Integer.parseInt(nk[1]);
int[][] roads = new int[n - 1][3];
for (int i = 0; i < n - 1; i++) {
String[] roadsRowItems = scanner.nextLine().split(" ");
scanner.skip("(\r\n|[\n\r\u2028\u2029\u0085])?");
for (int j = 0; j < 3; j++) {
int roadsItem = Integer.parseInt(roadsRowItems[j]);
roads[i][j] = roadsItem;
}
}
int[] machines = new int[k];
for (int i = 0; i < k; i++) {
int machinesItem = scanner.nextInt();
scanner.skip("(\r\n|[\n\r\u2028\u2029\u0085])?");
machines[i] = machinesItem;
}
int result = minTime(roads, machines);
bufferedWriter.write(String.valueOf(result));
bufferedWriter.newLine();
bufferedWriter.close();
scanner.close();
}
}Problem solution in C++ programming.
#include <cstdio>
#include <vector>
using namespace std;
#define forn(i,n) for (int i = 0; i < (n); i++)
typedef long long LL;
typedef pair<int, int> ii;
#define N 100004
const LL inf = 1000000000000000000LL;
int n, m;
bool marked[N];
LL f[N], g[N];
vector<ii> a[N];
void go(int v, int parent) {
LL sum = 0, mx = -inf;
for (vector<ii>::iterator it = a[v].begin(); it != a[v].end(); ++it) {
int x = it->first;
if (x == parent) continue;
go(x, v);
if (f[x] == inf) continue;
LL u = min(g[x], f[x] + it->second);
sum += u;
mx = max(mx, u - f[x]);
}
if (marked[v]) f[v] = sum, g[v] = inf;
else f[v] = sum - mx, g[v] = sum;
}
int main() {
scanf("%d%d", &n, &m);
forn(_, n-1) {
int x, y, z;
scanf("%d%d%d", &x, &y, &z);
a[x].push_back(ii(y, z));
a[y].push_back(ii(x, z));
}
forn(_, m) {
int x;
scanf("%d", &x);
marked[x] = 1;
}
go(0, -1);
printf("%lld\n", min(f[0], g[0]));
return 0;
}Problem solution in C programming.
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
typedef struct {
union {
struct {unsigned city_x, city_y;};
unsigned long packd;
};
unsigned cost;
} road_t;
typedef struct {
unsigned *indices, terminal;
road_t *items;
unsigned count;
} min_heap_t;
static inline road_t *min_heap_pop(min_heap_t *self) {
road_t *smallest = &self->items[self->indices[1]];
unsigned
location = self->indices[self->count],
min_cost = self->items[location].cost,
parent = 1,
child;
self->indices[self->count--] = self->terminal;
for (child = 2; child <= self->count; child <<= 1) {
child |= self->items[self->indices[child | 1U]].cost < self->items[self->indices[child]].cost;
if (self->items[self->indices[child]].cost <= min_cost) {
self->indices[parent] = self->indices[child];
parent = child;
} else
break ;
}
self->indices[parent] = location;
return smallest;
}
static inline void min_heap_push(min_heap_t *self, unsigned at) {
unsigned root;
for (root = ++self->count; root > 1 && self->items[at].cost < self->items[self->indices[root >> 1]].cost; root >>= 1)
self->indices[root] = self->indices[root >> 1];
self->indices[root] = at;
}
#define have_seen(self, id) ((self)[(id) >> 5] & (1U << ((id) & 31U)))
#define inv_seen(self, id) ((self)[(id) >> 5] ^= (1U << ((id) & 31U)))
unsigned
occupied[3125] = {[0 ... 3124] = 0},
set[3125] = {[0 ... 3124] = 0},
stack[100000],
history[100000];
int main() {
unsigned at, city_cnt, edge_cnt, machine_cnt;
scanf("%u %u", &city_cnt, &machine_cnt);
unsigned long indices[city_cnt + 1];
memset(indices, 0, sizeof(indices));
edge_cnt = city_cnt - 1;
road_t *road = malloc(sizeof(*road) * (edge_cnt << 1));
for (at = 0; at < edge_cnt; at++) {
scanf("%u %u %u", &road[at].city_x, &road[at].city_y, &road[at].cost);
road[at + edge_cnt].cost = road[at].cost;
road[at + edge_cnt].packd = (road[at].packd << 32) | (road[at].packd >> 32);
indices[road[at].city_x]++;
indices[road[at].city_y]++;
}
edge_cnt <<= 1;
road_t ordered[edge_cnt | 1];
for (at = 0; ++at < city_cnt; indices[at] += indices[at - 1]);
for (at = edge_cnt; at--; ordered[--indices[road[at].city_x]] = road[at]);
free(road);
indices[city_cnt] = edge_cnt;
ordered[edge_cnt].packd = ((unsigned long)city_cnt << 32) | city_cnt;
ordered[edge_cnt].cost = 0xFFFFFFFFU;
for (; machine_cnt--; inv_seen(occupied, at))
scanf("%u", &at);
// take all the edges and insert them into priority queue ordered by increasing weight
// while the queue is not empty pop and temporarily remove it,
// do a dfs on both cities,
// if they both lead to an occupied city, permanently remove the edge,
// otherwise restore the edge.
