HackerRank Maximizing Mission Points Solution
In this post, we will solve HackerRank Maximizing Mission Points Problem Solution.
Xander Cage has a list of cities he can visit on his new top-secret mission. He represents each city as a tuple of (latitude, longitude, height, points). The values of latitude.
longitude, and height are distinct across all cities.
We define a mission as a sequence of cities, C1, C2, C3, …, ck, that he visits. We define the total points of such a mission to be the sum of the points of all the cities in his mission list.
Being eccentric, he abides by the following rules on any mission:
- He can choose the number of cities he will visit (if any).
- He can start the mission from any city.
- He visits cities in order of strictly increasing height.
- The absolute difference in latitude between adjacent visited cities in his mission must be at most d1 at.
- The absolute difference in longitude between adjacent visited cities in his mission must be at most d1 ong.
Given d_lat, d_long, and the definitions for n cities, find and print the maximum possible total points that Xander can earn on a mission.
Input Format
The first line contains three space-separated integers describing the respective values of n
d_lat, and d_long.
Each line i of the n subsequent lines contains four space-separated integers denoting the respective latitude, longitude, height, and points for a city
Output Format
Print a single integer denoting the maximum possible points that Xander can earn on a mission.
Sample Input 0
3 1 1 1 1 1 3 2 2 2 -1 3 3 3 3
Sample Output 0
5
Explanation 0
Xander can start at city 1, then go to city 2, and then go to city 3 for a maximum value of
total points=3+-1+3=5
Note that he cannot go directly from city 1 to city 3 as that would violate his rules that the absolute difference in latitude between adjacent visited cities be < d_lat and the absolute difference in longitude between adjacent visited cities be <d_long. Because d_lat= 1 and d_long = 1, he cannot directly travel between those cities.
Maximizing Mission Points 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 D {
InputStream is;
PrintWriter out;
String INPUT = "";
void solve()
{
int n = ni();
int x = ni(), y = ni();
int[][] co = new int[n][];
for(int i = 0;i < n;i++){
co[i] = new int[]{ni(), ni(), ni(), ni()};
}
// Arrays.sort(co, new Comparator<int[]>() {
// public int compare(int[] a, int[] b) {
// return a[2] - b[2];
// }
// });
StaticRangeTreeRMQ2 st = new StaticRangeTreeRMQ2(co, 200005);
// for(int i = 0;i < n;i++){
// st.update(co[i][0], co[i][1], Long.MAX_VALUE / 2);
// }
mergesort(co, 0, n);
long max = Long.MIN_VALUE;
long[] dp = new long[n];
for(int i = 0;i < n;i++){
long min = -st.min(co[i][0]-x, co[i][0]+x+1, co[i][1]-y, co[i][1]+y+1);
long val = co[i][3] + Math.max(min, 0);
dp[i] = val;
st.update(co[i][0], co[i][1], -dp[i]);
max = Math.max(max, dp[i]);
}
out.println(max);
}
private static int[][] stemp = new int[200005][];
public static void mergesort(int[][] a, int s, int e)
{
if(e - s <= 1)return;
int h = s+e>>1;
mergesort(a, s, h);
mergesort(a, h, e);
int p = 0;
int i= s, j = h;
for(;i < h && j < e;)stemp[p++] = a[i][2] < a[j][2] ? a[i++] : a[j++];
while(i < h)stemp[p++] = a[i++];
while(j < e)stemp[p++] = a[j++];
System.arraycopy(stemp, 0, a, s, e-s);
}
public static void mergesort0(int[][] a, int s, int e)
{
if(e - s <= 1)return;
int h = s+e>>1;
