Queue
Array
Dynamic Programming
Monotonic Queue
Heap (Priority Queue)
Description
You are at a fruit market with different types of exotic fruits on display.
You are given a 1-indexed array prices
, where prices[i]
denotes the number of coins needed to purchase the ith
fruit.
The fruit market has the following offer:
If you purchase the ith
fruit at prices[i]
coins, you can get the next i
fruits for free.
Note that even if you can take fruit j
for free, you can still purchase it for prices[j]
coins to receive a new offer.
Return the minimum number of coins needed to acquire all the fruits .
Example 1:
Input: prices = [3,1,2]
Output: 4
Explanation: You can acquire the fruits as follows:
- Purchase the 1st fruit with 3 coins, you are allowed to take the 2nd fruit for free.
- Purchase the 2nd fruit with 1 coin, you are allowed to take the 3rd fruit for free.
- Take the 3rd fruit for free.
Note that even though you were allowed to take the 2nd fruit for free, you purchased it because it is more optimal.
It can be proven that 4 is the minimum number of coins needed to acquire all the fruits.
Example 2:
Input: prices = [1,10,1,1]
Output: 2
Explanation: You can acquire the fruits as follows:
- Purchase the 1st fruit with 1 coin, you are allowed to take the 2nd fruit for free.
- Take the 2nd fruit for free.
- Purchase the 3rd fruit for 1 coin, you are allowed to take the 4th fruit for free.
- Take the 4t h fruit for free.
It can be proven that 2 is the minimum number of coins needed to acquire all the fruits.
Constraints:
1 <= prices.length <= 1000
1 <= prices[i] <= 105
Solutions
Solution 1
Solution 2
Solution 3
Python3 Java C++ Go TypeScript
1
2
3
4
5
6
7
8
9
10
11
12
13 class Solution :
def minimumCoins ( self , prices : List [ int ]) -> int :
n = len ( prices )
q = deque ()
for i in range ( n , 0 , - 1 ):
while q and q [ 0 ] > i * 2 + 1 :
q . popleft ()
if i <= ( n - 1 ) // 2 :
prices [ i - 1 ] += prices [ q [ 0 ] - 1 ]
while q and prices [ q [ - 1 ] - 1 ] >= prices [ i - 1 ]:
q . pop ()
q . append ( i )
return prices [ 0 ]
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19 class Solution {
public int minimumCoins ( int [] prices ) {
int n = prices . length ;
Deque < Integer > q = new ArrayDeque <> ();
for ( int i = n ; i > 0 ; -- i ) {
while ( ! q . isEmpty () && q . peek () > i * 2 + 1 ) {
q . poll ();
}
if ( i <= ( n - 1 ) / 2 ) {
prices [ i - 1 ] += prices [ q . peek () - 1 ] ;
}
while ( ! q . isEmpty () && prices [ q . peekLast () - 1 ] >= prices [ i - 1 ] ) {
q . pollLast ();
}
q . offer ( i );
}
return prices [ 0 ] ;
}
}
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20 class Solution {
public :
int minimumCoins ( vector < int >& prices ) {
int n = prices . size ();
deque < int > q ;
for ( int i = n ; i ; -- i ) {
while ( q . size () && q . front () > i * 2 + 1 ) {
q . pop_front ();
}
if ( i <= ( n - 1 ) / 2 ) {
prices [ i - 1 ] += prices [ q . front () - 1 ];
}
while ( q . size () && prices [ q . back () - 1 ] >= prices [ i - 1 ]) {
q . pop_back ();
}
q . push_back ( i );
}
return prices [ 0 ];
}
};
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75 func minimumCoins ( prices [] int ) int {
n := len ( prices )
q := Deque {}
for i := n ; i > 0 ; i -- {
for q . Size () > 0 && q . Front () > i * 2 + 1 {
q . PopFront ()
}
if i <= ( n - 1 ) / 2 {
prices [ i - 1 ] += prices [ q . Front () - 1 ]
}
