# 2286. Booking Concert Tickets in Groups

## Description

A concert hall has n rows numbered from 0 to n - 1, each with m seats, numbered from 0 to m - 1. You need to design a ticketing system that can allocate seats in the following cases:

• If a group of k spectators can sit together in a row.
• If every member of a group of k spectators can get a seat. They may or may not sit together.

Note that the spectators are very picky. Hence:

• They will book seats only if each member of their group can get a seat with row number less than or equal to maxRow. maxRow can vary from group to group.
• In case there are multiple rows to choose from, the row with the smallest number is chosen. If there are multiple seats to choose in the same row, the seat with the smallest number is chosen.

Implement the BookMyShow class:

• BookMyShow(int n, int m) Initializes the object with n as number of rows and m as number of seats per row.
• int[] gather(int k, int maxRow) Returns an array of length 2 denoting the row and seat number (respectively) of the first seat being allocated to the k members of the group, who must sit together. In other words, it returns the smallest possible r and c such that all [c, c + k - 1] seats are valid and empty in row r, and r <= maxRow. Returns [] in case it is not possible to allocate seats to the group.
• boolean scatter(int k, int maxRow) Returns true if all k members of the group can be allocated seats in rows 0 to maxRow, who may or may not sit together. If the seats can be allocated, it allocates k seats to the group with the smallest row numbers, and the smallest possible seat numbers in each row. Otherwise, returns false.

Example 1:

Input
["BookMyShow", "gather", "gather", "scatter", "scatter"]
[[2, 5], [4, 0], [2, 0], [5, 1], [5, 1]]
Output
[null, [0, 0], [], true, false]

Explanation
BookMyShow bms = new BookMyShow(2, 5); // There are 2 rows with 5 seats each
bms.gather(4, 0); // return [0, 0]
// The group books seats [0, 3] of row 0.
bms.gather(2, 0); // return []
// There is only 1 seat left in row 0,
// so it is not possible to book 2 consecutive seats.
bms.scatter(5, 1); // return True
// The group books seat 4 of row 0 and seats [0, 3] of row 1.
bms.scatter(5, 1); // return False
// There is only one seat left in the hall.


Constraints:

• 1 <= n <= 5 * 104
• 1 <= m, k <= 109
• 0 <= maxRow <= n - 1
• At most 5 * 104 calls in total will be made to gather and scatter.

## Solutions

• class Node {
int l, r;
long mx, s;
}

class SegmentTree {
private Node[] tr;
private int m;

public SegmentTree(int n, int m) {
this.m = m;
tr = new Node[n << 2];
for (int i = 0; i < tr.length; ++i) {
tr[i] = new Node();
}
build(1, 1, n);
}

private void build(int u, int l, int r) {
tr[u].l = l;
tr[u].r = r;
if (l == r) {
tr[u].s = m;
tr[u].mx = m;
return;
}
int mid = (l + r) >> 1;
build(u << 1, l, mid);
build(u << 1 | 1, mid + 1, r);
pushup(u);
}

public void modify(int u, int x, long v) {
if (tr[u].l == x && tr[u].r == x) {
tr[u].s = v;
tr[u].mx = v;
return;
}
int mid = (tr[u].l + tr[u].r) >> 1;
if (x <= mid) {
modify(u << 1, x, v);
} else {
modify(u << 1 | 1, x, v);
}
pushup(u);
}

public long querySum(int u, int l, int r) {
if (tr[u].l >= l && tr[u].r <= r) {
return tr[u].s;
}
int mid = (tr[u].l + tr[u].r) >> 1;
long v = 0;
if (l <= mid) {
v += querySum(u << 1, l, r);
}
if (r > mid) {
v += querySum(u << 1 | 1, l, r);
}
return v;
}

public int queryIdx(int u, int l, int r, int k) {
if (tr[u].mx < k) {
return 0;
}
if (tr[u].l == tr[u].r) {
return tr[u].l;
}
int mid = (tr[u].l + tr[u].r) >> 1;
if (tr[u << 1].mx >= k) {
return queryIdx(u << 1, l, r, k);
}
if (r > mid) {
return queryIdx(u << 1 | 1, l, r, k);
}
return 0;
}

private void pushup(int u) {
tr[u].s = tr[u << 1].s + tr[u << 1 | 1].s;
tr[u].mx = Math.max(tr[u << 1].mx, tr[u << 1 | 1].mx);
}
}

class BookMyShow {
private int n;
private int m;
private SegmentTree tree;

public BookMyShow(int n, int m) {
this.n = n;
this.m = m;
tree = new SegmentTree(n, m);
}

public int[] gather(int k, int maxRow) {
++maxRow;
int i = tree.queryIdx(1, 1, maxRow, k);
if (i == 0) {
return new int[] {};
}
long s = tree.querySum(1, i, i);
tree.modify(1, i, s - k);
return new int[] {i - 1, (int) (m - s)};
}

public boolean scatter(int k, int maxRow) {
++maxRow;
if (tree.querySum(1, 1, maxRow) < k) {
return false;
}
int i = tree.queryIdx(1, 1, maxRow, 1);
for (int j = i; j <= n; ++j) {
long s = tree.querySum(1, j, j);
if (s >= k) {
tree.modify(1, j, s - k);
return true;
}
k -= s;
tree.modify(1, j, 0);
}
return true;
}
}