mergesort0(a, s, h);
mergesort0(a, h, e);
int p = 0;
int i= s, j = h;
for(;i < h && j < e;)stemp[p++] = a[i][0] < a[j][0] || a[i][0] == a[j][0] && a[i][1] < a[j][1] ? a[i++] : a[j++];
while(i < h)stemp[p++] = a[i++];
while(j < e)stemp[p++] = a[j++];
System.arraycopy(stemp, 0, a, s, e-s);
}
public static class StaticRangeTreeRMQ2 {
public int M, H, N;
public SegmentTreeRMQL[] st;
public int[][] maps;
public long[][] vals;
public int[] count;
public long I = Long.MAX_VALUE;
public StaticRangeTreeRMQ2(int[][] co, int n)
{
N = n;
M = Integer.highestOneBit(Math.max(N-1, 1))<<2;
H = M>>>1;
mergesort0(co, 0, co.length);
// Arrays.sort(co, new Comparator<int[]>() { // x asc
// public int compare(int[] a, int[] b) {
// if(a[0] != b[0])return a[0] - b[0];
// return a[1] - b[1];
// }
// });
maps = new int[M][];
vals = new long[M][];
st = new SegmentTreeRMQL[M];
count = new int[M];
for(int i = 0;i < co.length;i++){
count[H+co[i][0]]++;
}
int off = 0;
for(int i = 0;i < n;i++){
maps[H+i] = new int[count[H+i]];
for(int j = 0;j < count[H+i];j++,off++){
maps[H+i][j] = co[off][1];
}
st[H+i] = new SegmentTreeRMQL(count[H+i]);
}
for(int i = H-1;i >= 1;i--){
if(maps[2*i+1] == null){
maps[i] = maps[2*i];
count[i] = count[2*i];
}else{
count[i] = count[2*i] + count[2*i+1];
maps[i] = new int[count[i]];
int l = 0;
for(int j = 0, k = 0;j < count[2*i] || k < count[2*i+1];l++){
if(j == count[2*i]){
maps[i][l] = maps[2*i+1][k++];
}else if(k == count[2*i+1]){
maps[i][l] = maps[2*i][j++];
}else if(maps[2*i][j] < maps[2*i+1][k]){
maps[i][l] = maps[2*i][j++];
}else if(maps[2*i][j] > maps[2*i+1][k]){
maps[i][l] = maps[2*i+1][k++];
}else{
maps[i][l] = maps[2*i][j++];
k++;
}
}
if(l != count[i]){ // uniq
count[i] = l;
maps[i] = Arrays.copyOf(maps[i], l);
}
}
if(count[i] <= 25){ // 10% faster
vals[i] = new long[count[i]];
Arrays.fill(vals[i], Long.MAX_VALUE / 2);
}else{
st[i] = new SegmentTreeRMQL(count[i]);
}
}
}
public void update(int x, int y, long v)
{
outer:
for(int pos = H+x;pos >= 1;pos>>>=1){
if(st[pos] != null){
int ind = Arrays.binarySearch(maps[pos], y);
if(ind >= 0){
st[pos].update(ind, v);
continue;
}
}else{
for(int i = 0;i < count[pos];i++){
if(maps[pos][i] == y){
vals[pos][i] = v;
continue outer;
}
}
}
throw new RuntimeException(String.format("access to non-existing point : (%d,%d):%d", x, y, v));
}
}
public long min(int xl, int xr, int yl, int yr) { return min(xl, xr, yl, yr, 0, H, 1); }
public long min(int xl, int xr, int yl, int yr, int cl, int cr, int cur)
{
if(xl <= cl && cr <= xr){
if(st[cur] != null){
int indl = Arrays.binarySearch(maps[cur], yl);
int indr = Arrays.binarySearch(maps[cur], yr);
if(indl < 0)indl = -indl - 1;
if(indr < 0)indr = -indr - 1;
return st[cur].minx(indl, indr);
}else{
long min = I;
for(int i = 0;i < count[cur] && maps[cur][i] < yr;i++){
if(maps[cur][i] >= yl && vals[cur][i] < min) min = vals[cur][i];
}
return min;
}
}else{
int mid = cl+cr>>>1;
long ret = I;
if(cl < xr && xl < mid)ret = Math.min(ret, min(xl, xr, yl, yr, cl, mid, 2*cur));
if(mid < xr && xl < cr)ret = Math.min(ret, min(xl, xr, yl, yr, mid, cr, 2*cur+1));
return ret;
}
}
}
public static class SegmentTreeRMQL {
public int M, H, N;
public long[] st;
public SegmentTreeRMQL(int n)
{
N = n;
M = Integer.highestOneBit(Math.max(N-1, 1))<<2;
H = M>>>1;
st = new long[M];
Arrays.fill(st, 0, M, Long.MAX_VALUE/2);
}
public SegmentTreeRMQL(long[] a)
{
N = a.length;
M = Integer.highestOneBit(Math.max(N-1, 1))<<2;