for q . Size () > 0 && prices [ q . Back () - 1 ] >= prices [ i - 1 ] {
q . PopBack ()
}
q . PushBack ( i )
}
return prices [ 0 ]
}
// template
type Deque struct { l , r [] int }
func ( q Deque ) Empty () bool {
return len ( q . l ) == 0 && len ( q . r ) == 0
}
func ( q Deque ) Size () int {
return len ( q . l ) + len ( q . r )
}
func ( q * Deque ) PushFront ( v int ) {
q . l = append ( q . l , v )
}
func ( q * Deque ) PushBack ( v int ) {
q . r = append ( q . r , v )
}
func ( q * Deque ) PopFront () ( v int ) {
if len ( q . l ) > 0 {
q . l , v = q . l [: len ( q . l ) - 1 ], q . l [ len ( q . l ) - 1 ]
} else {
v , q . r = q . r [ 0 ], q . r [ 1 :]
}
return
}
func ( q * Deque ) PopBack () ( v int ) {
if len ( q . r ) > 0 {
q . r , v = q . r [: len ( q . r ) - 1 ], q . r [ len ( q . r ) - 1 ]
} else {
v , q . l = q . l [ 0 ], q . l [ 1 :]
}
return
}
func ( q Deque ) Front () int {
if len ( q . l ) > 0 {
return q . l [ len ( q . l ) - 1 ]
}
return q . r [ 0 ]
}
func ( q Deque ) Back () int {
if len ( q . r ) > 0 {
return q . r [ len ( q . r ) - 1 ]
}
return q . l [ 0 ]
}
func ( q Deque ) Get ( i int ) int {
if i < len ( q . l ) {
return q . l [ len ( q . l ) - 1 - i ]
}
return q . r [ i - len ( q . l )]
}
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113 function minimumCoins ( prices : number []) : number {
const n = prices . length ;
const q = new Deque < number > ();
for ( let i = n ; i ; -- i ) {
while ( q . getSize () && q . frontValue () ! > i * 2 + 1 ) {
q . popFront ();
}
if ( i <= ( n - 1 ) >> 1 ) {
prices [ i - 1 ] += prices [ q . frontValue () ! - 1 ];
}
while ( q . getSize () && prices [ q . backValue () ! - 1 ] >= prices [ i - 1 ]) {
q . popBack ();
}
q . pushBack ( i );
}
return prices [ 0 ];
}
class Node < T > {
value : T ;
next : Node < T > | null ;
prev : Node < T > | null ;
constructor ( value : T ) {
this . value = value ;
this . next = null ;
this . prev = null ;
}
}
class Deque < T > {
private front : Node < T > | null ;
private back : Node < T > | null ;
private size : number ;
constructor () {
this . front = null ;
this . back = null ;
this . size = 0 ;
}
pushFront ( val : T ) : void {
const newNode = new Node ( val );
if ( this . isEmpty ()) {
this . front = newNode ;
this . back = newNode ;
} else {
newNode . next = this . front ;
this . front ! . prev = newNode ;
this . front = newNode ;
}
this . size ++ ;
}
pushBack ( val : T ) : void {
const newNode = new Node ( val );
if ( this . isEmpty ()) {
this . front = newNode ;
this . back = newNode ;
} else {
newNode . prev = this . back ;
this . back ! . next = newNode ;
this . back = newNode ;
}
this . size ++ ;
}
popFront () : T | undefined {
if ( this . isEmpty ()) {
return undefined ;
}
const value = this . front ! . value ;
this . front = this . front ! . next ;
if ( this . front !== null ) {
this . front . prev = null ;
} else {
this . back = null ;
}
this . size -- ;
return value ;
}
popBack () : T | undefined {
if ( this . isEmpty ()) {
return undefined ;
}
const value = this . back ! . value ;
this . back = this . back ! . prev ;
if ( this . back !== null ) {
this . back . next = null ;
} else {
this . front = null ;
}
this . size -- ;
return value ;
}
frontValue () : T | undefined {
return this . front ? . value ;
}
backValue () : T | undefined {
return this . back ? . value ;
}
getSize () : number {
return this . size ;
}
isEmpty () : boolean {
return this . size === 0 ;
}
}
GitHub