Given a 2-dimensional integer array arr[] representing N ranges, each of type [starti, endi] (starti, endi ≤ 109) and Q queries represented in array query[], the task is to find the maximum occurrence of query[i] (query[i] ≤ 109) in the given ranges for all i in the range [0, Q-1].
Examples:
Input: arr[] = {{1, 5}, {3, 6}, {5, 7}, {12, 15}}, query[] = {1, 3, 5, 13}
Output: {1, 2, 3, 1}
Explanation: The occurrence of 1 in the range is 1.
The occurrence of 3 in the range is 2.
The occurrence of 5 in the range is 3.
The occurrence of 13 in the range is 1.Input: arr[] = {{2, 5}, {9, 11}, {3, 9}, {15, 20}}, query[] = {3, 9, 16, 55}
Output: {2, 2, 1, 0}
Naive approach: For each query, traverse the array and check whether query[j] is in the range of arr[i] = [starti, endi]. If it is in the range then increment the counter for the occurrence of that element and store this counter corresponding to query[j] in the result.
Time Complexity: O(Q * N)
Auxiliary Space: O(1)
Efficient approach: The problem can be solved based on the following idea:
Use the technique of prefix sum to store the occurrences of each element and it will help to find the answer for each query in constant time.
Follow the steps below to implement the above idea:
- Declare a one-dimensional array (say prefixSum[]) of length M (where M is the maximum element in arr[]) to store the occurrence of each element.
- Iterate over the array arr[] and do the following for each starti and endi :
- Increment the value at prefixSum[starti] by 1
- Decrement the value at prefixSum[endi + 1] by 1
- Iterate over prefixSum[] array and calculate prefix sum. Using this, the occurrences of each element in the given ranges will get calculated
- Iterate over the queries array and for each query get the value of prefixSum[query[i]] and store it into the resultant array.
- Return the result array.
Below is the implementation of the above approach:
C++
// C++ code to implement the approach#include <bits/stdc++.h>using namespace std;
#define MAX 10000000// Function to find occurrences of// each element in arrayvoid findTheOccurrence(vector<vector<int> >& arr,
vector<int>& q,
vector<int>& result)
{ vector<int> prefixSum(MAX);
// Iterating over arr
for (int i = 0; i < arr.size(); i++) {
int start = arr[i][0];
int end = arr[i][1];
// Increment the value of
// prefixSum at start
prefixSum[start]++;
// Decrement the value of
// prefixSum at end + 1
prefixSum[end + 1]--;
}
// Calculating the prefix sum
for (int i = 1; i < prefixSum.size(); i++) {
prefixSum[i]
= prefixSum[i - 1] + prefixSum[i];
}
// Resolving each queries
for (int i = 0; i < q.size(); i++) {
int occurrence = prefixSum[q[i]];
result.push_back(occurrence);
}
}// Driver codeint main()
{ vector<vector<int> > arr
= { { 1, 5 }, { 3, 6 }, { 5, 7 }, { 12, 15 } };
vector<int> query = { 1, 3, 5, 13 };
vector<int> result;
// Function call
findTheOccurrence(arr, query, result);
for (auto i : result)
cout << i << " ";
return 0;
} |
Java
// Java program for the above approachimport java.io.*;
import java.util.*;
class GFG
{ static int MAX = 10000000;
// Function to find occurrences of
// each element in array
static void findTheOccurrence(int[][] arr, int[] q,
ArrayList<Integer> result)
{
int[] prefixSum = new int[(MAX)];
// Iterating over arr
for (int i = 0; i < arr.length; i++) {
int start = arr[i][0];
int end = arr[i][1];
// Increment the value of
// prefixSum at start
prefixSum[start]++;
// Decrement the value of
// prefixSum at end + 1
prefixSum[end + 1]--;
}
// Calculating the prefix sum
for (int i = 1; i < prefixSum.length; i++) {
prefixSum[i]
= prefixSum[i - 1] + prefixSum[i];
