From 6a7942a3b27b13005a12e6eab14bca9b176dac5a Mon Sep 17 00:00:00 2001
From: Valentyn Kolesnikov <javadev75@gmail.com>
Date: Sun, 4 May 2025 17:07:27 +0300
Subject: [PATCH 1/5] Added tasks 3536-3539

---
 .../Solution.kt                               | 28 ++++++
 .../readme.md                                 | 49 ++++++++++
 .../s3537_fill_a_special_grid/Solution.kt     | 33 +++++++
 .../s3537_fill_a_special_grid/readme.md       | 67 ++++++++++++++
 .../Solution.kt                               | 48 ++++++++++
 .../readme.md                                 | 71 +++++++++++++++
 .../Solution.kt                               | 91 +++++++++++++++++++
 .../readme.md                                 | 55 +++++++++++
 .../SolutionTest.kt                           | 22 +++++
 .../s3537_fill_a_special_grid/SolutionTest.kt | 38 ++++++++
 .../SolutionTest.kt                           | 31 +++++++
 .../SolutionTest.kt                           | 28 ++++++
 12 files changed, 561 insertions(+)
 create mode 100644 src/main/kotlin/g3501_3600/s3536_maximum_product_of_two_digits/Solution.kt
 create mode 100644 src/main/kotlin/g3501_3600/s3536_maximum_product_of_two_digits/readme.md
 create mode 100644 src/main/kotlin/g3501_3600/s3537_fill_a_special_grid/Solution.kt
 create mode 100644 src/main/kotlin/g3501_3600/s3537_fill_a_special_grid/readme.md
 create mode 100644 src/main/kotlin/g3501_3600/s3538_merge_operations_for_minimum_travel_time/Solution.kt
 create mode 100644 src/main/kotlin/g3501_3600/s3538_merge_operations_for_minimum_travel_time/readme.md
 create mode 100644 src/main/kotlin/g3501_3600/s3539_find_sum_of_array_product_of_magical_sequences/Solution.kt
 create mode 100644 src/main/kotlin/g3501_3600/s3539_find_sum_of_array_product_of_magical_sequences/readme.md
 create mode 100644 src/test/kotlin/g3501_3600/s3536_maximum_product_of_two_digits/SolutionTest.kt
 create mode 100644 src/test/kotlin/g3501_3600/s3537_fill_a_special_grid/SolutionTest.kt
 create mode 100644 src/test/kotlin/g3501_3600/s3538_merge_operations_for_minimum_travel_time/SolutionTest.kt
 create mode 100644 src/test/kotlin/g3501_3600/s3539_find_sum_of_array_product_of_magical_sequences/SolutionTest.kt

diff --git a/src/main/kotlin/g3501_3600/s3536_maximum_product_of_two_digits/Solution.kt b/src/main/kotlin/g3501_3600/s3536_maximum_product_of_two_digits/Solution.kt
new file mode 100644
index 000000000..01dfff875
--- /dev/null
+++ b/src/main/kotlin/g3501_3600/s3536_maximum_product_of_two_digits/Solution.kt
@@ -0,0 +1,28 @@
+package g3501_3600.s3536_maximum_product_of_two_digits
+
+// #Easy #2025_05_04_Time_1_ms_(100.00%)_Space_40.93_MB_(100.00%)
+
+class Solution {
+    fun maxProduct(n: Int): Int {
+        var n = n
+        var m1 = n % 10
+        n /= 10
+        var m2 = n % 10
+        n /= 10
+        while (n > 0) {
+            val a = n % 10
+            if (a > m1) {
+                if (m1 > m2) {
+                    m2 = m1
+                }
+                m1 = a
+            } else {
+                if (a > m2) {
+                    m2 = a
+                }
+            }
+            n /= 10
+        }
+        return m1 * m2
+    }
+}
diff --git a/src/main/kotlin/g3501_3600/s3536_maximum_product_of_two_digits/readme.md b/src/main/kotlin/g3501_3600/s3536_maximum_product_of_two_digits/readme.md
new file mode 100644
index 000000000..11f945253
--- /dev/null
+++ b/src/main/kotlin/g3501_3600/s3536_maximum_product_of_two_digits/readme.md
@@ -0,0 +1,49 @@
+3536\. Maximum Product of Two Digits
+
+Easy
+
+You are given a positive integer `n`.
