In this post, we will solve HackerRank DAG Queries Problem Solution. You are given a Directed Acyclic Graph (DAG) with n vertices and m edges. Each vertex v has an integer, a,, associated with it and the initial value of a, is 0 for all vertices. You must perform q queries on the DAG, where each query is one of the following types: 1. 1 u x: Seta, to æ for all v such that there is a path in the DAG from u to v. 2.2 u x: Seta, to æ for all v such that there is a path from u to v and a, > x. 3.3 u: Print the value of a,, on a new line.
Input Format
The first line contains three space-separated integers describing the respective values of n (the number of vertices in the DAG), m (the number of edges in the DAG), and g (the number of queries to perform).
Each of the m subsequent lines contains two space-separated integers describing the respective values of u and u (where 1 <u, v < n. uv) denoting a directed edge from vertex u to vertex in the graph.
Each of the q subsequent lines contains a query in one of the three formats described above.
Output Format
For each query of type a (i.e., 3 u), print the value of au on a new line.
Sample Input 0
6 5 18
1 2
1 3
3 4
2 4
5 6
1 1 3
3 1
3 2
3 3
3 4
1 2 2
3 1
3 2
3 3
3 4
2 6 7
3 5
3 6
2 1 3
3 1
3 2
3 3
3 4Sample Output 0
3
3
3
3
3
2
3
2
0
0
3
2
3
2
DAG Queries C++ Solution
#include <bits/stdc++.h>
using namespace std;
#define sz(x) ((int) (x).size())
#define forn(i,n) for (int i = 0; i < int(n); ++i)
typedef long long ll;
typedef long long i64;
typedef long double ld;
typedef pair<int, int> pii;
const int inf = int(1e9) + int(1e5);
const ll infl = ll(2e18) + ll(1e10);
#define tm suka
const int maxc = 1e9;
//const int maxn = 1001;
const int maxn = 100100;
vector<int> g[maxn];
int tm[maxn];
int qt[maxn];
int qu[maxn];
int qx[maxn];
int qans[maxn];
//const int sn = 1;
const int sn = 600;
const int sn2 = 1000;
const int block = maxn / 3 + 2;
bitset<block> bs[maxn];
bool used[maxn];
int L, R;
int n;
vector<int> ord;
void pre(int u) {
used[u] = true;
for (int v: g[u])
if (!used[v])
pre(v);
ord.push_back(u);
}
void uin(int &a, int b) {
a = min(a, b);
}
void uax(int &a, int b) {
a = max(a, b);
}
int a[maxn / sn + 2][maxn];
int upd[maxn];
vector<pii> o;
void put1(int u, int x) {
o.emplace_back(u, x);
if (sz(o) < sn2)
return;
forn (i, n)
upd[i] = -1;
for (auto p: o)
uax(upd[p.first], p.second);
o.clear();
for (int ii = n - 1; ii >= 0; --ii) {
int u = ord[ii];
tm[u] = max(tm[u], upd[u]);
for (int v: g[u])
uax(upd[v], upd[u]);
}
}
int get1(int u) {
int res = tm[u];
for (auto op: o)
if (bs[op.first][u - L])
uax(res, op.second);
return res;
}
vector<int> q2;
void calc2(int l, int r) {
int k = l / sn;
forn (i, n)
a[k][i] = maxc;
for (int i = l; i < r; ++i) {
int id = q2[i];
uin(a[k][qu[id]], qx[id]);
}
for (int ii = n - 1; ii >= 0; --ii) {
int u = ord[ii];
for (int v: g[u])
uin(a[k][v], a[k][u]);
}
}
int get2(int u, int l, int r) {
l = lower_bound(q2.begin(), q2.end(), l) - q2.begin();
r = lower_bound(q2.begin(), q2.end(), r) - q2.begin();
int res = maxc;
int l2 = ((l + sn - 1) / sn) * sn;