/**
* Your BookMyShow object will be instantiated and called as such:
* BookMyShow obj = new BookMyShow(n, m);
* int[] param_1 = obj.gather(k,maxRow);
* boolean param_2 = obj.scatter(k,maxRow);
*/

• class Node {
public:
int l, r;
long s, mx;
};

class SegmentTree {
public:
SegmentTree(int n, int m) {
this->m = m;
tr.resize(n << 2);
for (int i = 0; i < n << 2; ++i) {
tr[i] = new Node();
}
build(1, 1, n);
}

void modify(int u, int x, int v) {
if (tr[u]->l == x && tr[u]->r == x) {
tr[u]->s = tr[u]->mx = v;
return;
}
int mid = (tr[u]->l + tr[u]->r) >> 1;
if (x <= mid) {
modify(u << 1, x, v);
} else {
modify(u << 1 | 1, x, v);
}
pushup(u);
}

long querySum(int u, int l, int r) {
if (tr[u]->l >= l && tr[u]->r <= r) {
return tr[u]->s;
}
int mid = (tr[u]->l + tr[u]->r) >> 1;
long v = 0;
if (l <= mid) {
v += querySum(u << 1, l, r);
}
if (r > mid) {
v += querySum(u << 1 | 1, l, r);
}
return v;
}

int queryIdx(int u, int l, int r, int k) {
if (tr[u]->mx < k) {
return 0;
}
if (tr[u]->l == tr[u]->r) {
return tr[u]->l;
}
int mid = (tr[u]->l + tr[u]->r) >> 1;
if (tr[u << 1]->mx >= k) {
return queryIdx(u << 1, l, r, k);
}
if (r > mid) {
return queryIdx(u << 1 | 1, l, r, k);
}
return 0;
}

private:
vector<Node*> tr;
int m;

void build(int u, int l, int r) {
tr[u]->l = l;
tr[u]->r = r;
if (l == r) {
tr[u]->s = m;
tr[u]->mx = m;
return;
}
int mid = (l + r) >> 1;
build(u << 1, l, mid);
build(u << 1 | 1, mid + 1, r);
pushup(u);
}

void pushup(int u) {
tr[u]->s = tr[u << 1]->s + tr[u << 1 | 1]->s;
tr[u]->mx = max(tr[u << 1]->mx, tr[u << 1 | 1]->mx);
}
};

class BookMyShow {
public:
BookMyShow(int n, int m) {
this->n = n;
this->m = m;
tree = new SegmentTree(n, m);
}

vector<int> gather(int k, int maxRow) {
++maxRow;
int i = tree->queryIdx(1, 1, maxRow, k);
if (i == 0) {
return {};
}
long s = tree->querySum(1, i, i);
tree->modify(1, i, s - k);
return {i - 1, (int) (m - s)};
}

bool scatter(int k, int maxRow) {
++maxRow;
if (tree->querySum(1, 1, maxRow) < k) {
return false;
}
int i = tree->queryIdx(1, 1, maxRow, 1);
for (int j = i; j <= n; ++j) {
long s = tree->querySum(1, j, j);
if (s >= k) {
tree->modify(1, j, s - k);
return true;
}
k -= s;
tree->modify(1, j, 0);
}
return true;
}

private:
SegmentTree* tree;
int m, n;
};

/**
* Your BookMyShow object will be instantiated and called as such:
* BookMyShow* obj = new BookMyShow(n, m);
* vector<int> param_1 = obj->gather(k,maxRow);
* bool param_2 = obj->scatter(k,maxRow);
*/

• class Node:
def __init__(self):
self.l = self.r = 0
self.s = self.mx = 0

class SegmentTree:
def __init__(self, n, m):
self.m = m
self.tr = [Node() for _ in range(n << 2)]
self.build(1, 1, n)

def build(self, u, l, r):
self.tr[u].l, self.tr[u].r = l, r
if l == r:
self.tr[u].s = self.tr[u].mx = self.m
return
mid = (l + r) >> 1
self.build(u << 1, l, mid)
self.build(u << 1 | 1, mid + 1, r)
self.pushup(u)

def modify(self, u, x, v):
if self.tr[u].l == x and self.tr[u].r == x:
self.tr[u].s = self.tr[u].mx = v
return
mid = (self.tr[u].l + self.tr[u].r) >> 1
if x <= mid:
self.modify(u << 1, x, v)
else:
self.modify(u << 1 | 1, x, v)
self.pushup(u)

def query_sum(self, u, l, r):
if self.tr[u].l >= l and self.tr[u].r <= r:
return self.tr[u].s
mid = (self.tr[u].l + self.tr[u].r) >> 1
v = 0
if l <= mid:
v += self.query_sum(u << 1, l, r)
if r > mid:
v += self.query_sum(u << 1 | 1, l, r)
return v