+
+Return the **maximum** product of any two digits in `n`.
+
+**Note:** You may use the **same** digit twice if it appears more than once in `n`.
+
+**Example 1:**
+
+**Input:** n = 31
+
+**Output:** 3
+
+**Explanation:**
+
+*   The digits of `n` are `[3, 1]`.
+*   The possible products of any two digits are: `3 * 1 = 3`.
+*   The maximum product is 3.
+
+**Example 2:**
+
+**Input:** n = 22
+
+**Output:** 4
+
+**Explanation:**
+
+*   The digits of `n` are `[2, 2]`.
+*   The possible products of any two digits are: `2 * 2 = 4`.
+*   The maximum product is 4.
+
+**Example 3:**
+
+**Input:** n = 124
+
+**Output:** 8
+
+**Explanation:**
+
+*   The digits of `n` are `[1, 2, 4]`.
+*   The possible products of any two digits are: `1 * 2 = 2`, `1 * 4 = 4`, `2 * 4 = 8`.
+*   The maximum product is 8.
+
+**Constraints:**
+
+*   <code>10 <= n <= 10<sup>9</sup></code>
\ No newline at end of file
diff --git a/src/main/kotlin/g3501_3600/s3537_fill_a_special_grid/Solution.kt b/src/main/kotlin/g3501_3600/s3537_fill_a_special_grid/Solution.kt
new file mode 100644
index 000000000..a5ff7d47e
--- /dev/null
+++ b/src/main/kotlin/g3501_3600/s3537_fill_a_special_grid/Solution.kt
@@ -0,0 +1,33 @@
+package g3501_3600.s3537_fill_a_special_grid
+
+// #Medium #2025_05_04_Time_2_ms_(100.00%)_Space_88.71_MB_(61.54%)
+
+import kotlin.math.pow
+
+class Solution {
+    fun specialGrid(n: Int): Array<IntArray> {
+        if (n == 0) {
+            return arrayOf<IntArray>(intArrayOf(0))
+        }
+        val len = 2.0.pow(n.toDouble()).toInt()
+        val ans = Array<IntArray>(len) { IntArray(len) }
+        val num = intArrayOf(2.0.pow(2.0 * n).toInt() - 1)
+        backtrack(ans, len, len, 0, 0, num)
+        return ans
+    }
+
+    private fun backtrack(ans: Array<IntArray>, m: Int, n: Int, x: Int, y: Int, num: IntArray) {
+        if (m == 2 && n == 2) {
+            ans[x][y] = num[0]
+            ans[x + 1][y] = num[0] - 1
+            ans[x + 1][y + 1] = num[0] - 2
+            ans[x][y + 1] = num[0] - 3
+            num[0] -= 4
+            return
+        }
+        backtrack(ans, m / 2, n / 2, x, y, num)
+        backtrack(ans, m / 2, n / 2, x + m / 2, y, num)
+        backtrack(ans, m / 2, n / 2, x + m / 2, y + n / 2, num)
+        backtrack(ans, m / 2, n / 2, x, y + n / 2, num)
+    }
+}
diff --git a/src/main/kotlin/g3501_3600/s3537_fill_a_special_grid/readme.md b/src/main/kotlin/g3501_3600/s3537_fill_a_special_grid/readme.md
new file mode 100644
index 000000000..e0ee432a9
--- /dev/null
+++ b/src/main/kotlin/g3501_3600/s3537_fill_a_special_grid/readme.md
@@ -0,0 +1,67 @@
+3537\. Fill a Special Grid
+
+Medium
+
+You are given a non-negative integer `n` representing a <code>2<sup>n</sup> x 2<sup>n</sup></code> grid. You must fill the grid with integers from 0 to <code>2<sup>2n</sup> - 1</code> to make it **special**. A grid is **special** if it satisfies **all** the following conditions:
+
+*   All numbers in the top-right quadrant are smaller than those in the bottom-right quadrant.