}
// Resolving each queries
for (int i = 0; i < q.length; i++) {
int occurrence = prefixSum[q[i]];
result.add(occurrence);
}
}
// Driver Code
public static void main(String args[])
{
int[][] arr
= { { 1, 5 }, { 3, 6 }, { 5, 7 }, { 12, 15 } };
int[] query = { 1, 3, 5, 13 };
ArrayList<Integer> result
= new ArrayList<Integer>();
// Function call
findTheOccurrence(arr, query, result);
for (int i : result)
System.out.print(i + " ");
}
}// This code is contributed by sanjoy_62. |
Python3
# Python3 code to implement the approachMAX = 10000;
# Function to find occurrences of# each element in arraydef findTheOccurrence(arr, q, result):
prefixSum = [0] * MAX
# Iterating over arr
for i in range(len(arr)):
start = arr[i][0];
end = arr[i][1];
# Increment the value of
# prefixSum at start
prefixSum[start] += 1
# Decrement the value of
# prefixSum at end + 1
prefixSum[end + 1] -= 1
# Calculating the prefix sum
for i in range(1, len(prefixSum)):
prefixSum[i] = prefixSum[i - 1] + prefixSum[i];
# Resolving each queries
for i in range(0, len(q)):
occurrence = prefixSum[q[i]];
result.append(occurrence);
return result;
# Driver codearr = [[ 1, 5 ], [ 3, 6 ], [ 5, 7 ], [ 12, 15 ] ];
query = [ 1, 3, 5, 13 ];
result = [];
# Function callfindTheOccurrence(arr, query, result);for i in range(len(result)):
print(result[i], end=" ");
# This code is contributed by Saurabh Jaiswal |
C#
// C# program to implement// the above approachusing System;
using System.Collections.Generic;
class GFG
{ static int MAX = 10000000;
// Function to find occurrences of
// each element in array
static void findTheOccurrence(int[,] arr, int[] q,
List<int> result)
{
int[] prefixSum = new int[(MAX)];
// Iterating over arr
for (int i = 0; i < arr.GetLength(0); i++) {
int start = arr[i, 0];
int end = arr[i, 1];
// Increment the value of
// prefixSum at start
prefixSum[start]++;
// Decrement the value of
// prefixSum at end + 1
prefixSum[end + 1]--;
}
// Calculating the prefix sum
for (int i = 1; i < prefixSum.Length; i++) {
prefixSum[i]
= prefixSum[i - 1] + prefixSum[i];
}
// Resolving each queries
for (int i = 0; i < q.Length; i++) {
int occurrence = prefixSum[q[i]];
result.Add(occurrence);
}
}
// Driver Codepublic static void Main()
{ int[,] arr
= { { 1, 5 }, { 3, 6 }, { 5, 7 }, { 12, 15 } };
int[] query = { 1, 3, 5, 13 };
List<int> result
= new List<int>();
// Function call
findTheOccurrence(arr, query, result);
foreach (int i in result)
Console.Write(i + " ");
}}// This code is contributed by avijitmondal998. |
Javascript
<script>// JS code to implement the approachlet MAX = 10000;// Function to find occurrences of// each element in arrayfunction findTheOccurrence(arr, q, result)
{ prefixSum = new Array(MAX).fill(0);
// Iterating over arr
for (var i = 0; i < arr.length; i++)
{
var start = arr[i][0];
var end = arr[i][1];
// Increment the value of
// prefixSum at start
prefixSum[start]++;
// Decrement the value of
// prefixSum at end + 1
prefixSum[end + 1]--;
}
// Calculating the prefix sum
for (var i = 1; i < prefixSum.length; i++) {
prefixSum[i] = prefixSum[i - 1] + prefixSum[i];
}
// Resolving each queries
for (var i = 0; i < q.length; i++) {
var occurrence = prefixSum[q[i]];
result.push(occurrence);
}
return result;
}// Driver codevar arr = [[ 1, 5 ], [ 3, 6 ], [ 5, 7 ], [ 12, 15 ] ];
var query = [ 1, 3, 5, 13 ];
var result = [];
// Function callfindTheOccurrence(arr, query, result);for (var i = 0; i < result.length; i++)
document.write(result[i] + " ");
// This code is contributed by phasing17</script> |
Output
1 2 3 1
Time Complexity: O(M), where M is the maximum element of the array.
