Queries for number of distinct integers in Suffix
Given an array of N elements and Q queries, where each query contains an integer K. For each query, the task is to find the number of distinct integers in the suffix from Kth element to Nth element.
Examples:
Input :
N=5, Q=3
arr[] = {2, 4, 6, 10, 2}
1
3
2
Output :
4
3
4
Approach:
The problem can be solved by precomputing the solution for all index from N-1 to 0. The idea is to use an unordered_set in C++ as set does not allows duplicate elements.
Traverse the array from end and add the current element into a set and the answer for the current index would be the size of the set. So, store the size of set at current index in an auxiliary array say suffixCount.
Below is the implementation of the above approach:
C++
// C++ program to find distinct // elements in suffix #include <bits/stdc++.h> using namespace std; // Function to answer queries for distinct // count in Suffix void printQueries(int n, int a[], int q, int qry[]) { // Set to keep the distinct elements unordered_set<int> occ; int suffixCount[n + 1]; // Precompute the answer for each suffix for (int i = n - 1; i >= 0; i--) { occ.insert(a[i]); suffixCount[i + 1] = occ.size(); } // Print the precomputed answers for (int i = 0; i < q; i++) cout << suffixCount[qry[i]] << endl; } // Driver Code int main() { int n = 5, q = 3; int a[n] = { 2, 4, 6, 10, 2 }; int qry[q] = { 1, 3, 2 }; printQueries(n, a, q, qry); return 0; } |
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Python3
# Python3 program to find distinct # elements in suffix # Function to answer queries for distinct # count in Suffix def printQueries(n, a, q, qry): # Set to keep the distinct elements occ = dict() suffixCount = [0 for i in range(n + 1)] # Precompute the answer for each suffix for i in range(n - 1, -1, -1): occ[a[i]] = 1 suffixCount[i + 1] = len(occ) # Pr the precomputed answers for i in range(q): print(suffixCount[qry[i]]) # Driver Code n = 5q = 3a = [2, 4, 6, 10, 2] qry = [1, 3, 2] printQueries(n, a, q, qry) # This code is contributed by Mohit Kumar 29 |
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PHP
<?php // PHP program to find distinct // elements in suffix // Function to answer queries for distinct // count in Suffix function printQueries($n, $a, $q, $qry) { // Set to keep the distinct elements $occ = array(); $suffixCount = array_fill(0, $n + 1, 0); // Precompute the answer for each suffix for ($i = $n - 1; $i >= 0; $i--) { array_push($occ, $a[$i]); # give array of distinct element $occ = array_unique($occ); $suffixCount[$i + 1] = sizeof($occ); } // Print the precomputed answers for ($i = 0; $i < $q; $i++) echo $suffixCount[$qry[$i]], "\n"; } // Driver Code $n = 5; $q = 3; $a = array(2, 4, 6, 10, 2); $qry = array(1, 3, 2); printQueries($n, $a, $q, $qry); // This code is contributed by Ryuga ?> |
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Output:
4 3 4
Time Complexity: O(N)
Auxiliary Space: O(N)
Approach without STL: Since queries need to be addressed, precomputation needs to be done. Otherwise, a simple traversal over the suffix would have sufficed.
An auxiliary array aux[] is maintained from the right side of the array. An array mark[] stores whether an element has occurred or not in the suffix traversed yet. If the element has not occurred, then update aux[i] = aux[i+1] + 1. Otherwise aux[i] = aux[i+1].
Answer for every query would be aux[q[i]].
Below is the implementation of the above approach.
// C++ implementation of the above approach. #include <bits/stdc++.h> #define MAX 100002 using namespace std; // Function to print no of unique elements // in specified suffix for each query. void printUniqueElementsInSuffix(const int* arr, int n, const int* q, int m) { // aux[i] stores no of unique elements in arr[i..n] int aux[MAX]; // mark[i] = 1 if i has occurred in the suffix at least once. int mark[MAX]; memset(mark, 0, sizeof(mark)); // Initialization for the last element. aux[n - 1] = 1; mark[arr[n - 1]] = 1; for (int i = n - 2; i >= 0; i--) { if (mark[arr[i]] == 0) { aux[i] = aux[i + 1] + 1; mark[arr[i]] = 1; } else { aux[i] = aux[i + 1]; } } for (int i = 0; i < m; i++) { cout << aux[q[i] - 1] << "\n"; } } // Driver code int main() { int arr[] = { 1, 2, 3, 4, 1, 2, 3, 4, 10000, 999 }; int n = sizeof(arr) / sizeof(arr[0]); int q[] = { 1, 3, 6 }; int m = sizeof(q) / sizeof(q[0]); printUniqueElementsInSuffix(arr, n, q, m); return 0; } |
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Output:
6 6 5
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