int r2 = (r / sn) * sn;
if (l2 > r2) {
for (int i = l; i < r; ++i) {
int id = q2[i];
int v = qu[id];
if (bs[v][u - L])
uin(res, qx[id]);
}
} else {
for (int i = l; i < l2; ++i) {
int id = q2[i];
int v = qu[id];
if (bs[v][u - L])
uin(res, qx[id]);
}
for (int i = r2; i < r; ++i) {
int id = q2[i];
int v = qu[id];
if (bs[v][u - L])
uin(res, qx[id]);
}
l2 /= sn, r2 /= sn;
for (int i = l2; i < r2; ++i)
uin(res, a[i][u]);
}
return res;
}
int main() {
#ifdef LOCAL
assert(freopen("test.in", "r", stdin));
#endif
int m, q;
cin >> n >> m >> q;
forn (i, m) {
int u, v;
scanf("%d%d", &u, &v);
--u, --v;
g[u].push_back(v);
}
forn (i, n)
if (!used[i])
pre(i);
forn (i, q) {
int t, u, x = -1;
scanf("%d%d", &t, &u);
--u;
if (t != 3)
scanf("%d", &x);
qt[i] = t, qu[i] = u, qx[i] = x;
}
forn (i, q) {
if (qt[i] != 2)
continue;
q2.push_back(i);
}
for (int i = 0; i + sn <= sz(q2); i += sn)
calc2(i, i + sn);
for (L = 0; L < n; L += block) {
R = min(n, L + block);
forn (i, n) {
bs[i].reset();
tm[i] = -1;
}
o.clear();
forn (i, n) {
int u = ord[i];
if (L <= u && u < R)
bs[u][u - L] = true;
for (int v: g[u])
bs[u] |= bs[v];
}
forn (id, q) {
if (qt[id] == 3) {
int u = qu[id];
if (u < L || u >= R)
continue;
int lb = get1(u);
int val = lb >= 0 ? qx[lb] : 0;
uin(val, get2(u, lb, id));
qans[id] = val;
}
if (qt[id] == 1)
put1(qu[id], id);
}
}
forn (i, q) {
if (qt[i] == 3)
cout << qans[i] << '\n';
}
}DAG Queries Scala Solution
object Assert {
def check(e: Boolean) {
if (!e) {
throw new AssertionError();
}
}
}
class Scanner(is: java.io.InputStream) {
val buffer: Array[Byte] = new Array[Byte](1 << 16);
var len: Int = 0;
var pos: Int = 0;
def nextChar(): Int = {
if (pos == len) {
val read: Int = is.read(buffer);
if (read == -1) {
return -1;
}
len = read;
pos = 0;
}
Assert.check(pos < len);
val value: Int = buffer(pos) & 0xFF;
pos += 1;
return value;
}
def nextInt(): Int = {
var c: Int = nextChar();
while (c == ' ' || c == '\n' || c == '\r' || c == '\t') {
c = nextChar();
}
Assert.check('0' <= c && c <= '9');
var value: Int = c - '0';
c = nextChar();
while ('0' <= c && c <= '9') {
val digit: Int = c - '0';
Assert.check(value < Int.MaxValue / 10 || value == Int.MaxValue / 10 && digit <= Int.MaxValue % 10);
value = value * 10 + digit;
c = nextChar();
}
return value;
}
}
class IntArrayList {
var a: Array[Int] = new Array[Int](4);
var size: Int = 0;
def add(x: Int): Unit = {
if (size == a.length) {
a = java.util.Arrays.copyOf(a, a.length * 2);
}
a(size) = x;
size += 1;
}
def get(i: Int): Int = {
Assert.check(i < size);
return a(i);
}
}
class Query(val typ: Int, val node: Int, val value: Int) {}
object Solution {
def reorder(parents: Array[IntArrayList], queries: Array[Query]): Unit = {
val nV: Int = parents.size;
val startOrder: Array[Int] = new Array[Int](nV);
{
var i: Int = 0;
while (i < nV) {
startOrder(i) = i;
i += 1;
}
}
var rnd: java.util.Random = new java.util.Random(20161106);
{
var i: Int = nV - 1;
while (i > 0) {
val j: Int = rnd.nextInt(i + 1);
val t: Int = startOrder(i);
startOrder(i) = startOrder(j);
startOrder(j) = t;
i -= 1;
}
}
val orderedId: Array[Int] = new Array[Int](nV);
