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Improved task 3165
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  • src/main/kotlin/g3101_3200/s3165_maximum_sum_of_subsequence_with_non_adjacent_elements

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+104
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‎src/main/kotlin/g3101_3200/s3165_maximum_sum_of_subsequence_with_non_adjacent_elements/Solution.kt

Lines changed: 104 additions & 102 deletions
Original file line numberDiff line numberDiff line change
@@ -1,124 +1,126 @@
11
package g3101_3200.s3165_maximum_sum_of_subsequence_with_non_adjacent_elements
22

33
// #Hard #Array #Dynamic_Programming #Divide_and_Conquer #Segment_Tree
4-
// #2024_06_03_Time_1301_ms_(22.22%)_Space_69.8_MB_(100.00%)
4+
// #2024_11_09_Time_109_ms_(100.00%)_Space_87.9_MB_(100.00%)
55

6-
import java.util.stream.Stream
76
import kotlin.math.max
87

98
class Solution {
109
fun maximumSumSubsequence(nums: IntArray, queries: Array<IntArray>): Int {
11-
var ans = 0
12-
val segTree = SegTree(nums)
13-
for (q in queries) {
14-
val idx = q[0]
15-
val `val` = q[1]
16-
segTree.update(idx, `val`)
17-
ans = (ans + segTree.max!!) % MOD
10+
val tree: Array<LongArray?> = build(nums)
11+
var result: Long = 0
12+
for (i in queries.indices) {
13+
result += set(tree, queries[i][0], queries[i][1])
14+
result %= MOD.toLong()
1815
}
19-
return ans
16+
return result.toInt()
2017
}
2118

22-
internal class SegTree(private val nums: IntArray) {
23-
private class Record {
24-
var takeFirstTakeLast: Int = 0
25-
var takeFirstSkipLast: Int = 0
26-
var skipFirstSkipLast: Int = 0
27-
var skipFirstTakeLast: Int = 0
28-
29-
val max: Int
30-
get() = Stream.of(
31-
this.takeFirstSkipLast,
32-
this.takeFirstTakeLast,
33-
this.skipFirstSkipLast,
34-
this.skipFirstTakeLast
35-
)
36-
.max { x: Int?, y: Int? -> x!!.compareTo(y!!) }
37-
.orElse(null)
19+
companion object {
20+
private const val YY = 0
21+
private const val YN = 1
22+
private const val NY = 2
23+
private const val NN = 3
24+
private const val MOD = 1000000007
3825

39-
fun skipLast(): Int? {
40-
return Stream.of(this.takeFirstSkipLast, this.skipFirstSkipLast)
41-
.max { x: Int?, y: Int? -> x!!.compareTo(y!!) }
42-
.orElse(null)
26+
private fun build(nums: IntArray): Array<LongArray?> {
27+
val len = nums.size
28+
var size = 1
29+
while (size < len) {
30+
size = size shl 1
4331
}
44-
45-
fun takeLast(): Int? {
46-
return Stream.of(this.skipFirstTakeLast, this.takeFirstTakeLast)
47-
.max { x: Int?, y: Int? -> x!!.compareTo(y!!) }
48-
.orElse(null)
32+
val tree = Array<LongArray?>(size * 2) { LongArray(4) }
33+
for (i in 0 until len) {
34+
tree[size + i]!![YY] = nums[i].toLong()
4935
}
50-
}
51-
52-
private val seg = arrayOfNulls<Record>(4 * nums.size)
53-
54-
init {
55-
for (i in 0 until 4 * nums.size) {
56-
seg[i] = Record()
36+
for (i in size - 1 downTo 1) {
37+
tree[i]!![YY] = max(
38+
(tree[2 * i]!![YY] + tree[2 * i + 1]!![NY]),
39+
(
40+
tree[2 * i]!![YN] + max(
41+
tree[2 * i + 1]!![YY],
42+
tree[2 * i + 1]!![NY]
43+
)
44+
)
45+
)
46+
tree[i]!![YN] = max(
47+
(tree[2 * i]!![YY] + tree[2 * i + 1]!![NN]),
48+
(
49+
tree[2 * i]!![YN] + max(
50+
tree[2 * i + 1]!![YN],
51+
tree[2 * i + 1]!![NN]
52+
)
53+
)
54+
)
55+
tree[i]!![NY] = max(
56+
(tree[2 * i]!![NY] + tree[2 * i + 1]!![NY]),
57+
(
58+
tree[2 * i]!![NN] + max(
59+
tree[2 * i + 1]!![YY],
60+
tree[2 * i + 1]!![NY]
61+
)
62+
)
63+
)
64+
tree[i]!![NN] = max(
65+
(tree[2 * i]!![NY] + tree[2 * i + 1]!![NN]),
66+
(
67+
tree[2 * i]!![NN] + max(
68+
tree[2 * i + 1]!![YN],
69+
tree[2 * i + 1]!![NN]
70+
)
71+
)
72+
)
5773
}
58-
build(0, nums.size - 1, 0)
74+
return tree
5975
}
6076

