Queries to find first occurrence of a character in a given range

Given a string S of length N and an array Q[][] of dimension M × 3 consisting of queries of type {L, R, C}, the task is to print the first index of the character C in the range [L, R], if found. Otherwise, print -1.

Examples:

Input: S= “abcabcabc”, Q[][] = { { 0, 3, ‘a’ }, { 0, 2, ‘b’ }, { 2, 4, ‘z’ } }
Output: 0 1 -1
Explanation:

• First query: Print 0 which is the first index of character ‘a’ in the range [0, 3].
• Second query: Print 1, which is the first index of character ‘b’ in the range [0, 2].
• Third query: Print -1 as the character ‘z’ does not occur in the range [2, 4].

Input: S= “geeksforgeeks”, Q[][] = { { 0, 12, ‘f’ }, { 0, 2, ‘g’ }, { 6, 12, ‘f’ } }
Output: 5 0 -1
Explanation: 

• First query: Print 5, which is the first index of character ‘f’ in the range [0, 12].
• Second query: Print 0 which is 
  the first index of character ‘g’ in the range [0, 2].
• Third query: Print -1 as the character ‘f’ does not occur in the range [6, 12].

Naive Approach: The simplest approach is to traverse the string over the range of indices [L, R] for each query and print the first occurrence of character C if found. Otherwise, print -1. 
Time Complexity: O(M * Q)
Auxiliary Space: O(1)

Efficient Approach: The above approach can be optimized by pre-storing the indices of characters in the map of vectors and using binary search to find the index in the range [L, R] in the vector of characters C. Follow the steps below to solve the problem:

• Initialize a Map < char, vector < int > >, say V, to store indices of all occurrences of a character.
• Traverse the string and update V.
• Traverse the array Q:
  • If the size of V[C] is zero then print -1.
  • Otherwise, find the index by using binary search in vector V[C] i.e lower_bound(V[C].begin(), V[C].end(), L) – V[C].begin() and store it in a variable, say idx.
  • If idx = N or idx > R, then print -1.
  • Otherwise, print the index idx.

Below is the implementation of the above approach:

C++

// C++ implementation
// for the above approach

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

// Function to find the first occurrence
// for a given range
int firstOccurrence(string s,
                   vector<pair<pair<int, int>, char> > Q)
{
    // N = length of string
    int N = s.size();

    // M = length of queries
    int M = Q.size();

    // Stores the indices of a character
    map<char, vector<int> > v;

    // Traverse the string
    for (int i = 0; i < N; i++) {

        // Push the index i
        // into the vector[s[i]]
        v[s[i]].push_back(i);
    }

    // Traverse the query
    for (int i = 0; i < M; i++) {

        // Stores the value L
        int left = Q[i].first.first;

        // Stores the value R
        int right = Q[i].first.second;

        // Stores the character C
        char c = Q[i].second;

        if (v.size() == 0) {
            cout << "-1 ";
            continue;
        }

        // Find index >= L in
        // the vector v
        int idx
            = lower_bound(v.begin(),
                          v.end(), left)
              - v.begin();

        // If there is no index of C >= L
        if (idx == (int)v.size()) {

            cout << "-1 ";
            continue;
        }

        // Stores the value at idx
        idx = v[idx];

        // If idx > R
        if (idx > right) {
            cout << "-1 ";
        }

        // Otherwise
        else {
            cout << idx << " ";
        }
    }
}

// Driver Code
int main()
{
    string S = "abcabcabc";
    vector<pair<pair<int, int>, char> > Q
        = { { { 0, 3 }, 'a' },
            { { 0, 2 }, 'b' },
            { { 2, 4 }, 'z' } };

    firstOccurrence(S, Q);
    return 0;
}

Python3

# Python3 implementation
# for the above approach
from bisect import bisect_left

# Function to find the first occurrence
# for a given range
def firstOccurrence(s, Q):

    # N = length of string
    N = len(s)

    # M = length of queries
    M = len(Q)

    # Stores the indices of a character
    v = [[] for i in range(26)]

    # Traverse the string
    for i in range(N):

        # Push the index i
        # into the vector[s[i]]
        v[ord(s[i]) - ord('a')].append(i)

    # Traverse the query
    for i in range(M):

        # Stores the value L
        left = Q[i][0]

        # Stores the value R
        right = Q[i][1]

        # Stores the character C
        c = Q[i][2]

        if (len(v[ord(c) - ord('a')]) == 0):
            print ("-1")
            continue

        # Find index >= L in
        # the vector v
        idx = bisect_left(v[ord(c) - ord('a')], left)

        # If there is no index of C >= L
        if (idx == len(v[ord(c) - ord('a')])):
            print("-1 ")
            continue

        # Stores the value at idx
        idx = v[ord(c) - ord('a')][idx]

        # If idx > R
        if (idx > right):
            print ("-1 ")

        # Otherwise
        else:
            print(idx, end=" ")

# Driver Code
if __name__ == '__main__':
    S = "abcabcabc";
    Q = [ [ 0, 3 , 'a'],[ 0, 2 , 'b' ],[ 2, 4, 'z']]

    firstOccurrence(S, Q)

    # This code is contributed by mohit kumar 29.

Output:

0 1 -1

Time Complexity: O(M * log(N))
Auxiliary Space: O(N)