H = M>>>1;
st = new long[M];
for(int i = 0;i < N;i++){
st[H+i] = a[i];
}
Arrays.fill(st, H+N, M, Long.MAX_VALUE);
for(int i = H-1;i >= 1;i--)propagate(i);
}
public void update(int pos, long x)
{
st[H+pos] = x;
for(int i = (H+pos)>>>1;i >= 1;i >>>= 1)propagate(i);
}
private void propagate(int i)
{
st[i] = Math.min(st[2*i], st[2*i+1]);
}
public long minx(int l, int r){
long min = Long.MAX_VALUE;
if(l >= r)return min;
while(l != 0){
int f = l&-l;
if(l+f > r)break;
long v = st[(H+l)/f];
if(v < min)min = v;
l += f;
}
while(l < r){
int f = r&-r;
long v = st[(H+r)/f-1];
if(v < min)min = v;
r -= f;
}
return min;
}
public long min(int l, int r){ return l >= r ? 0 : min(l, r, 0, H, 1);}
private long min(int l, int r, int cl, int cr, int cur)
{
if(l <= cl && cr <= r){
return st[cur];
}else{
int mid = cl+cr>>>1;
long ret = Long.MAX_VALUE;
if(cl < r && l < mid){
ret = Math.min(ret, min(l, r, cl, mid, 2*cur));
}
if(mid < r && l < cr){
ret = Math.min(ret, min(l, r, mid, cr, 2*cur+1));
}
return ret;
}
}
public int firstle(int l, long v) {
int cur = H+l;
while(true){
if(st[cur] <= v){
if(cur < H){
cur = 2*cur;
}else{
return cur-H;
}
}else{
cur++;
if((cur&cur-1) == 0)return -1;
if((cur&1)==0)cur>>>=1;
}
}
}
public int lastle(int l, long v) {
int cur = H+l;
while(true){
if(st[cur] <= v){
if(cur < H){
cur = 2*cur+1;
}else{
return cur-H;
}
}else{
if((cur&cur-1) == 0)return -1;
cur--;
if((cur&1)==1)cur>>>=1;
}
}
}
}
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 D().run(); }
private byte[] inbuf = new byte[1024];
public 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)); }
}Maximizing Mission Points C++ Solution
//start of jonathanirvings' template v3.0.3 (BETA)
#include <bits/stdc++.h>
using namespace std;
typedef long long LL;
typedef pair<int,int> pii;
typedef pair<LL,LL> pll;
typedef pair<string,string> pss;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<pii> vii;
typedef vector<LL> vl;
typedef vector<vl> vvl;
double EPS = 1e-9;
int INF = 1000000005;
long long INFF = 1000000000000000005LL;
double PI = acos(-1);
int dirx[8] = {-1,0,0,1,-1,-1,1,1};
int diry[8] = {0,1,-1,0,-1,1,-1,1};
#ifdef TESTING
#define DEBUG fprintf(stderr,"====TESTING====\n")
#define VALUE(x) cerr << "The value of " << #x << " is " << x << endl
#define debug(...) fprintf(stderr, __VA_ARGS__)
#else
#define DEBUG
#define VALUE(x)
#define debug(...)
#endif
#define FOR(a,b,c) for (int (a)=(b);(a)<(c);++(a))
#define FORN(a,b,c) for (int (a)=(b);(a)<=(c);++(a))
#define FORD(a,b,c) for (int (a)=(b);(a)>=(c);--(a))
#define FORSQ(a,b,c) for (int (a)=(b);(a)*(a)<=(c);++(a))
#define FORC(a,b,c) for (char (a)=(b);(a)<=(c);++(a))
#define FOREACH(a,b) for (auto &(a) : (b))
#define REP(i,n) FOR(i,0,n)
#define REPN(i,n) FORN(i,1,n)
#define MAX(a,b) a = max(a,b)
#define MIN(a,b) a = min(a,b)
#define SQR(x) ((LL)(x) * (x))
#define RESET(a,b) memset(a,b,sizeof(a))
#define fi first
#define se second
#define mp make_pair
#define pb push_back
#define ALL(v) v.begin(),v.end()
#define ALLA(arr,sz) arr,arr+sz
#define SIZE(v) (int)v.size()
#define SORT(v) sort(ALL(v))
#define REVERSE(v) reverse(ALL(v))
#define SORTA(arr,sz) sort(ALLA(arr,sz))
#define REVERSEA(arr,sz) reverse(ALLA(arr,sz))
#define PERMUTE next_permutation
#define TC(t) while(t--)
inline string IntToString(LL a){
char x[100];
sprintf(x,"%lld",a); string s = x;
return s;
}
inline LL StringToInt(string a){
char x[100]; LL res;