unsigned buffer[edge_cnt | 1];
min_heap_t edges = {.indices = buffer, .items = ordered, .count = 0, .terminal = edge_cnt};
for (at = edge_cnt | 1; at--; edges.indices[at] = edge_cnt);
for (at = edge_cnt; at--; min_heap_push(&edges, at));
unsigned length, city;
unsigned long total = 0;
road_t *neighbors;
while (edges.count) {
road = min_heap_pop(&edges);
if (road->city_x == road->city_y) // edge has being removed ...
continue;
unsigned
city_x = road->city_x,
city_y = road->city_y;
length = 0;
stack[0] = city_x;
road->city_y = city_x;
for (at = 1; at && have_seen(occupied, stack[at - 1]) == 0; ) {
city = stack[--at];
inv_seen(set, city);
history[length++] = city;
for (neighbors = &ordered[indices[city]]; neighbors->city_x == city; neighbors++)
if (have_seen(set, neighbors->city_y) == 0)
stack[at++] = neighbors->city_y;
}
if (at) { // city_x lead to an occupied city check city_y;
road_t *other_road;
for (other_road = &ordered[indices[city_y]]; other_road->city_y != city_x; other_road++);
other_road->city_y = city_y;
stack[0] = city_y;
for (at = 1; at && have_seen(occupied, stack[at - 1]) == 0; ) {
city = stack[--at];
inv_seen(set, city);
history[length++] = city;
for (neighbors = &ordered[indices[city]]; neighbors->city_x == city; neighbors++)
if (have_seen(set, neighbors->city_y) == 0)
stack[at++] = neighbors->city_y;
}
if (at == 0) // restore edge, since we didn't reach an occupied city.
other_road->city_y = city_x;
}
if (at)
total += road->cost;
else
road->city_y = city_y;
for (; length--; inv_seen(set, history[length]));
}
printf("%lu", total);
return 0;
}Problem solution in JavaScript programming.
'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', function() {
inputString = inputString.replace(/\s*$/, '')
.split('\n')
.map(str => str.replace(/\s*$/, ''));
main();
});
function readLine() {
return inputString[currentLine++];
}
// Complete the minTime function below.
function minTime(roads, machines) {
machines = new Set(machines);
let edges = Array(roads.length + 1);
for(let i = 0; i < edges.length; i++) {
edges[i] = {};
}
for(let i = 0; i < roads.length; i++) {
let f = roads[i][0];
let t = roads[i][1];
let cost = roads[i][2];
edges[f][t] = cost;
edges[t][f] = cost;
}
let machineList = Array.from(machines);
let cost = 0;
let deleteCount = 0;
for(let i = 0; i < machineList.length; i++) {
let removals = findMinimumEdge(machines, edges, machineList[i]);
console.log(removals);
for(let j = 0; j < removals.length; j++) {
let removal = removals[j];
let t = removal[0];
let f = removal[1];
if(!edges[t][f]) {
continue;
}
cost += edges[t][f];
delete edges[t][f];
delete edges[f][t];
console.log(cost);
}
console.log(cost);
}
return cost;
}
function findMinimumEdge(machines, edges, start, path, visited) {
if(!visited) {
visited = {};
}
if(!path) {
path = [start];
}
visited[start] = true;
let minEdges = [];
for(let edge in edges[start]) {
edge = parseInt(edge);
if(visited[edge]) {
continue;
}
let newPath = path.slice(0);
newPath.push(edge);
if(machines.has(edge)) {
newPath.push(edge);
let min = edges[newPath[0]][newPath[1]];
let minEdge = [newPath[0],newPath[1]];
for(let i = 1; i < newPath.length - 1; i++) {
if(edges[newPath[i]][newPath[i+1]] < min) {
min = edges[newPath[i]][newPath[i+1]];
minEdge = [newPath[i],newPath[i + 1]];
}
}
minEdges.push(minEdge);
continue;
}
let result = findMinimumEdge(machines, edges, edge, newPath, visited);
minEdges.push(...result);
}
return minEdges;
}
function main() {
const ws = fs.createWriteStream(process.env.OUTPUT_PATH);
const nk = readLine().split(' ');
const n = parseInt(nk[0], 10);
const k = parseInt(nk[1], 10);
let roads = Array(n - 1);
for (let i = 0; i < n - 1; i++) {
let line = readLine();
if(line.indexOf('green') != -1) {
i--;
continue;
}
roads[i] = line.split(' ').map(roadsTemp => parseInt(roadsTemp, 10));
}
let machines = [];
for (let i = 0; i < k; i++) {
const machinesItem = parseInt(readLine(), 10);
machines.push(machinesItem);
}
const result = minTime(roads, machines);
ws.write(result + '\n');
ws.end();
}
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