Efficient way to find accumulated unique element count at each index in a vector in C++

So I have a gene alignment result (I think it's from RNA-seq) in which specific sequences are matched to certain genes (those genes repeat themselves sometimes). I am now using C++ to find the earliest possible position at which most unique genes have been counted and I can confidently use only the first part for further analysis. The problem is that the file I have is sorted (so sequences from the same gene are put together), but I want to calculate that for non-sorted files.

What I am doing now is to manually std::shuffle my std::vector<string> geneList before iterating through it. In each iteration I would generate a unique gene list at the same time and compare every coming gene from the geneList to the whole unique list to see if they are unique. Then I would sample count_gene and count_unique_gene with some interval and finally get the x% position. This is very costly...with only 140,000 genes costing me several minutes. Sample code (also included my input code for better understanding):

#include <stdlib.h>
#include <stdint.h>
#include <iostream>
#include <string>
#include <vector>
#include <set>
#include <fstream>
#include <sstream>
#include <random>
#include <algorithm>

class COUNT{

public:
//    COUNT() : sampRate(1) {};
//    ~COUNT(){};
    void initialize();
    void readData();
    void calcCount();
    void writeCount();

private:
    int sampRate;    
    int countRead;
    int countUniqGene;
    string fname;
    vector<string> geneList;
    vector<int> sampCountRead, sampCountUniqGene;
};


void COUNT::readData(){
    std::cout<<"Type in fname: "<<endl;
//    std::cin>>fname;
    fname = "testdata.sam";
    std::cout<<"Type in sample rate: "<<endl;
    std::cin>>sampRate;
    std::string line;
    std::fstream readFile(fname);
    while (getline(readFile, line)) {
        if (((char)line.back() == '-') | ((char)line.back() == '+')) {
            std::istringstream ss(line);
            std::string others, oriGeneName, realGeneName;
            ss >> others; ss >> others; ss >> others; ss >> others; ss >> others; ss >> others; ss >> others; ss >> others; ss >> others; ss >> others; ss >> others; ss >> others; ss >> others; ss >> others; ss >> others; ss >> others; ss >> others; ss >> others;
            if (ss >> others) {
                ss >> oriGeneName;
                realGeneName = oriGeneName.substr(5, oriGeneName.size());
                geneList.push_back(realGeneName);
            }
            else continue;
        }
        else continue;
    }
    readFile.close();
}

void COUNT::calcCount() {
    set<string> uniqGeneList = {"test"};
    auto rng = std::default_random_engine{};
    std::shuffle(std::begin(geneList), std::end(geneList), rng);  // this is fast (0.02s)
    vector<string>::iterator uniqIter;
    string geneName;
    for (vector<string>::iterator iter = geneList.begin(); iter != geneList.end(); ++iter) {  //this is very slow
        geneName = string(iter[0]);
        if (all_of(uniqGeneList.begin(), uniqGeneList.end(), [geneName](const std::string gene) {return geneName != gene; })) {
            uniqGeneList.insert(geneName);
            countUniqGene++;
        }
        countRead++;
        if (countRead % sampRate < 1) {
            sampCountRead.push_back(countRead);
            sampCountUniqGene.push_back(countUniqGene);
        }
    }
}

int main(){
    (not important, plotting and intersecting)
}

Also sample data (I extracted genename from the 'GE:Z:<gene_name>' item):

V300067289_HH26L1C001R0010008289    784 7   141178046   3   2S48M   *   0   0   CCCCACCTGCTTGCGGACCCTAATGTGACGTTGGCGGATGAGCACACGGG  F)BF;E2A3*F<+AFFB-B,FE?FEFFF@EF3BFB;<:FECEF2DFF@CE  NH:i:2  HI:i:1  AS:i:47 nM:i:0  CB:Z:53_34_81098_51183  UR:Z:GTTTTATTA  UY:Z:E/E@EAG?F
V300067289_HH26L1C001R0010008294    1040    3   34078775    255 50M *   0   0   CCTTGTCTGGGTGATTTAATAGCATAATCCGGCGATGAGCATCCCTGATC  FGFBGFFFDEGEBFEFBDFEEFFGCFFFADEEFGFFFFGFGFFDFFEEFF  NH:i:1  HI:i:1  AS:i:49 nM:i:0  CB:Z:49_31_75043_46832  UR:Z:CCGGACCCA  UY:Z:EEEFDBFEA  XF:Z:CODING GE:Z:Dnajc19    GS:Z:-
V300067289_HH26L1C001R0010008295    1040    3   34078777    255 2S48M   *   0   0   CGTTGTCTGGGTGATTTAATACCAAAATCCGGCGATGAGCATCCCTGATC  E(FC6D>+EDEFECA?@?:C.'D4&03@&;:3?7CFAEF@C7A4.4.@B?  NH:i:1  HI:i:1  AS:i:43 nM:i:2  CB:Z:49_31_75043_46832  UR:Z:CCGGACCCA  UY:Z:CFFD?EEDF  XF:Z:CODING GE:Z:Dnajc19    GS:Z:-
V300067289_HH26L1C001R0010008298    1040    15  82351046    255 50M *   0   0   ACTTTATCCCGTCCTTGTTTCACCGTGATATCCAGCTGCATTAAGTGCAC  )EFFF=FE?DC=FABGFFF7F&=FEF9FBEE=BEB9FFF;FFCF9DBF86  NH:i:1  HI:i:1  AS:i:49 nM:i:0  CB:Z:49_34_74093_51329  UR:Z:CAATATAGG  UY:Z:DFFFFFFFF  XF:Z:CODING GE:Z:Ndufa6 GS:Z:-

I have thought of assuming gene appearance to follow a Poisson distribution and just count the unique gene number and calculate the confidence level of attaining x% at each position. But better use a simulation first. Thanks in advance!