+*   All numbers in the bottom-right quadrant are smaller than those in the bottom-left quadrant.
+*   All numbers in the bottom-left quadrant are smaller than those in the top-left quadrant.
+*   Each of its quadrants is also a special grid.
+
+Return the **special** <code>2<sup>n</sup> x 2<sup>n</sup></code> grid.
+
+**Note**: Any 1x1 grid is special.
+
+**Example 1:**
+
+**Input:** n = 0
+
+**Output:** [[0]]
+
+**Explanation:**
+
+The only number that can be placed is 0, and there is only one possible position in the grid.
+
+**Example 2:**
+
+**Input:** n = 1
+
+**Output:** [[3,0],[2,1]]
+
+**Explanation:**
+
+The numbers in each quadrant are:
+
+*   Top-right: 0
+*   Bottom-right: 1
+*   Bottom-left: 2
+*   Top-left: 3
+
+Since `0 < 1 < 2 < 3`, this satisfies the given constraints.
+
+**Example 3:**
+
+**Input:** n = 2
+
+**Output:** [[15,12,3,0],[14,13,2,1],[11,8,7,4],[10,9,6,5]]
+
+**Explanation:**
+
+![](https://assets.leetcode.com/uploads/2025/03/05/4123example3p1drawio.png)
+
+The numbers in each quadrant are:
+
+*   Top-right: 3, 0, 2, 1
+*   Bottom-right: 7, 4, 6, 5
+*   Bottom-left: 11, 8, 10, 9
+*   Top-left: 15, 12, 14, 13
+*   `max(3, 0, 2, 1) < min(7, 4, 6, 5)`
+*   `max(7, 4, 6, 5) < min(11, 8, 10, 9)`
+*   `max(11, 8, 10, 9) < min(15, 12, 14, 13)`
+
+This satisfies the first three requirements. Additionally, each quadrant is also a special grid. Thus, this is a special grid.
+
+**Constraints:**
+
+*   `0 <= n <= 10`
\ No newline at end of file
diff --git a/src/main/kotlin/g3501_3600/s3538_merge_operations_for_minimum_travel_time/Solution.kt b/src/main/kotlin/g3501_3600/s3538_merge_operations_for_minimum_travel_time/Solution.kt
new file mode 100644
index 000000000..30fdabcdf
--- /dev/null
+++ b/src/main/kotlin/g3501_3600/s3538_merge_operations_for_minimum_travel_time/Solution.kt
@@ -0,0 +1,48 @@
+package g3501_3600.s3538_merge_operations_for_minimum_travel_time
+
+// #Hard #2025_05_04_Time_10_ms_(100.00%)_Space_46.96_MB_(100.00%)
+
+import kotlin.math.min
+
+@Suppress("unused")
+class Solution {
+    fun minTravelTime(l: Int, n: Int, k: Int, position: IntArray, time: IntArray): Int {
+        val dp = Array<Array<IntArray>>(n) { Array<IntArray>(k + 1) { IntArray(k + 1) } }
+        for (i in 0..<n) {
+            for (j in 0..k) {
+                for (m in 0..k) {
+                    dp[i][j][m] = Int.Companion.MAX_VALUE
+                }
+            }
+        }
+        dp[0][0][0] = 0
+        for (i in 0..<n - 1) {
+            var currTime = 0
+            var curr = 0
+            while (curr <= k && curr <= i) {
+                currTime += time[i - curr]
+                for (used in 0..k) {
+                    if (dp[i][curr][used] == Int.Companion.MAX_VALUE) {
+                        continue
+                    }
+                    var next = 0
+                    while (next <= k - used && next <= n - i - 2) {
+                        val nextI = i + next + 1
+                        dp[nextI][next][next + used] = min(
+                            dp[nextI][next][next + used],
+                            dp[i][curr][used] +
+                                (position[nextI] - position[i]) * currTime,
+                        )
+                        next++
+                    }
+                }
+                curr++
+            }
+        }
+        var ans = Int.Companion.MAX_VALUE
+        for (curr in 0..k) {
+            ans = min(ans, dp[n - 1][curr][k])
+        }
+        return ans
+    }
+}
diff --git a/src/main/kotlin/g3501_3600/s3538_merge_operations_for_minimum_travel_time/readme.md b/src/main/kotlin/g3501_3600/s3538_merge_operations_for_minimum_travel_time/readme.md
new file mode 100644
index 000000000..047bffd70
--- /dev/null
+++ b/src/main/kotlin/g3501_3600/s3538_merge_operations_for_minimum_travel_time/readme.md
@@ -0,0 +1,71 @@
+3538\. Merge Operations for Minimum Travel Time
+
+Hard
+
+You are given a straight road of length `l` km, an integer `n`, an integer `k`**,** and **two** integer arrays, `position` and `time`, each of length `n`.
