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Improved task 3165 #1857

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Merged
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Nov 9, 2024
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Improved task 3165 #1857

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158 changes: 55 additions & 103 deletions ...java/g3101_3200/s3165_maximum_sum_of_subsequence_with_non_adjacent_elements/Solution.java
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Original file line number Diff line number Diff line change
@@ -1,125 +1,77 @@
package g3101_3200.s3165_maximum_sum_of_subsequence_with_non_adjacent_elements;

// #Hard #Array #Dynamic_Programming #Divide_and_Conquer #Segment_Tree
// #2024_06_02_Time_1927_ms_(87.75%)_Space_82.1_MB_(5.31%)

import java.util.stream.Stream;
// #2024_11_09_Time_64_ms_(100.00%)_Space_64.1_MB_(97.01%)

public class Solution {
private static final int YY = 0;
private static final int YN = 1;
private static final int NY = 2;
private static final int NN = 3;
private static final int MOD = 1_000_000_007;

public int maximumSumSubsequence(int[] nums, int[][] queries) {
int ans = 0;
SegTree segTree = new SegTree(nums);
for (int[] q : queries) {
int idx = q[0];
int val = q[1];
segTree.update(idx, val);
ans = (ans + segTree.getMax()) % MOD;
long[][] tree = build(nums);
long result = 0;
for (int i = 0; i < queries.length; ++i) {
result += set(tree, queries[i][0], queries[i][1]);
result %= MOD;
}
return ans;
return (int) result;
}

static class SegTree {
private static class Record {
int takeFirstTakeLast;
int takeFirstSkipLast;
int skipFirstSkipLast;
int skipFirstTakeLast;

public Integer getMax() {
return Stream.of(
this.takeFirstSkipLast,
this.takeFirstTakeLast,
this.skipFirstSkipLast,
this.skipFirstTakeLast)
.max(Integer::compare)
.orElse(null);
}

public Integer skipLast() {
return Stream.of(this.takeFirstSkipLast, this.skipFirstSkipLast)
.max(Integer::compare)
.orElse(null);
}

public Integer takeLast() {
return Stream.of(this.skipFirstTakeLast, this.takeFirstTakeLast)
.max(Integer::compare)
.orElse(null);
}
private static long[][] build(int[] nums) {
final int len = nums.length;
int size = 1;
while (size < len) {
size <<= 1;
}

private final Record[] seg;
private final int[] nums;

public SegTree(int[] nums) {
this.nums = nums;
seg = new Record[4 * nums.length];
for (int i = 0; i < 4 * nums.length; ++i) {
seg[i] = new Record();
}
build(0, nums.length - 1, 0);
long[][] tree = new long[size * 2][4];
for (int i = 0; i < len; ++i) {
tree[size + i][YY] = nums[i];
}

private void build(int i, int j, int k) {
if (i == j) {
seg[k].takeFirstTakeLast = nums[i];
return;
}
int mid = (i + j) >> 1;
build(i, mid, 2 * k + 1);
build(mid + 1, j, 2 * k + 2);
merge(k);
}

// merge [2*k+1, 2*k+2] into k
private void merge(int k) {
seg[k].takeFirstSkipLast =
for (int i = size - 1; i > 0; --i) {
tree[i][YY] =
Math.max(
seg[2 * k + 1].takeFirstSkipLast + seg[2 * k + 2].skipLast(),
seg[2 * k + 1].takeFirstTakeLast + seg[2 * k + 2].skipFirstSkipLast);

seg[k].takeFirstTakeLast =
tree[2 * i][YY] + tree[2 * i + 1][NY],
tree[2 * i][YN] + Math.max(tree[2 * i + 1][YY], tree[2 * i + 1][NY]));
tree[i][YN] =
Math.max(
seg[2 * k + 1].takeFirstSkipLast + seg[2 * k + 2].takeLast(),
seg[2 * k + 1].takeFirstTakeLast + seg[2 * k + 2].skipFirstTakeLast);

seg[k].skipFirstTakeLast =
tree[2 * i][YY] + tree[2 * i + 1][NN],
tree[2 * i][YN] + Math.max(tree[2 * i + 1][YN], tree[2 * i + 1][NN]));
tree[i][NY] =
Math.max(
seg[2 * k + 1].skipFirstSkipLast + seg[2 * k + 2].takeLast(),
seg[2 * k + 1].skipFirstTakeLast + seg[2 * k + 2].skipFirstTakeLast);

seg[k].skipFirstSkipLast =
tree[2 * i][NY] + tree[2 * i + 1][NY],
tree[2 * i][NN] + Math.max(tree[2 * i + 1][YY], tree[2 * i + 1][NY]));
tree[i][NN] =
Math.max(
seg[2 * k + 1].skipFirstSkipLast + seg[2 * k + 2].skipLast(),
seg[2 * k + 1].skipFirstTakeLast + seg[2 * k + 2].skipFirstSkipLast);
}

// child -> parent
public void update(int idx, int val) {
int i = 0;
int j = nums.length - 1;
int k = 0;
update(idx, val, k, i, j);
}

private void update(int idx, int val, int k, int i, int j) {
if (i == j) {
seg[k].takeFirstTakeLast = val;
return;
}
int mid = (i + j) >> 1;
if (idx <= mid) {
update(idx, val, 2 * k + 1, i, mid);
} else {
update(idx, val, 2 * k + 2, mid + 1, j);
}
merge(k);
tree[2 * i][NY] + tree[2 * i + 1][NN],
tree[2 * i][NN] + Math.max(tree[2 * i + 1][YN], tree[2 * i + 1][NN]));
}
return tree;
}

public int getMax() {
return seg[0].getMax();
private static long set(long[][] tree, int idx, int val) {
int size = tree.length / 2;
tree[size + idx][YY] = val;
for (int i = (size + idx) / 2; i > 0; i /= 2) {
tree[i][YY] =
Math.max(
tree[2 * i][YY] + tree[2 * i + 1][NY],
tree[2 * i][YN] + Math.max(tree[2 * i + 1][YY], tree[2 * i + 1][NY]));
tree[i][YN] =
Math.max(
tree[2 * i][YY] + tree[2 * i + 1][NN],
tree[2 * i][YN] + Math.max(tree[2 * i + 1][YN], tree[2 * i + 1][NN]));
tree[i][NY] =
Math.max(
tree[2 * i][NY] + tree[2 * i + 1][NY],
tree[2 * i][NN] + Math.max(tree[2 * i + 1][YY], tree[2 * i + 1][NY]));
tree[i][NN] =
Math.max(
tree[2 * i][NY] + tree[2 * i + 1][NN],
tree[2 * i][NN] + Math.max(tree[2 * i + 1][YN], tree[2 * i + 1][NN]));
}
return Math.max(tree[1][YY], Math.max(tree[1][YN], Math.max(tree[1][NY], tree[1][NN])));
}
}
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