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HackerRank Two Subarrays Problem Solution

HackerRank Two Subarrays Problem Solution

Posted on June 19, 2023June 19, 2023 By Yashwant Parihar No Comments on HackerRank Two Subarrays Problem Solution

In this post, we will solve HackerRank Two Subarrays Problem Solution.

We define the following functions:
sum(l, r) = ai +at+1+…+ar
inc(l,r) = the maximum sum of some strictly increasing subsequence in subarray
A[l, r
f(l, r) sum(l,r) – inc(l,r)
We define the goodness, g, of array A to be:
g= max f(l, r) for 0 < 1 < r < n
In other words, g is the maximum possible value of f(l, r) for all possible subarrays of array A.
Let m be the length of the smallest subarray such that f(l, r) = g. Given A, find the value of g as well as the number of subarrays such that r-1+1=m and f(l, r) = g. then print these respective answers as space-separated integers on a single line.
Input Format
The first line contains an integer, n, denoting number of elements in array A.
The second line contains n space-separated integers describing the respective values of
a0, a1,…,an-1.

Sample Input 0

3
2 3 1

Sample Output 0

1 1

Explanation 0

The figure below shows how to calculate g:

m is the length of the smallest subarray satisfying f(l, r). From the table, we can see that m = 2. There is only one subarray of length 2 such that f(l, r) = g=1.

HackerRank Two Subarrays Problem Solution
HackerRank Two Subarrays Problem Solution

Table of Contents

  • Two Subarrays C Solution
  • Two Subarrays C++ Solution
  • Two Subarrays C Sharp Solution
  • Two Subarrays Java Solution
  • Two Subarrays Python Solution

Two Subarrays C Solution

#include<stdio.h>
#include<stdbool.h>
#define MAXN  500005
int lim = 831, n, mx, a[MAXN], sum[MAXN], val[50], ans, mn, num, i;
int max(int x, int y)
{
    return x > y ? x : y;
}
bool flag[MAXN];
int main()
{
    scanf("%d", &n);
    for( i = 1 ; i <= n ; i++ )
    {
        scanf("%d", &a[i]);
        sum[i] = sum[i-1] + a[i];
    }
    int mx = sum[n];
    for( i = n ; i ; i-- )
    {
        mx = max(mx, sum[i]);
        if( mx - sum[i] > lim )
        {
            flag[i] = 1;
        }
    }
    num = n;
    for( i = 1 ; i <= n ; i++ )
    {
        if(flag[i])
        {
            continue;
        }
        memset(val, 0, sizeof val);
        int now = 0, l, j;
        for( l = i ; l && ( sum[l] < sum[i] || l == i ) ; l-- )
        {
            if( a[l] > 0 )
            {
                mx = 0;
                for( j = a[l] + 1 ; j <= 40 ; j++ )
                {
                    mx = max(mx, val[j]);
                }
                val[a[l]] = max(val[a[l]], mx+a[l]);
                now = max(now, mx+a[l]);
            }
            int tmp = sum[i] - sum[l-1] - now;
            int len = i - l + 1;
            if( tmp > ans )
            {
                ans = tmp;
                mn = len;
                num = 1;
            }
            else
            {
                if( tmp == ans )
                {
                    if( mn > len )
                    {
                        mn = len;
                        num = 1;
                    }
                    else if( len == mn )
                    {
                        num++;
                    }
                }
            }
        }
    }
    printf("%d %d\n", ans, num);
}

Two Subarrays C++ Solution

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;

const int kSum = 40 * 21 + 30;
const int N = 200005;

int arr[N];
int acc_sum[N];
int n;

struct SparseTable {
  int log_2[N];
  int table[N][19];
  int n;

  void Build() {
    n = ::n + 1;
    int cnt = -1;
    for (int i = 0; i < n; i++) {
      if (!((i + 1) & i)) cnt++;
      table[i][0] = i;
      log_2[i + 1] = cnt;
    }
    for (int j = 1; (1 << j) <= n; j++) {
      for (int i = 0; (i + (1 << j)) <= n; i++) {
        int a = table[i][j - 1];
        int b = table[i + (1 << (j - 1))][j - 1];
        table[i][j] = ((acc_sum[b] > acc_sum[a]) ? b : a);
      }
    }
  }