+
+The array `position` lists the positions (in km) of signs in **strictly** increasing order (with `position[0] = 0` and `position[n - 1] = l`).
+
+Each `time[i]` represents the time (in minutes) required to travel 1 km between `position[i]` and `position[i + 1]`.
+
+You **must** perform **exactly** `k` merge operations. In one merge, you can choose any **two** adjacent signs at indices `i` and `i + 1` (with `i > 0` and `i + 1 < n`) and:
+
+*   Update the sign at index `i + 1` so that its time becomes `time[i] + time[i + 1]`.
+*   Remove the sign at index `i`.
+
+Return the **minimum** **total** **travel time** (in minutes) to travel from 0 to `l` after **exactly** `k` merges.
+
+**Example 1:**
+
+**Input:** l = 10, n = 4, k = 1, position = [0,3,8,10], time = [5,8,3,6]
+
+**Output:** 62
+
+**Explanation:**
+
+*   Merge the signs at indices 1 and 2. Remove the sign at index 1, and change the time at index 2 to `8 + 3 = 11`.
+    
+*   After the merge:
+    *   `position` array: `[0, 8, 10]`
+    *   `time` array: `[5, 11, 6]`
+    
+| Segment   | Distance (km) | Time per km (min) | Segment Travel Time (min)  |
+|-----------|---------------|-------------------|----------------------------|
+| 0 → 8     | 8             | 5                 | 8 × 5 = 40                 |
+| 8 → 10    | 2             | 11                | 2 × 11 = 22                |
+
+    
+*   Total Travel Time: `40 + 22 = 62`, which is the minimum possible time after exactly 1 merge.
+
+**Example 2:**
+
+**Input:** l = 5, n = 5, k = 1, position = [0,1,2,3,5], time = [8,3,9,3,3]
+
+**Output:** 34
+
+**Explanation:**
+
+*   Merge the signs at indices 1 and 2. Remove the sign at index 1, and change the time at index 2 to `3 + 9 = 12`.
+*   After the merge:
+    *   `position` array: `[0, 2, 3, 5]`
+    *   `time` array: `[8, 12, 3, 3]`
+    
+| Segment   | Distance (km) | Time per km (min) | Segment Travel Time (min)  |
+|-----------|---------------|-------------------|----------------------------|
+| 0 → 2     | 2             | 8                 | 2 × 8 = 16                 |
+| 2 → 3     | 1             | 12                | 1 × 12 = 12                |
+| 3 → 5     | 2             | 3                 | 2 × 3 = 6                  |
+    
+*   Total Travel Time: `16 + 12 + 6 = 34`**,** which is the minimum possible time after exactly 1 merge.
+
+**Constraints:**
+
+*   <code>1 <= l <= 10<sup>5</sup></code>
+*   `2 <= n <= min(l + 1, 50)`
+*   `0 <= k <= min(n - 2, 10)`
+*   `position.length == n`
+*   `position[0] = 0` and `position[n - 1] = l`
+*   `position` is sorted in strictly increasing order.
