# Algorithm correctness for Bank Kattis problem

<a href="https://open.kattis.com/problems/bank" target="_blank">This</a>&nbsp;is the problem I am referring to. In quick summary:

This is the problem I am referring to. In quick summary:

Input: An integer time T; the time in minutes in which a bank closes and a set of pairs c and t that denotes the amount of cash (integer) this person carries and the time in minutes from now after which person leaves if not served. It takes one minute to serve a person and you must begin serving a person at time t at the latest.

Output: Maximum amount of money that can be collected within closing time.

My approach was this: place all the people in a map that maps money to time. I sort this map by money. I then make a queue-like structure where I take the person with the most money and place him/her as far back as possible. If the spot is occupied, then I move forward until I find a spot. If I can't then I just don't add the person.

Below is my helper function to determine whether or not I can insert a person.

```// returns index where we can insert, otherwise -1
int canInsert(bool* queue, int timeToInsert) {
if (!queue[timeToInsert]) {
return timeToInsert;
} else {
int index = timeToInsert-1;
while (index >= 0) {
if (!queue[index]) {
return index;
} else {
index--;
}
}
return -1;
}
}
```

Here is the main driver function:

```// moneyToTime is a map that maps a person's money to the time value
int Bank(int T, map<int, int> moneyToTime) {
bool queue[47] = {0};
for (map<int,int>::reverse_iterator i = moneyToTime.rbegin(); i != moneyToTime.rend(); i++) {
if (T > 0) {
// try to insert. If we can, then add to sum. Otherwise, don't.
int potentialIndex = canInsert(queue, i->second);
if (potentialIndex != -1) {
queue[potentialIndex] = 1;
T--;
}
} else {
break;
}
}
}
```

Logically, this makes sense to me and it is passing almost all the test cases. There are a couple that are failing; I can not see what they are. The test case errors are in fact indicating wrong answer, as opposed to bad runtime errors. Can someone help me see the fallacy in my approach?

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