解题思路

解析输入数据：

首先解析银行对账单和登记记录的数据。

存储对账单信息：

将对账单中的交易存储在一个字典中，键为交易类型和编号，值为金额。

处理登记记录：

遍历登记记录中的每笔交易，检查其是否在对账单中，金额是否正确，是否重复，以及计算是否正确。

生成输出：

根据检查结果生成相应的输出，并在最后输出遗漏的交易。

解题方法

读取对账单：

读取起始余额和最终余额。

读取所有交易并存储到字典中，键为 (type, $N$)，值为 $X$。

读取登记记录：

读取起始余额。

读取交易和后续余额，检查每笔交易的正确性。

检查交易：

检查交易是否在对账单中。

检查交易是否重复。

检查金额是否正确。

检查计算是否正确。

输出遗漏交易：遍历对账单中的所有交易，检查是否在登记记录中出现过，未出现的按顺序输出。

C++代码实现：

#include <iostream>
#include <vector>
#include <map>
#include <set>
#include <string>
#include <algorithm>
#include <iomanip>
#include <sstream>
#include <cmath>

using namespace std;

struct Transaction {
    string type;
    int number;
    double amount;
};

struct TransactionComparator {
    bool operator()(const pair<string, int>& a, const pair<string, int>& b) const {
        if (a.first == b.first) {
            return a.second < b.second;
        }
        return a.first < b.first;
    }
};

void processInput() {
    string line;
    double startBalance, endBalance;
    map<pair<string, int>, double, TransactionComparator> statementTransactions;
    set<pair<string, int>, TransactionComparator> registerTransactions;
    set<pair<string, int>, TransactionComparator> missingTransactions;
    vector<pair<Transaction, double> > registerEntries;
    
    // Read bank statement
    cin >> line >> startBalance;
    while (cin >> line && line != "balance") {
        string type = line;
        int number;
        double amount;
        cin >> number >> amount;
        pair<string, int> key = make_pair(type, number);
        statementTransactions[key] = amount;
    }
    cin >> endBalance;
    
    // Read register entries
    double currentRegisterBalance;
    cin >> currentRegisterBalance;
    while (cin >> line) {
        string type = line;
        int number;
        double amount;
        cin >> number >> amount;
        Transaction t;
        t.type = type;
        t.number = number;
        t.amount = amount;
        double newBalance;
        cin >> newBalance;
        registerEntries.push_back(make_pair(t, newBalance));
    }
    
    // Process each register entry
    for (size_t i = 0; i < registerEntries.size(); ++i) {
        const pair<Transaction, double>& entry = registerEntries[i];
        const Transaction& t = entry.first;
        double registeredAmount = t.amount;
        double registeredNewBalance = entry.second;
        double expectedNewBalance;
        pair<string, int> key = make_pair(t.type, t.number);
        bool inStatement = statementTransactions.find(key) != statementTransactions.end();
        bool repeated = registerTransactions.find(key) != registerTransactions.end();
        bool correctAmount = false;
        if (inStatement) {
            correctAmount = fabs(statementTransactions[key] - registeredAmount) < 1e-9;
        }
        bool mathMistake = false;
        bool mathUsesCorrectValue = false;
        
        vector<string> errors;
        
        if (!inStatement) {
            errors.push_back("is not in statement");
        }
        if (repeated) {
            errors.push_back("repeated transaction");
        }
        if (inStatement && !correctAmount) {
            errors.push_back("incorrect amount");
        }
        
        // Calculate expected new balance with registered amount
        if (i == 0) {
            expectedNewBalance = startBalance;
        } else {
            expectedNewBalance = registerEntries[i-1].second;
        }
        if (t.type == "check") {
            expectedNewBalance -= registeredAmount;
        } else if (t.type == "deposit") {
            expectedNewBalance += registeredAmount;
        }
        
        if (fabs(expectedNewBalance - registeredNewBalance) >= 1e-9) {
            mathMistake = true;
            if (inStatement && !correctAmount) {
                // Calculate expected new balance with correct amount
                double expectedNewBalanceWithCorrectAmount;
                if (i == 0) {
                    expectedNewBalanceWithCorrectAmount = startBalance;
                } else {
                    expectedNewBalanceWithCorrectAmount = registerEntries[i-1].second;
                }
                if (t.type == "check") {
                    expectedNewBalanceWithCorrectAmount -= statementTransactions[key];
                } else {
                    expectedNewBalanceWithCorrectAmount += statementTransactions[key];
                }
                if (fabs(expectedNewBalanceWithCorrectAmount - registeredNewBalance) < 1e-9) {
                    mathUsesCorrectValue = true;
                }
            }
        }
        
        if (mathUsesCorrectValue) {
            errors.push_back("math uses correct value");
        } else if (mathMistake) {
            errors.push_back("math mistake");
        }
        
        // Output the result for this transaction
        cout << t.type << " " << t.number;
        if (errors.empty()) {
            cout << " is correct" << endl;
        } else {
            for (size_t j = 0; j < errors.size(); ++j) {
                if (j == 0) {
                    cout << " ";
                } else {
                    cout << " ";
                }
                cout << errors[j];
            }
            cout << endl;
        }
        
        // Mark as processed
        registerTransactions.insert(key);
    }
    
    // Collect missing transactions
    for (map<pair<string, int>, double, TransactionComparator>::const_iterator it = statementTransactions.begin();
         it != statementTransactions.end(); ++it) {
        if (registerTransactions.find(it->first) == registerTransactions.end()) {
            missingTransactions.insert(it->first);
        }
    }
    
    // Output missing transactions in order
    vector<pair<string, int> > sortedMissing(missingTransactions.begin(), missingTransactions.end());
    sort(sortedMissing.begin(), sortedMissing.end(), TransactionComparator());
    
    for (vector<pair<string, int> >::const_iterator it = sortedMissing.begin();
         it != sortedMissing.end(); ++it) {
        cout << "missed " << it->first << " " << it->second << endl;
    }
}

int main() {
    processInput();
    return 0;
}