java.util.Arrays.fill(orderedId, -1);
val stack: IntArrayList = new IntArrayList();
val ip: IntArrayList = new IntArrayList();
var nextId: Int = 0;
{
var i: Int = 0;
while (i < nV) {
if (orderedId(startOrder(i)) == -1) {
stack.add(startOrder(i));
ip.add(0);
while (stack.size > 0) {
val cur: Int = stack.a(stack.size - 1);
if (ip.get(ip.size - 1) == parents(cur).size) {
orderedId(cur) = nextId;
nextId += 1;
stack.size -= 1;
ip.size -= 1;
} else {
val p: Int = parents(cur).get(ip.get(ip.size - 1));
ip.a(ip.size - 1) += 1;
if (orderedId(p) == -1) {
stack.add(p);
ip.add(0);
}
}
}
}
i += 1;
}
}
if (false) {
print("new ids: ");
var first: Boolean = true;
{
var i: Int = 0;
while (i < nV) {
if (first) {
first = false;
} else {
print(", ");
}
print((i + 1) + " -> " + (orderedId(i) + 1));
i += 1;
}
}
println();
}
Assert.check(nextId == nV);
{
var i: Int = 0;
while (i < orderedId.length) {
Assert.check(orderedId(i) >= 0);
i += 1;
}
}
val orderedParents: Array[IntArrayList] = new Array[IntArrayList](nV);
{
var i: Int = 0;
while (i < nV) {
orderedParents(i) = new IntArrayList();
i += 1;
}
}
{
var i: Int = 0;
while (i < nV) {
{
var ip: Int = 0;
while (ip < parents(i).size) {
val p: Int = parents(i).get(ip);
orderedParents(orderedId(i)).add(orderedId(p));
ip += 1;
}
}
i += 1;
}
}
{
var i: Int = 0;
while (i < nV) {
java.util.Arrays.sort(orderedParents(i).a, 0, orderedParents(i).size);
parents(i) = orderedParents(i);
i += 1;
}
}
{
var i: Int = 0;
while (i < queries.length) {
val typ: Int = queries(i).typ;
val node: Int = queries(i).node;
val value: Int = queries(i).value;
Assert.check(0 <= node && node < nV);
queries(i) = new Query(typ, orderedId(node), value);
i += 1;
}
}
}
def process(
parents: Array[IntArrayList],
queries: Array[Query],
qFirst: Int,
qAfter: Int,
a: Array[Int],
codes: Array[Long],
add: Array[Int],
min: Array[Int],
result: IntArrayList
): Unit = {
val nV: Int = parents.length;
val q12: IntArrayList = new IntArrayList();
{
var q = qFirst;
while (q < qAfter) {
if (queries(q).typ < 3) {
q12.add(q);
}
q += 1;
}
}
if (q12.size == 0) {
var q: Int = qFirst;
while (q < qAfter) {
Assert.check(queries(q).typ == 3);
val node: Int = queries(q).node;
Assert.check(0 <= node && node < nV);
result.add(a(node));
q += 1;
}
return;
}
val n: Int = q12.size;
Assert.check(n <= 8 * 14);
Assert.check(nV <= 100000);
java.util.Arrays.fill(codes, 0, nV * 2, 0);
{
var i: Int = 0;
while (i < n) {
val node: Int = queries(q12.get(i)).node;
val word: Int = i / 56;
val shift: Int = i % 56 / 14 * 16 + i % 14; // 14 used bits, 2 free
codes(node * 2 + word) |= 1L << shift;
i += 1;
}
}
{
var i: Int = 0;
while (i < nV) {
{
val pari: IntArrayList = parents(i);
var ip: Int = 0;
while (ip < pari.size) {
val p: Int = pari.get(ip);
codes((i << 1) + 0) |= codes((p << 1) + 0);
codes((i << 1) + 1) |= codes((p << 1) + 1);
ip += 1;
}
}
i += 1;
}
}
var q: Int = qFirst;
var part: Int = 0;
while (part * 14 < n) {
val begin: Int = part * 14;
val end: Int = Math.min(n, begin + 14);
val codesAdd: Int = part / 4;
val codesShift: Int = part % 4 * 16;