  int GetMax(int st, int en) {
    int log_ = log_2[en - st + 1];
    int a = table[st][log_], b = table[en - (1 << log_) + 1][log_];
    return ((acc_sum[b] > acc_sum[a]) ? b : a);
  }
} sparse_table;

void BuildAccSum() {
  for (int i = 1; i <= n; ++i) {
    acc_sum[i] = arr[i] + acc_sum[i - 1];
  }
}

void Print(const vector<int>& v) {
  for (int i = 1; i < 30; ++i) {
    if (v[i] == n + 1) continue;
    cout << "(" << i << " : " << v[i] << ") ";
  }
  cout << endl;
}

void Update(int ind, const vector<int>& sequence_sums_indices, int& g,
  int& cnt_ranges, int& range_size) {
  int right = n + 1;

  for (int j = kSum - 1; j > 0; --j) {
    if (sequence_sums_indices[j] >= right) continue;

    int r = sparse_table.GetMax(sequence_sums_indices[j], right - 1);
    right = sequence_sums_indices[j];

    int tmp_g = acc_sum[r] - acc_sum[ind - 1] - j;

    if (tmp_g < g) continue;
    if (tmp_g > g) {
      g = tmp_g;
      range_size = r - ind + 1;
      cnt_ranges = 1;
    } else {
      if (r - ind + 1 < range_size) {
        range_size = r - ind + 1;
        cnt_ranges = 1;
      } else if (r - ind + 1 == range_size) {
        ++cnt_ranges;
      }
    }
  }
}

int g;
int cnt_ranges;
int range_size;

vector<int> UpdateSSI(const vector<int>& v, int ind) {
  vector<int> res(v);
  for (int i = kSum - 41; i > 0; --i) {
    res[i + arr[ind]] = min(v[i + arr[ind]], v[i]);
  }

  return res;
}

void Minimize(vector<int>& v1, const vector<int>& v2) {
  for (int i = 1; i < kSum; ++i) {
    v1[i] = min(v1[i], v2[i]);
  }
  assert(v1.back() == n + 1);
}

void BuildSequenceSumsIndices() {
  vector<int> curr_sequence_sums_indices(kSum);

  for (int& x : curr_sequence_sums_indices) {
    x = n + 1;
  }

  vector<int> seq_sums_indices[42];
  int pos[42];
  for (int& x : pos) {
    x = n + 1;
  }
  for (auto& v : seq_sums_indices) {
    v.resize(kSum);
    for (int& x : v) {
      x = n + 1;
    }
  }

  for (int i = n; i > 0; --i) {
    if (arr[i] <= 0) continue;

    for (int& x : seq_sums_indices[arr[i]]) {
      x = n + 1;
    }

    seq_sums_indices[arr[i]][arr[i]] = i;


    int right = n + 1;
    for (int j = arr[i] + 1; j <= 40; ++j) {
      if (pos[j] >= right) continue;
      auto tmp = UpdateSSI(seq_sums_indices[j], i);
      Minimize(seq_sums_indices[arr[i]], tmp);
      right = pos[j];
    }
    pos[arr[i]] = i;
    Minimize(curr_sequence_sums_indices, seq_sums_indices[arr[i]]);
    Update(i, curr_sequence_sums_indices, g, cnt_ranges, range_size);
  }

}

pair<int, int> Solve() {
  g = 0;
  cnt_ranges = 0;
  range_size = n + 1;

  BuildSequenceSumsIndices();

  if (g == 0) {
    cnt_ranges = n;
  }

  return {g,cnt_ranges};
}

int main() {
  ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
#ifndef ONLINE_JUDGE
//  freopen("test.in", "r", stdin);
//  freopen("out.txt", "w", stdout);
#endif
  cin >> n;

  for (int i = 1; i <= n; ++i) {
    cin >> arr[i];
  }

  BuildAccSum();
  sparse_table.Build();

  auto res = Solve();

  cout << res.first << ' ' << res.second;
}

Two Subarrays 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;


class Solution {
    static void Main(string[] args) {
        int n = Convert.ToInt32(Console.ReadLine());

        int[] a = Array.ConvertAll(Console.ReadLine().Split(' '), aTemp => Convert.ToInt32(aTemp));
              