def query_idx(self, u, l, r, k):
if self.tr[u].mx < k:
return 0
if self.tr[u].l == self.tr[u].r:
return self.tr[u].l
mid = (self.tr[u].l + self.tr[u].r) >> 1
if self.tr[u << 1].mx >= k:
return self.query_idx(u << 1, l, r, k)
if r > mid:
return self.query_idx(u << 1 | 1, l, r, k)
return 0

def pushup(self, u):
self.tr[u].s = self.tr[u << 1].s + self.tr[u << 1 | 1].s
self.tr[u].mx = max(self.tr[u << 1].mx, self.tr[u << 1 | 1].mx)

class BookMyShow:
def __init__(self, n: int, m: int):
self.n = n
self.tree = SegmentTree(n, m)

def gather(self, k: int, maxRow: int) -> List[int]:
maxRow += 1
i = self.tree.query_idx(1, 1, maxRow, k)
if i == 0:
return []
s = self.tree.query_sum(1, i, i)
self.tree.modify(1, i, s - k)
return [i - 1, self.tree.m - s]

def scatter(self, k: int, maxRow: int) -> bool:
maxRow += 1
if self.tree.query_sum(1, 1, maxRow) < k:
return False
i = self.tree.query_idx(1, 1, maxRow, 1)
for j in range(i, self.n + 1):
s = self.tree.query_sum(1, j, j)
if s >= k:
self.tree.modify(1, j, s - k)
return True
k -= s
self.tree.modify(1, j, 0)
return True

# Your BookMyShow object will be instantiated and called as such:
# obj = BookMyShow(n, m)
# param_1 = obj.gather(k,maxRow)
# param_2 = obj.scatter(k,maxRow)


• type BookMyShow struct {
n, m int
tree *segmentTree
}

func Constructor(n int, m int) BookMyShow {
return BookMyShow{n, m, newSegmentTree(n, m)}
}

func (this *BookMyShow) Gather(k int, maxRow int) []int {
maxRow++
i := this.tree.queryIdx(1, 1, maxRow, k)
if i == 0 {
return []int{}
}
s := this.tree.querySum(1, i, i)
this.tree.modify(1, i, s-k)
return []int{i - 1, this.m - s}
}

func (this *BookMyShow) Scatter(k int, maxRow int) bool {
maxRow++
if this.tree.querySum(1, 1, maxRow) < k {
return false
}
i := this.tree.queryIdx(1, 1, maxRow, 1)
for j := i; j <= this.n; j++ {
s := this.tree.querySum(1, j, j)
if s >= k {
this.tree.modify(1, j, s-k)
return true
}
k -= s
this.tree.modify(1, j, 0)
}
return true
}

type node struct {
l, r, s, mx int
}

type segmentTree struct {
tr []*node
m  int
}

func newSegmentTree(n, m int) *segmentTree {
tr := make([]*node, n<<2)
for i := range tr {
tr[i] = &node{}
}
t := &segmentTree{tr, m}
t.build(1, 1, n)
return t
}

func (t *segmentTree) build(u, l, r int) {
t.tr[u].l, t.tr[u].r = l, r
if l == r {
t.tr[u].s, t.tr[u].mx = t.m, t.m
return
}
mid := (l + r) >> 1
t.build(u<<1, l, mid)
t.build(u<<1|1, mid+1, r)
t.pushup(u)
}

func (t *segmentTree) modify(u, x, v int) {
if t.tr[u].l == x && t.tr[u].r == x {
t.tr[u].s, t.tr[u].mx = v, v
return
}
mid := (t.tr[u].l + t.tr[u].r) >> 1
if x <= mid {
t.modify(u<<1, x, v)
} else {
t.modify(u<<1|1, x, v)
}
t.pushup(u)
}

func (t *segmentTree) querySum(u, l, r int) int {
if t.tr[u].l >= l && t.tr[u].r <= r {
return t.tr[u].s
}
mid := (t.tr[u].l + t.tr[u].r) >> 1
v := 0
if l <= mid {
v = t.querySum(u<<1, l, r)
}
if r > mid {
v += t.querySum(u<<1|1, l, r)
}
return v
}

func (t *segmentTree) queryIdx(u, l, r, k int) int {
if t.tr[u].mx < k {
return 0
}
if t.tr[u].l == t.tr[u].r {
return t.tr[u].l
}
mid := (t.tr[u].l + t.tr[u].r) >> 1
if t.tr[u<<1].mx >= k {
return t.queryIdx(u<<1, l, r, k)
}
if r > mid {
return t.queryIdx(u<<1|1, l, r, k)
}
return 0
}

func (t *segmentTree) pushup(u int) {
t.tr[u].s = t.tr[u<<1].s + t.tr[u<<1|1].s
t.tr[u].mx = max(t.tr[u<<1].mx, t.tr[u<<1|1].mx)
}

/**
* Your BookMyShow object will be instantiated and called as such:
* obj := Constructor(n, m);
* param_1 := obj.Gather(k,maxRow);
* param_2 := obj.Scatter(k,maxRow);
*/