Auxiliary Space: O(MAX)
Note: This approach will not work here because of the given constraints
Space Optimized approach: The idea is similar to the above approach, but there will be the following changes:
We will use a map to store the frequency of elements in given ranges instead of creating a prefix sum array. If the range of elements in arr[] is high as 109 then we can not create such a big length array. But in the map (ordered map) we can calculate the prefix sum while iterating over the map and can perform the rest of the operations as done in the above approach.
Follow the steps below to implement the above idea:
- Create a map (ordered map), where the key represents the element and the value represents the frequency of the key.
- Iterate over arr[]:
- Increment the frequency of starti by 1
- Decrement the frequency of (endi + 1) by 1
- Initialize two arrays to store the elements that appear in the map and the frequencies corresponding to that element.
- Iterate over the map and use prefix sum technique to calculate the frequency of each element and store them in the created arrays.
- Iterate over the query array and for each query:
- Find the closest integer (say x) which just greater or equal to query[i] and is present in the map.
- Check if x and query[i] are the same:
- If they are the same then the corresponding frequency of x is the required frequency.
- Otherwise, the frequency of the elements corresponding to the element just before x is the answer.
- Store this frequency in the resultant array.
- Return the result array.
Below is the implementation of the above approach:
C++
// C++ code to implement the approach#include <bits/stdc++.h>using namespace std;
// Function to find the frequency// of element in array arrvector<int> findTheOccurrence(vector<vector<int> >& arr,
vector<int>& q,
vector<int>& result)
{ int n = arr.size();
// Map to store the elements
// with their frequency
map<long long, long long> mp;
for (auto& i : arr) {
mp[i[0]]++;
mp[(long long)i[1] + 1]--;
}
vector<long long> range, freq;
long long prefixSum = 0;
for (auto i : mp) {
// Calculate the frequency of element
// using prefix sum technique.
prefixSum = prefixSum
+ (long long)i.second;
// Store the element of arr in range
range.push_back(i.first);
// Store its corresponding frequency
freq.push_back(prefixSum);
}
// Iterate over the query
for (auto p : q) {
// Find the lower_bound of query p
int idx = lower_bound(range.begin(),
range.end(), p)
- range.begin();
// If the lower_bound doesn't exist
if (idx >= 0 && idx < range.size()) {
// Check if element
// which we are searching
// exists in the range or not.
// If it doesn't exist then
// lower bound will return
// the next element which is
// just greater than p
if (range[idx] != p)
idx--;
if (idx >= 0)
result.push_back(freq[idx]);
// If no such element exist
else
result.push_back(0);
}
// If idx is range size,
// it means all elements
// are smaller than p.
// So next smaller element will be
// at range.size() - 1
else {
result.push_back(freq[range.size()
- 1]);
}
}
// Return the final result
return result;
}// Driver codeint main()
{ vector<vector<int> > arr
= { { 1, 5 }, { 3, 6 }, { 5, 7 }, { 12, 15 } };
vector<int> q = { 1, 3, 5, 13 };
vector<int> result;
// Function call
findTheOccurrence(arr, q, result);
for (auto i : result)
cout << i << " ";
return 0;
} |
Java
// Java code to implement the approachimport java.util.*;
class GFG
{ // This function returns the position
// of the leftmost array element that is
// greater than or equal to the key element
static int lower_bound(ArrayList<Integer> arr, int ele)
{
for (var i = 0; i < arr.size(); i++) {
if (arr.get(i) >= ele)
return i;
}
return arr.size();
}
// Function to find the frequency
// of element in array arr
static ArrayList<Integer>
findTheOccurrence(int[][] arr, int[] q,
ArrayList<Integer> result)
{
int n = arr.length;
// Map to store the elements
// with their frequency
TreeMap<Integer, Integer> mp
= new TreeMap<Integer, Integer>();
for (int i = 0; i < arr.length; i++) {
if (!mp.containsKey(arr[i][0]))
mp.put(arr[i][0], 0);
if (!mp.containsKey(arr[i][1] + 1))
mp.put(arr[i][1] + 1, 0);
mp.put(arr[i][0], mp.get(arr[i][0]) + 1);
mp.put(arr[i][1] + 1,
mp.get(arr[i][1] + 1) - 1);
}
ArrayList<Integer> range = new ArrayList<Integer>();
ArrayList<Integer> freq = new ArrayList<Integer>();
int prefixSum = 0;
for (Map.Entry<Integer, Integer> i :
mp.entrySet()) {
// Calculate the frequency of element
// using prefix sum technique.
