# TreeMath

[Git Source](https://github.com/traderjoe-xyz/joe-v2/blob/16f011d25e6bf6d0a0c479974345b623d491104f/src/libraries/math/TreeMath.sol)

**Author:**\
Trader Joe

This library contains functions to interact with a tree of TreeUint24.

## Functions

### contains

*Returns true if the tree contains the id*

```solidity
function contains(TreeUint24 storage tree, uint24 id) internal view returns (bool);
```

**Parameters**

| Name   | Type         | Description |
| ------ | ------------ | ----------- |
| `tree` | `TreeUint24` | The tree    |
| `id`   | `uint24`     | The id      |

**Returns**

| Name     | Type   | Description                      |
| -------- | ------ | -------------------------------- |
| `<none>` | `bool` | True if the tree contains the id |

### add

*Adds the id to the tree and returns true if the id was not already in the tree*\
*It will also propagate the change to the parent levels.*

```solidity
function add(TreeUint24 storage tree, uint24 id) internal returns (bool);
```

**Parameters**

| Name   | Type         | Description |
| ------ | ------------ | ----------- |
| `tree` | `TreeUint24` | The tree    |
| `id`   | `uint24`     | The id      |

**Returns**

| Name     | Type   | Description                                |
| -------- | ------ | ------------------------------------------ |
| `<none>` | `bool` | True if the id was not already in the tree |

### remove

*Removes the id from the tree and returns true if the id was in the tree.*\
*It will also propagate the change to the parent levels.*

```solidity
function remove(TreeUint24 storage tree, uint24 id) internal returns (bool);
```

**Parameters**

| Name   | Type         | Description |
| ------ | ------------ | ----------- |
| `tree` | `TreeUint24` | The tree    |
| `id`   | `uint24`     | The id      |

**Returns**

| Name     | Type   | Description                    |
| -------- | ------ | ------------------------------ |
| `<none>` | `bool` | True if the id was in the tree |

### findFirstRight

*Returns the first id in the tree that is lower than or equal to the given id.*\
*It will return type(uint24).max if there is no such id.*

```solidity
function findFirstRight(TreeUint24 storage tree, uint24 id) internal view returns (uint24);
```

**Parameters**

| Name   | Type         | Description |
| ------ | ------------ | ----------- |
| `tree` | `TreeUint24` | The tree    |
| `id`   | `uint24`     | The id      |

**Returns**

| Name     | Type     | Description                                                          |
| -------- | -------- | -------------------------------------------------------------------- |
| `<none>` | `uint24` | The first id in the tree that is lower than or equal to the given id |

### findFirstLeft

*Returns the first id in the tree that is higher than or equal to the given id.*\
*It will return 0 if there is no such id.*

```solidity
function findFirstLeft(TreeUint24 storage tree, uint24 id) internal view returns (uint24);
```

**Parameters**

| Name   | Type         | Description |
| ------ | ------------ | ----------- |
| `tree` | `TreeUint24` | The tree    |
| `id`   | `uint24`     | The id      |

**Returns**

| Name     | Type     | Description                                                           |
| -------- | -------- | --------------------------------------------------------------------- |
| `<none>` | `uint24` | The first id in the tree that is higher than or equal to the given id |

### \_closestBitRight

*Returns the first bit in the given leaves that is strictly lower than the given bit.*\
*It will return type(uint256).max if there is no such bit.*

```solidity
function _closestBitRight(bytes32 leaves, uint8 bit) private pure returns (uint256);
```

**Parameters**

| Name     | Type      | Description |
| -------- | --------- | ----------- |
| `leaves` | `bytes32` | The leaves  |
| `bit`    | `uint8`   | The bit     |

**Returns**

| Name     | Type      | Description                                                                 |
| -------- | --------- | --------------------------------------------------------------------------- |
| `<none>` | `uint256` | The first bit in the given leaves that is strictly lower than the given bit |

### \_closestBitLeft

*Returns the first bit in the given leaves that is strictly higher than the given bit.*\
*It will return type(uint256).max if there is no such bit.*

```solidity
function _closestBitLeft(bytes32 leaves, uint8 bit) private pure returns (uint256);
```

**Parameters**

| Name     | Type      | Description |
| -------- | --------- | ----------- |
| `leaves` | `bytes32` | The leaves  |
| `bit`    | `uint8`   | The bit     |

**Returns**

| Name     | Type      | Description                                                                  |
| -------- | --------- | ---------------------------------------------------------------------------- |
| `<none>` | `uint256` | The first bit in the given leaves that is strictly higher than the given bit |

## Structs

### TreeUint24

```solidity
struct TreeUint24 {
    bytes32 level0;
    mapping(bytes32 => bytes32) level1;
    mapping(bytes32 => bytes32) level2;
}
```


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