// a = Math.min(a + add, min)
add(0) = 0;
min(0) = 1000 * 1000 * 1000;
var bit: Int = 0;
while (bit < end - begin) {
val qType: Int = queries(q12.get(begin + bit)).typ;
val value: Int = queries(q12.get(begin + bit)).value;
val extra: Int = 1 << bit;
if (qType == 1) { // assign
var code: Int = 0;
while (code < extra) {
add(code + extra) = 1000 * 1000 * 1000;
min(code + extra) = value;
code += 1;
}
} else {
Assert.check(qType == 2); // min
var code: Int = 0;
while (code < extra) {
add(code + extra) = add(code);
min(code + extra) = Math.min(value, min(code));
code += 1;
}
}
bit += 1;
}
var mask = 0;
while (end == n && q != qAfter || end != n && q != q12.get(end)) {
if (queries(q).typ < 3) {
mask <<= 1;
mask |= 1;
} else {
Assert.check(queries(q).typ == 3);
val node: Int = queries(q).node;
val code: Int = ((codes((node << 1) + codesAdd) >> codesShift) & mask).toInt;
val answer: Int = Math.min(a(node) + add(code), min(code));
result.add(answer);
}
q += 1;
}
var i = 0;
while (i < nV) {
val code: Int = ((codes((i << 1) + codesAdd) >> codesShift) & 0xFFFF).toInt;
a(i) = Math.min(a(i) + add(code), min(code));
i += 1;
}
part += 1;
}
}
def solveFast(parents: Array[IntArrayList], queries: Array[Query]): IntArrayList = {
val nV: Int = parents.length;
{
var i: Int = 0;
while (i < nV) {
{
var ip: Int = 0;
while (ip < parents(i).size) {
val p: Int = parents(i).get(ip);
Assert.check(p < i); // parents before children
ip += 1;
}
}
i += 1;
}
}
val a: Array[Int] = new Array[Int](nV);
val codes: Array[Long] = new Array[Long](100000 * 2);
val add: Array[Int] = new Array[Int](1 << 14);
val min: Array[Int] = new Array[Int](1 << 14);
val result: IntArrayList = new IntArrayList();
val MAX12Q = 8 * 14;
var first: Int = 0;
var n12q: Int = 0;
val nQ: Int = queries.length;
{
var i: Int = 0;
while (i < nQ) {
if (queries(i).typ < 3) {
n12q += 1;
}
if (n12q == MAX12Q || i == nQ - 1) {
process(parents, queries, first, i + 1, a, codes, add, min, result);
first = i + 1;
n12q = 0;
}
i += 1;
}
}
return result;
}
def main(args: Array[String]): Unit = {
val in: Scanner = new Scanner(System.in);
val nV: Int = in.nextInt();
val nE: Int = in.nextInt();
val nQ: Int = in.nextInt();
val parents: Array[IntArrayList] = new Array[IntArrayList](nV);
{
var i: Int = 0;
while (i < nV) {
parents(i) = new IntArrayList();
i += 1;
}
}
{
var i: Int = 0;
while (i < nE) {
val parent: Int = in.nextInt() - 1;
val child: Int = in.nextInt() - 1;
parents(child).add(parent);
i += 1;
}
}
val queries: Array[Query] = new Array[Query](nQ);
{
var i: Int = 0;
while (i < nQ) {
val qType: Int = in.nextInt();
if (qType == 1 || qType == 2) {
val parent: Int = in.nextInt() - 1;
val value: Int = in.nextInt();
queries(i) = new Query(qType, parent, value);
} else {
Assert.check(qType == 3);
val node: Int = in.nextInt() - 1;
queries(i) = new Query(qType, node, -1);
}
i += 1;
}
}
reorder(parents, queries);
val result: IntArrayList = solveFast(parents, queries);
{
var i: Int = 0;
while (i < result.size) {
println(result.get(i));
i += 1;
}
}
}
}DAG Queries Java Solution
import java.io.*;
import java.util.*;