prefixSum = prefixSum + i.getValue();
// Store the element of arr in range
range.add(i.getKey());
// Store its corresponding frequency
freq.add(prefixSum);
}
// Iterate over the query
for (Integer p : q) {
// Find the lower_bound of query p
int idx = lower_bound(range, p);
// If the lower_bound doesn't exist
if (idx >= 0 && idx < range.size()) {
// Check if element
// which we are searching
// exists in the range or not.
// If it doesn't exist then
// lower bound will return
// the next element which is
// just greater than p
if (range.get(idx) != p)
idx--;
if (idx >= 0)
result.add(freq.get(idx));
// If no such element exist
else
result.add(0);
}
// If idx is range size,
// it means all elements
// are smaller than p.
// So next smaller element will be
// at range.size() - 1
else {
result.add(freq.get(range.size() - 1));
}
}
// Return the final result
return result;
}
// Driver code
public static void main(String[] args)
{
int[][] arr
= { { 1, 5 }, { 3, 6 }, { 5, 7 }, { 12, 15 } };
int[] q = { 1, 3, 5, 13 };
ArrayList<Integer> result
= new ArrayList<Integer>();
// Function call
findTheOccurrence(arr, q, result);
for (Integer i : result)
System.out.print(i + " ");
}
}// This code is contributed by phasing17 |
Python3
# Python3 code to implement the approachimport bisect
# Function to find the frequency# of element in array arrdef findTheOccurrence(arr, q, result):
n = len(arr)
# Map to store the elements
# with their frequency
mp = {}
for i in arr:
if i[0] not in mp:
mp[i[0]] = 0
if (i[1] + 1) not in mp:
mp[i[1] + 1] = 0
mp[i[0]] += 1
mp[i[1] + 1] -= 1
range = []
freq = []
prefixSum = 0
for i in sorted(mp.keys()):
# Calculate the frequency of element
# using prefix sum technique.
prefixSum = prefixSum + mp[i]
# Store the element of arr in range
range.append(i)
# Store its corresponding frequency
freq.append(prefixSum)
# Iterate over the query
for p in q:
# Find the lower_bound of query p
idx = bisect.bisect_left(range, p)
# If the lower_bound doesn't exist
if (idx >= 0 and idx < len(range)):
# Check if element
# which we are searching
# exists in the range or not.
# If it doesn't exist then
# lower bound will return
# the next element which is
# just greater than p
if (range[idx] != p):
idx -= 1
if (idx >= 0):
result.append(freq[idx])
# If no such element exist
else:
result.append(0)
# If idx is range size,
# it means all elements
# are smaller than p.
# So next smaller element will be
# at range.size() - 1
else :
result.append(freq[len(range) - 1])
# Return the final result
return result
# Driver codearr = [[ 1, 5 ], [ 3, 6 ], [ 5, 7 ], [ 12, 15 ] ]
q = [ 1, 3, 5, 13 ]
result = []
# Function callresult = findTheOccurrence(arr, q, result);
print(" ".join(list(map(str, result))))
# This code is contributed by phasing17 |
C#
// C# code to implement the approachusing System;
using System.Collections.Generic;
class GFG {
// This function returns the position
// of the leftmost array element that is
// greater than or equal to the key element
static int lower_bound(List<int> arr, int ele)
{
for (var i = 0; i < arr.Count; i++) {
if (arr[i] >= ele)
return i;
}
return arr.Count;
}
// Function to find the frequency
// of element in array arr
static List<int> findTheOccurrence(int[, ] arr, int[] q,
List<int> result)
{
// Map to store the elements
// with their frequency
Dictionary<int, int> mp
= new Dictionary<int, int>();
for (int i = 0; i < arr.GetLength(0); i++) {
if (!mp.ContainsKey(arr[i, 0]))
mp[arr[i, 0]] = 0;
if (!mp.ContainsKey(arr[i, 1] + 1))
mp[arr[i, 1] + 1] = 0;
mp[arr[i, 0]] += 1;
mp[arr[i, 1] + 1] -= 1;
}
List<int> range = new List<int>();
List<int> freq = new List<int>();
int prefixSum = 0;
var mpKeys = new List<int>(mp.Keys);
mpKeys.Sort();
foreach(var i in mpKeys)
{
// Calculate the frequency of element
// using prefix sum technique.