61-
private fun build(i: Int, j: Int, k: Int) {
62-
if (i == j) {
63-
seg[k]!!.takeFirstTakeLast = nums[i]
64-
return
77+
private fun set(tree: Array<LongArray?>, idx: Int, `val`: Int): Long {
78+
val size = tree.size / 2
79+
tree[size + idx]!![YY] = `val`.toLong()
80+
var i = (size + idx) / 2
81+
while (i > 0) {
82+
tree[i]!![YY] = max(
83+
(tree[2 * i]!![YY] + tree[2 * i + 1]!![NY]),
84+
(
85+
tree[2 * i]!![YN] + max(
86+
tree[2 * i + 1]!![YY],
87+
tree[2 * i + 1]!![NY]
88+
)
89+
)
90+
)
91+
tree[i]!![YN] = max(
92+
(tree[2 * i]!![YY] + tree[2 * i + 1]!![NN]),
93+
(
94+
tree[2 * i]!![YN] + max(
95+
tree[2 * i + 1]!![YN],
96+
tree[2 * i + 1]!![NN]
97+
)
98+
)
99+
)
100+
tree[i]!![NY] = max(
101+
(tree[2 * i]!![NY] + tree[2 * i + 1]!![NY]),
102+
(
103+
tree[2 * i]!![NN] + max(
104+
tree[2 * i + 1]!![YY],
105+
tree[2 * i + 1]!![NY]
106+
)
107+
)
108+
)
109+
tree[i]!![NN] = max(
110+
(tree[2 * i]!![NY] + tree[2 * i + 1]!![NN]),
111+
(
112+
tree[2 * i]!![NN] + max(
113+
tree[2 * i + 1]!![YN],
114+
tree[2 * i + 1]!![NN]
115+
)
116+
)
117+
)
118+
i /= 2
65119
}
66-
val mid = (i + j) shr 1
67-
build(i, mid, 2 * k + 1)
68-
build(mid + 1, j, 2 * k + 2)
69-
merge(k)
70-
}
71-
72-
// merge [2*k+1, 2*k+2] into k
73-
private fun merge(k: Int) {
74-
seg[k]!!.takeFirstSkipLast = max(
75-
(seg[2 * k + 1]!!.takeFirstSkipLast + seg[2 * k + 2]!!.skipLast()!!),
76-
(seg[2 * k + 1]!!.takeFirstTakeLast + seg[2 * k + 2]!!.skipFirstSkipLast)
120+
return max(
121+
tree[1]!![YY],
122+
max(tree[1]!![YN], max(tree[1]!![NY], tree[1]!![NN]))
77123
)
78-
79-
seg[k]!!.takeFirstTakeLast = max(
80-
(seg[2 * k + 1]!!.takeFirstSkipLast + seg[2 * k + 2]!!.takeLast()!!),
81-
(seg[2 * k + 1]!!.takeFirstTakeLast + seg[2 * k + 2]!!.skipFirstTakeLast)
82-
)
83-
84-
seg[k]!!.skipFirstTakeLast = max(
85-
(seg[2 * k + 1]!!.skipFirstSkipLast + seg[2 * k + 2]!!.takeLast()!!),
86-
(seg[2 * k + 1]!!.skipFirstTakeLast + seg[2 * k + 2]!!.skipFirstTakeLast)
87-
)
88-
89-
seg[k]!!.skipFirstSkipLast = max(
90-
(seg[2 * k + 1]!!.skipFirstSkipLast + seg[2 * k + 2]!!.skipLast()!!),
91-
(seg[2 * k + 1]!!.skipFirstTakeLast + seg[2 * k + 2]!!.skipFirstSkipLast)
92-
)
93-
}
94-
95-
// child -> parent
96-
fun update(idx: Int, `val`: Int) {
97-
val i = 0
98-
val j = nums.size - 1
99-
val k = 0
100-
update(idx, `val`, k, i, j)
101124
}
102-
103-
private fun update(idx: Int, `val`: Int, k: Int, i: Int, j: Int) {
104-
if (i == j) {
105-
seg[k]!!.takeFirstTakeLast = `val`
106-
return
107-
}
108-
val mid = (i + j) shr 1
109-
if (idx <= mid) {
110-
update(idx, `val`, 2 * k + 1, i, mid)
111-
} else {
112-
update(idx, `val`, 2 * k + 2, mid + 1, j)
113-
}
114-
merge(k)
115-
}
116-
117-
val max: Int?
118-
get() = seg[0]?.max
119-
}
120-
121-
companion object {
122-
private const val MOD = 1000000007
123125
}
124126
}

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