public class Solution {
static class MyBitSet {
private final static int ADDRESS_BITS_PER_WORD = 6;
private long[] words;
private transient int wordsInUse = 0;
private static int wordIndex(int bitIndex) {
return bitIndex >> ADDRESS_BITS_PER_WORD;
}
public MyBitSet(int nbits) {
words = new long[wordIndex(nbits - 1) + 1];
}
public void clear() {
while (wordsInUse > 0)
words[--wordsInUse] = 0;
}
public void set(int bitIndex) {
int wordIndex = wordIndex(bitIndex);
expandTo(wordIndex);
words[wordIndex] |= (1L << bitIndex);
}
private void expandTo(int wordIndex) {
int wordsRequired = wordIndex + 1;
if (wordsInUse < wordsRequired) {
wordsInUse = wordsRequired;
}
}
public void or(MyBitSet set) {
int wordsInCommon = Math.min(wordsInUse, set.wordsInUse);
if (wordsInUse < set.wordsInUse) {
wordsInUse = set.wordsInUse;
}
for (int i = 0; i < wordsInCommon; i++) {
words[i] |= set.words[i];
}
if (wordsInCommon < set.wordsInUse) {
System.arraycopy(set.words, wordsInCommon, words, wordsInCommon,
wordsInUse - wordsInCommon);
}
}
public boolean get(int bitIndex) {
int wordIndex = wordIndex(bitIndex);
return (wordIndex < wordsInUse) && ((words[wordIndex] & (1L << bitIndex)) != 0);
}
}
static class PS {
int opt;
int u;
int x;
int i;
}
static class QS {
int u;
int i;
public QS(int u, int i) {
this.u = u;
this.i = i;
}
}
static Set<Integer>[] graph;
static int[] indeg;
static int[] topo;
static int ttot = 1;
static void topo_dfs(int node) {
topo[ttot++] = node;
for (int i = ptr[node]; i > 0; i = nxt[i]) {
if (--indeg[succ[i]] == 0) {
topo_dfs(succ[i]);
}
}
}
static int[] nxt;
static int[] succ;
static int[] ptr;
static int index = 1;
static void addedge(int u, int v) {
nxt[index] = ptr[u];
ptr[u] = index;
succ[index++] = v;
}
static final int B = 316;
static int[] solve2(int[][] queries, int n, int nQue) {
int q = queries[0].length - 1;
int[] ans = new int[q + 1];
QS[] que = new QS[nQue + 1];
PS[] perform = new PS[q + 1];
int ptot = 0;
int qtot = 0;
for (int i = 1; i <= q; i++) {
perform[ptot] = new PS();
perform[ptot].opt = queries[0][i];
if (perform[ptot].opt <= 2) {
perform[ptot].u = queries[1][i];
perform[ptot].x = queries[2][i];
perform[ptot++].i = i;
} else {
que[qtot++] = new QS(queries[1][i], i);
}
ans[i] = Integer.MAX_VALUE;
}
MyBitSet[] b = new MyBitSet[n + 1];
for (int i = n; i > 0; i--) {
b[i] = new MyBitSet(320);
}
boolean[] cover = new boolean[n + 1];
int[] minVal = new int[n + 1];
for (int l = (ptot - 1) - (ptot - 1) % B, r = ptot - 1; l >= 0; r = l - 1, l -= B) {
for (int i = n; i > 0; i--) {
b[i].clear();
}
for (int i = l; i <= r; ++i) {
b[perform[i].u].set(i - l);
}
for (int i = 1; i <= n; i++) {
for (int j = ptr[topo[i]]; j > 0; j = nxt[j]) {
b[succ[j]].or(b[topo[i]]);
}
}
Arrays.fill(cover, false);
for (int i = l; i <= r; i++) {
if (perform[i].opt == 1) {
cover[perform[i].u] = true;
}
}
for (int i = 1; i <= n; i++) {
if (cover[topo[i]]) {
for (int j = ptr[topo[i]]; j > 0; j = nxt[j]) {
cover[succ[j]] = true;
}
}
}
Arrays.fill(minVal, Integer.MAX_VALUE);
for (int i = l; i <= r; i++) {
if (perform[i].opt == 2) {