prefixSum = prefixSum + mp[i];
// Store the element of arr in range
range.Add(i);
// Store its corresponding frequency
freq.Add(prefixSum);
}
// Iterate over the query
foreach(var p in q)
{
// Find the lower_bound of query p
int idx = lower_bound(range, p);
// If the lower_bound doesn't exist
if (idx >= 0 && idx < range.Count) {
// Check if element
// which we are searching
// exists in the range or not.
// If it doesn't exist then
// lower bound will return
// the next element which is
// just greater than p
if (range[idx] != p)
idx--;
if (idx >= 0)
result.Add(freq[idx]);
// If no such element exist
else
result.Add(0);
}
// If idx is range size,
// it means all elements
// are smaller than p.
// So next smaller element will be
// at range.size() - 1
else {
result.Add(freq[range.Count - 1]);
}
}
// Return the final result
return result;
}
// Driver code
public static void Main(string[] args)
{
int[, ] arr
= { { 1, 5 }, { 3, 6 }, { 5, 7 }, { 12, 15 } };
int[] q = { 1, 3, 5, 13 };
List<int> result = new List<int>();
// Function call
findTheOccurrence(arr, q, result);
foreach(var i in result) Console.Write(i + " ");
}
}// This code is contributed by phasing17 |
Javascript
// JavaScript code to implement the approach//This function returns the position//of the leftmost array element that is//greater than or equal to the key elementfunction lower_bound(arr, ele)
{ for (var i = 0; i < arr.length; i++)
{
if (arr[i] >= ele)
return i;
}
return arr.length - 1;
}// Function to find the frequency// of element in array arrfunction findTheOccurrence(arr, q, result)
{ let n = arr.length;
// Map to store the elements
// with their frequency
let mp = {};
for (var i of arr) {
if (!mp.hasOwnProperty(i[0]))
mp[i[0]] = 0;
if (!mp.hasOwnProperty(i[1] + 1))
mp[i[1] + 1] = 0;
mp[i[0]]++;
mp[i[1] + 1]--;
}
let range = [];
let freq = [];
let prefixSum = 0;
for (let [i, val] of Object.entries(mp)) {
// Calculate the frequency of element
// using prefix sum technique.
prefixSum = prefixSum + val;
// Store the element of arr in range
range.push(parseInt(i));
// Store its corresponding frequency
freq.push(prefixSum);
}
// Iterate over the query
for (var p of q) {
// Find the lower_bound of query p
let idx = lower_bound(range, p);
// If the lower_bound doesn't exist
if (idx >= 0 && idx < range.length) {
// Check if element
// which we are searching
// exists in the range or not.
// If it doesn't exist then
// lower bound will return
// the next element which is
// just greater than p
if (range[idx] != p)
idx--;
if (idx >= 0)
result.push(freq[idx]);
// If no such element exist
else
result.push(0);
}
// If idx is range size,
// it means all elements
// are smaller than p.
// So next smaller element will be
// at range.size() - 1
else {
result.push(freq[range.length - 1]);
}
}
// Return the final result
return result;
}// Driver codelet arr = [[ 1, 5 ], [ 3, 6 ], [ 5, 7 ], [ 12, 15 ] ];let q = [ 1, 3, 5, 13 ];let result = [];// Function callresult = findTheOccurrence(arr, q, result);for (var i of result)
process.stdout.write(i + " ");
//This code is contributed by phasing17 |
Output
1 2 3 1
Time Complexity: O(N * log(N))
Auxiliary Space: O(N)
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