strcpy(x,a.c_str()); sscanf(x,"%lld",&res);
return res;
}
inline string GetString(void){
char x[1000005];
scanf("%s",x); string s = x;
return s;
}
inline string uppercase(string s){
int n = SIZE(s);
REP(i,n) if (s[i] >= 'a' && s[i] <= 'z') s[i] = s[i] - 'a' + 'A';
return s;
}
inline string lowercase(string s){
int n = SIZE(s);
REP(i,n) if (s[i] >= 'A' && s[i] <= 'Z') s[i] = s[i] - 'A' + 'a';
return s;
}
inline void OPEN (string s) {
#ifndef TESTING
freopen ((s + ".in").c_str (), "r", stdin);
freopen ((s + ".out").c_str (), "w", stdout);
#endif
}
//end of jonathanirvings' template v3.0.3 (BETA)
int n,x,y;
pair<pii,pii> data[200005];
pii P[200005];
int p[200005];
vector<int> pos[800005];
vector<LL> val[800005];
int sz[800005];
void preassign(int ix,int L,int R,int x)
{
++sz[ix];
if (L == R) return;
int M = (L + R) >> 1;
if (x <= M) preassign(ix*2+1,L,M,x);
else preassign(ix*2+2,M+1,R,x);
}
void assign(int ix,int L,int R,int x,int y)
{
// pos[ix].pb(y);
--sz[ix];
pos[ix][sz[ix]] = y;
if (L == R) return;
int M = (L + R) >> 1;
if (x <= M) assign(ix*2+1,L,M,x,y);
else assign(ix*2+2,M+1,R,x,y);
}
inline void update1D(int ix1,int ix2,int L,int R,int y,LL v)
{
// debug("<<<<<<%d %d %d %d %d %lld\n",ix1,ix2,L,R,y,v);
MAX(val[ix1][ix2],v);
if (L == R) return;
int M = (L + R) >> 1;
if (y <= pos[ix1][M]) update1D(ix1,ix2*2+1,L,M,y,v);
else update1D(ix1,ix2*2+2,M+1,R,y,v);
}
inline void update2D(int ix,int L,int R,int x,int y,LL v)
{
// debug("<<%d %d %d %d %d %lld\n",ix,L,R,x,y,v);
// int temp = lower_bound(ALL(pos[ix]),y) - pos[ix].begin();
update1D(ix,0,0,SIZE(pos[ix])-1,y,v);
if (L == R) return;
int M = (L + R) >> 1;
if (x <= M) update2D(ix*2+1,L,M,x,y,v);
else update2D(ix*2+2,M+1,R,x,y,v);
}
inline LL query1D(int ix1,int ix2,int L,int R,int ya,int yb)
{
// debug(">>>>>%d %d %d %d %d %d\n",ix1,ix2,L,R,ya,yb);
if (ya <= pos[ix1][L] && pos[ix1][R] <= yb) return val[ix1][ix2];
if (pos[ix1][R] < ya || yb < pos[ix1][L]) return 0;
int M = (L + R) >> 1;
return max(query1D(ix1,ix2*2+1,L,M,ya,yb),query1D(ix1,ix2*2+2,M+1,R,ya,yb));
}
inline LL query2D(int ix,int L,int R,int xa,int xb,int ya,int yb)
{
// debug(">>%d %d %d %d %d %d %d\n",ix,L,R,xa,xb,ya,yb);
if (xa <= L && R <= xb)
{
if (pos[ix].empty()) return 0;
// if (tempa > tempb) return 0;
return query1D(ix,0,0,SIZE(pos[ix])-1,ya,yb);
}
if (R < xa || xb < L) return 0;
int M = (L + R) >> 1;
return max(query2D(ix*2+1,L,M,xa,xb,ya,yb),query2D(ix*2+2,M+1,R,xa,xb,ya,yb));
}
bool f(pair<pii,pii> a, pair<pii,pii> b)
{
return a.se.se > b.se.se;
}
int main()
{
scanf("%d %d %d",&n,&x,&y);
REP(i,n)
{
scanf("%d %d %d %d",&data[i].se.fi,&data[i].se.se,&data[i].fi.fi,&data[i].fi.se);
}
sort(ALLA(data,n),f);
REP(i,n) preassign(0,0,200000,data[i].se.fi);
FORN(i,0,800000)
{
// SORT(pos[i]);
pos[i].resize(sz[i]);
val[i].resize(sz[i]*4);
}
REP(i,n) assign(0,0,200000,data[i].se.fi,data[i].se.se);
SORTA(data,n);
REP(i,n)
{
P[i] = data[i].se;
p[i] = data[i].fi.se;
}
// REP(i,n) assign(0,0,200000,P[i].fi,P[i].se);
// FORN(i,0,800000)
// {
// // SORT(pos[i]);
// val[i].resize(SIZE(pos[i])*4);
// }
LL risan = 0;
// return 0;
FORD(i,n-1,0)
{
// VALUE(i);
int xa = max(0,P[i].fi-x);
int xb = min(200000,P[i].fi+x);
int ya = max(0,P[i].se-y);
int yb = min(200000,P[i].se+y);
LL temp = query2D(0,0,200000,xa,xb,ya,yb);
// VALUE(temp);
temp += p[i];
MAX(risan,temp);
update2D(0,0,200000,P[i].fi,P[i].se,temp);
}
printf("%lld\n",risan);
return 0;
}