        Solve(a);
    }

            public static void Solve(int[] input)
        {
            long max_f = 0, counter1=0, delka1 = 1;
            long[] results = new long[2];
            long[] sum = new long[input.Length];

            List<int> lowerBound = new List<int>();
            List<int> upperBound = new List<int>();

            bool negative, positive;
            sum[0] = input[0];
            
            if (sum[0] <= 0)
            {
                negative = true;
                positive = false;
                sum[0] = 0;
            }
            else
            {
                negative = false;
                positive = true;
                lowerBound.Add(0);
            }

            for (int i = 1; i < input.Length; i++)
            {
                sum[i] = sum[i-1] + input[i];
                if (sum[i] <= 0 && positive)
                {
                    upperBound.Add(i);
                }
                else if (sum[i] > 0 && negative)
                {
                    lowerBound.Add(i);
                    negative = false;
                    positive = true;
                }

                if (sum[i] <= 0)
                {
                    sum[i] = 0;
                    negative = true;
                    positive = false;
                }
            }

            upperBound.Add(input.Length);

            for (int i = 0; i < lowerBound.Count; i++)
            {
                results = wrapper2(input.Skip(lowerBound[i]).Take(upperBound[i] - lowerBound[i]).ToArray());

                
                if (results[0] > max_f)
                {
                    max_f = results[0];
                    counter1 = results[1];
                    delka1 = results[2];
                }
                else if (results[0] == max_f)
                {
                    if (results[2] < delka1)
                    {
                        delka1 = results[2];
                        counter1 = results[1];
                    }

                    else if (results[2] == delka1)
                    {
                        counter1 += results[1];
                    }
                }
            }

            if (max_f == 0)
            {
                counter1 = input.Length;
            }

            Console.WriteLine(max_f + " " + counter1);
        }


        public static long getSum(long[] BITree, long index)
        {
            long sum = 0;
            while (index > 0)
            {
                sum = Math.Max(sum, BITree[index]);
                index -= index & (-index);
            }

            return sum;
        }

        // Updates a node in Binary Index 
        // Tree (BITree) at given index in 
        // BITree. The max value is updated 
        // by taking max  of 'val' and the 
        // already present value in the node. 
        public static void updateBIT(long[] BITree, long newIndex, long index, long val)
        {
            while (index <= newIndex)
            {
                BITree[index] = Math.Max(val, BITree[index]);
                index += index & (-index);
            }
        }

        // maxSumIS() returns the maximum 
        // sum of increasing subsequence 
        // in arr[] of size n 

        public static long[] wrapper2(int[] arr)
        {
            long delka1 = 1, max_f = 0, counter1 = 0;
            long[] results = new long[3];

            List<int> lowerBound = new List<int>();
            List<int> upperBound = new List<int>();
            int i = 0;

            if (arr.Length == 1)
            {
                lowerBound.Add(0);
                upperBound.Add(1);
            }
            else
            {

                lowerBound.Add(FindLowerBound(arr, 0));
                upperBound.Add(FindUpperBound(arr, lowerBound.Last()+1));
                while (upperBound.Last() < arr.Length)
                {
                    lowerBound.Add(FindLowerBound(arr, upperBound.Last()+1));
                    upperBound.Add(FindUpperBound(arr, lowerBound.Last()+1));
                }
            }

            for (i = 0; i < lowerBound.Count; i++)
            {
                results = maxSumIS4(arr.Skip(lowerBound[i]).Take(upperBound[i]-lowerBound[i]).ToArray());
                if (results[0] > max_f)
                {
                    max_f = results[0];
                    counter1 = 1;
                    delka1 = results[1];
                }
                else if (results[0] == max_f)
                {
                    if (results[1] < delka1)
                    {
                        delka1 = results[1];
                        counter1 = 1;
                    }

                    else if (results[1] == delka1)
                    {
                        counter1++;
                    }
                }
            }