minVal[perform[i].u] = Math.min(minVal[perform[i].u], perform[i].x);
}
}
for (int i = 1; i <= n; ++i) {
for (int j = ptr[topo[i]]; j > 0; j = nxt[j]) {
minVal[succ[j]] = Math.min(minVal[succ[j]], minVal[topo[i]]);
}
}
int i = qtot;
while (i > 0 && que[i - 1].i > perform[l].i) {
i--;
}
while (i < qtot) {
if (que[i].i < perform[r].i) {
int j = r;
while (perform[j].i > que[i].i) {
--j;
}
for (; j >= l; j--)
if (b[que[i].u].get(j - l)) {
ans[que[i].i] = Math.min(ans[que[i].i], perform[j].x);
if (perform[j].opt == 1) {
--qtot;
QS temp = que[i];
que[i] = que[qtot];
que[qtot] = temp;
break;
}
}
i += j < l ? 1 : 0;
} else if (cover[que[i].u]) {
int j = r;
for (; perform[j].opt == 2 || !b[que[i].u].get(j - l); j--) {
if (perform[j].opt == 2 && b[que[i].u].get(j - l)) {
ans[que[i].i] = Math.min(ans[que[i].i], perform[j].x);
}
}
ans[que[i].i] = Math.min(ans[que[i].i], perform[j].x);
--qtot;
QS temp = que[i];
que[i] = que[qtot];
que[qtot] = temp;
} else {
ans[que[i].i] = Math.min(ans[que[i].i], minVal[que[i].u]);
i++;
}
}
}
while (qtot-- > 0) {
ans[que[qtot].i] = 0;
}
return ans;
}
public static void main(String[] args) throws IOException {
BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
BufferedWriter bw = new BufferedWriter(new FileWriter(System.getenv("OUTPUT_PATH")));
StringTokenizer st = new StringTokenizer(br.readLine());
int n = Integer.parseInt(st.nextToken());
int m = Integer.parseInt(st.nextToken());
int q = Integer.parseInt(st.nextToken());
graph = new Set[n + 1];
Set<Integer>[] parent = new Set[n + 1];
for (int i = 1; i <= n; i++) {
graph[i] = new HashSet<>();
parent[i] = new HashSet<>();
}
for (int i = 0; i < m; i++) {
st = new StringTokenizer(br.readLine());
int u = Integer.parseInt(st.nextToken());
int v = Integer.parseInt(st.nextToken());
graph[u].add(v);
parent[v].add(u);
}
int[][] queries = new int[3][q + 1];
int[] convert = new int[n + 1];
int nodes = 0;
int op3 = 0;
for (int i = 1; i <= q; i++) {
st = new StringTokenizer(br.readLine());
queries[0][i] = Integer.parseInt(st.nextToken());
int u = Integer.parseInt(st.nextToken());
if (convert[u] == 0) {
nodes++;
convert[u] = nodes;
}
queries[1][i] = convert[u];
if (queries[0][i] <= 2) {
int x = Integer.parseInt(st.nextToken());
queries[2][i] = x;
} else {
op3++;
}
}
for (int u = 1; u <= n; u++) {
if (convert[u] == 0) {
for (int v : parent[u]) {
graph[v].remove(u);
graph[v].addAll(graph[u]);
}
for (int v : graph[u]) {
parent[v].remove(u);
parent[v].addAll(parent[u]);
}
parent[u] = null;
graph[u] = null;
}
}
indeg = new int[nodes + 1];
boolean[] existDeg = new boolean[nodes + 1];
nxt = new int[m + 1];
ptr = new int[nodes + 1];
succ = new int[m + 1];
for (int u1 = 1; u1 <= n; u1++) {
int u = convert[u1];
if (u > 0) {
for (int v1 : graph[u1]) {
int v = convert[v1];
indeg[v]++;
existDeg[v] = true;
addedge(u, v);
}
}
}
topo = new int[nodes + 1];
for (int i = nodes; i > 0; i--) {
if (!existDeg[i]) {
topo_dfs(i);
}
}
int[] ans = solve2(queries, nodes, op3);
for (int i = 1; i <= q; i++) {
if (ans[i] < Integer.MAX_VALUE) {
bw.write(ans[i] + "\n");
}
}
bw.close();
br.close();
}
}