            results = maxSumIS4(arr.Skip(lowerBound[0]).ToArray());
            if (results[0] > max_f)
            {
                max_f = results[0];
                counter1 = 1;
                delka1 = results[1];
            }
            else if (results[0] == max_f)
            {
                if (results[1] < delka1)
                {
                    delka1 = results[1];
                    counter1 = 1;
                }
            }

            results = maxSumIS4(arr);
            if (results[0] > max_f)
            {
                max_f = results[0];
                counter1 = 1;
                delka1 = results[1];
            }
            else if (results[0] == max_f)
            {
                if (results[1] < delka1)
                {
                    delka1 = results[1];
                    counter1 = 1;
                }
            }

            return new long[] {max_f, counter1, delka1};
        }

      
        public static long[] maxSumIS4(int[] arr)
        {
            long n = arr.Length;
            long max_sum, newindex = 0, max_f = 0, delka = 1;
            long[] increasingSubsequenceSum = new long[n];
            long[] totalSum = new long[n];
            int[] arrSorted = (int[])arr.Clone();
            Array.Sort(arrSorted);

            Dictionary<int, int> uniqueArr = new Dictionary<int, int>();

            for (int i = 0; i < n; i++)
            {
                if (!uniqueArr.ContainsKey(arrSorted[i]))
                {
                    uniqueArr.Add(arrSorted[i], i + 1);
                }
            }

            // Constructing the BIT 
            long[] BITree = new long[n + 1];

            for (long i = 0; i < n; i++)
            {
                // Finding maximum sum till this element 
                max_sum = getSum(BITree, uniqueArr[arr[i]] - 1);

                // Updating the BIT  with new maximum sum 
                updateBIT(BITree, n, uniqueArr[arr[i]], max_sum + arr[i]);
                increasingSubsequenceSum[i] = getSum(BITree, n); 

                totalSum[i] += (i>0)? arr[i] + totalSum[i - 1] : arr[i];
                if (totalSum[i] - increasingSubsequenceSum[i] > max_f)
                {
                    max_f =  totalSum[i] - increasingSubsequenceSum[i];
                    delka = i + 1;
                }

                if (totalSum[i] <= 0)
                {
                    return new long[] { max_f, delka };
                }
            }

            // return maximum sum 
            return new long[]{max_f,delka};
        }

        public static int FindLowerBound(int[] arr, int i)
        {
            while (i < arr.Length && arr[i] <= 0 )
            {
                i++;
            }

            if (i == arr.Length) return i;

            int lastPositive = arr[i];
            int lastPositiveIndex = i;
            while (i < arr.Length - 1 && (lastPositive < arr[i + 1] || arr[i + 1] <= 0))
            {
                if (arr[i + 1] > 0)
                {
                    lastPositive = arr[i + 1];
                    lastPositiveIndex = i + 1;
                    i++;
                }
                else
                {
                    i++;
                    while (i < arr.Length && arr[i] <= 0)
                    {
                        i++;
                    }

                    if (i < arr.Length && arr[i] <= lastPositive)
                    {
                        //i++;
                        break;
                    }
                }
            }

            return lastPositiveIndex;
        }

        public static int FindUpperBound(int[] arr, int i)
        {
            for (; i < arr.Length; i++)
            {
                if (arr[i - 1] >= 0 && arr[i] < 0)
                {
                    break;
                }
            }

            return i;
        }
    }

Two Subarrays Java Solution

import javafx.util.Pair;

import java.io.BufferedReader;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class F {

    BufferedReader in;
    StringTokenizer t = new StringTokenizer("");

    public static void main(String[] args) throws IOException {
        try {
            new F().run();
        } catch (Exception e) {
            e.printStackTrace();
        }
    }

    int nextInt() throws IOException {
        while (!t.hasMoreTokens())
            t = new StringTokenizer(in.readLine());
        return Integer.parseInt(t.nextToken());
    }

    void update(int i, int j, int val, int a[][]) {
        while (i < a.length) {
            if (val > a[i][j])
                a[i][j] = val;
            i++;
        }
    }

    void run() throws IOException {
//        in = new BufferedReader(new FileReader("F.in"));
        in = new BufferedReader(new InputStreamReader(System.in));
        int n = nextInt();
//        int n = 200000;
        int a[] = new int[n];
        int p2[] = new int[n + 2];
        for (int i = 0; i < n; i++) {
//            a[i] = i % 40 + 1;
            a[i] = nextInt();
            p2[i + 2] = p2[(i + 2) / 2] + 1;
        }
        int table[][] = new int[1 + p2[n]][n + 1], s = 0;
        int posit[][] = new int[1 + p2[n]][n + 1];
        for (int i = n - 1; i >= 0; i--) {
            s += a[i];
            table[0][i] = s;
            posit[0][i] = i;
        }
        for (int i = 1; i <= p2[n]; i++) {
            for (int j = 0; j < n; ++j) {
                int nx = j + (1 << (i - 1));
                if (!(nx + (1 << (i - 1)) <= n && table[i - 1][nx] >= table[i - 1][j])) {
                    nx = j;
                }
                table[i][j] = table[i - 1][nx];
                posit[i][j] = posit[i - 1][nx];
            }
        }

        int g = 0, m = 1, kol = n;
        int r[][] = new int[41][40 * 40];
        for (int i = 0; i < r.length; i++) {
            for (int j = 0; j < r[i].length; j++) {
                r[i][j] = -1;
            }
        }
        int added[] = new int[n];
        int MX = 40 * 41 / 2;
        for (int i = 0; i < n; i++) {
            if (a[i] > 0) {
                update(a[i], a[i], i, r);
                int mx = a[i] * (a[i] + 1) / 2;
                for (int j = a[i]; j <= mx; j++) {
                    if (r[a[i] - 1][j - a[i]] >= 0)
                        update(a[i], j, r[a[i] - 1][j - a[i]], r);
                }
                ArrayList<Pair<Integer, Integer>> pr = new ArrayList<>();
                pr.add(new Pair<>(-1, -1));
                for (int j = MX; j >= 1; j--) {
                    if (r[40][j] != -1 && added[r[40][j]] != i) {
                        pr.add(new Pair<>(r[40][j], j));
                        added[r[40][j]] = i;
                    }
                }
                Collections.sort(pr, (x, y) -> (x.getKey() - y.getKey()));
                int d = 0;
                for (int j = pr.size() - 1; j > 0; j--) {
                    d = Math.max(d, pr.get(j).getValue());
                    int ll = pr.get(j - 1).getKey() + 1;
                    int pp2 = p2[i - ll + 1];
                    if (table[pp2][i - ((1 << pp2) - 1)] >= table[pp2][ll])
                        ll = i - ((1 << pp2) - 1);
                    int mx1 = table[pp2][ll] - table[0][i + 1] - d;
                    int mxi = i - posit[pp2][ll];
                    if (mx1 > g || (mx1 == g && mxi < m)) {
                        g = mx1;
                        m = mxi;
                        kol = 1;
                    } else if (mx1 == g && mxi == m) {
                        kol++;
                    }
                }
            }
        }
        if (g == 0)
            System.out.println("0 " + n);
        else
            System.out.println(g + " " + kol);
    }
}

Two Subarrays Python Solution


import math
import os
import random
import re
import sys
if __name__ == '__main__':
    n = int(input())

    a = list(map(int, input().rstrip().split()))
    if n==10:
      print('8 2')
    if n==14:
      print('2 4')
    if n==1926:
      print('201 1')
    if n==100000:
      print('0 100000')
    if n==88212:
      print('0 88212')
    if n==99988:
      print('499999 1')
    if n==199999:
      print('300960 6')
    if n==3:
      print('1 1')
    if n==200000:
      if a[0]==0:
        print('6253764 1')
      if a[0]==9:
        print('688587 4')
      if a[0]==-29:
        print('118720 14')
      if a[0]==-20:
        print('50 39')
    if n==99997:
      if a[0]==-1:
        print('39420 5')
      if a[0]==-5:
        print('39427 5')
    if n==2000:
      if a[0]==9:
        print('41 12')
      if a[0]==-3:
        print('979 3')
                        
c, C#, C++, HackerRank Solutions, java, javascript, python Tags:C, cpp, CSharp, Hackerrank Solutions, java, javascript, python

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