+*   `time.length == n`
+*   `1 <= time[i] <= 100`
+*   `1 <= sum(time) <= 100`
\ No newline at end of file
diff --git a/src/main/kotlin/g3501_3600/s3539_find_sum_of_array_product_of_magical_sequences/Solution.kt b/src/main/kotlin/g3501_3600/s3539_find_sum_of_array_product_of_magical_sequences/Solution.kt
new file mode 100644
index 000000000..23efcf986
--- /dev/null
+++ b/src/main/kotlin/g3501_3600/s3539_find_sum_of_array_product_of_magical_sequences/Solution.kt
@@ -0,0 +1,91 @@
+package g3501_3600.s3539_find_sum_of_array_product_of_magical_sequences
+
+// #Hard #2025_05_04_Time_58_ms_(_%)_Space_49.73_MB_(_%)
+
+class Solution {
+    fun magicalSum(m: Int, k: Int, nums: IntArray): Int {
+        val n = nums.size
+        val pow = Array<LongArray>(n) { LongArray(m + 1) }
+        for (j in 0..<n) {
+            pow[j][0] = 1L
+            for (c in 1..m) {
+                pow[j][c] = pow[j][c - 1] * nums[j] % MOD
+            }
+        }
+        var dp = Array<Array<LongArray>>(m + 1) { Array<LongArray>(k + 1) { LongArray(m + 1) } }
+        var next = Array<Array<LongArray>>(m + 1) { Array<LongArray>(k + 1) { LongArray(m + 1) } }
+        dp[0][0][0] = 1L
+        for (i in 0..<n) {
+            for (t in 0..m) {
+                for (o in 0..k) {
+                    next[t][o].fill(0L)
+                }
+            }
+            for (t in 0..m) {
+                for (o in 0..k) {
+                    for (c in 0..m) {
+                        if (dp[t][o][c] == 0L) {
+                            continue
+                        }
+                        for (cc in 0..m - t) {
+                            val total = c + cc
+                            if (o + (total and 1) > k) {
+                                continue
+                            }
+                            next[t + cc][o + (total and 1)][total ushr 1] =
+                                (
+                                    (
+                                        next[t + cc][o + (total and 1)][total ushr 1] +
+                                            dp[t][o][c] *
+                                            C[m - t][cc] %
+                                            MOD
+                                            * pow[i][cc] %
+                                            MOD
+                                        ) %
+                                        MOD
+                                    )
+                        }
+                    }
+                }
+            }
+            val tmp = dp
+            dp = next
+            next = tmp
+        }
+        var res: Long = 0
+        for (o in 0..k) {
+            for (c in 0..m) {
+                if (o + P[c] == k) {
+                    res = (res + dp[m][o][c]) % MOD
+                }
+            }
+        }
+        return res.toInt()
+    }
+
+    companion object {
+        private const val MOD = 1000000007
+        private val C: Array<IntArray> = precomputeBinom(31)
+        private val P: IntArray = precomputePop(31)
+
+        private fun precomputeBinom(max: Int): Array<IntArray> {
+            val res = Array<IntArray>(max) { IntArray(max) }
+            for (i in 0..<max) {
+                res[i][i] = 1
+                res[i][0] = res[i][i]
+                for (j in 1..<i) {
+                    res[i][j] = (res[i - 1][j - 1] + res[i - 1][j]) % MOD
+                }
+            }
+            return res
+        }
+
+        private fun precomputePop(max: Int): IntArray {
+            val res = IntArray(max)
+            for (i in 1..<max) {
+                res[i] = res[i shr 1] + (i and 1)
+            }
+            return res
+        }
+    }
+}
diff --git a/src/main/kotlin/g3501_3600/s3539_find_sum_of_array_product_of_magical_sequences/readme.md b/src/main/kotlin/g3501_3600/s3539_find_sum_of_array_product_of_magical_sequences/readme.md
new file mode 100644
index 000000000..47499759b
--- /dev/null
+++ b/src/main/kotlin/g3501_3600/s3539_find_sum_of_array_product_of_magical_sequences/readme.md
@@ -0,0 +1,55 @@
+3539\. Find Sum of Array Product of Magical Sequences
+
+Hard
+
+You are given two integers, `m` and `k`, and an integer array `nums`.
+
+A sequence of integers `seq` is called **magical** if:
+
+*   `seq` has a size of `m`.
+*   `0 <= seq[i] < nums.length`
+*   The **binary representation** of <code>2<sup>seq[0]</sup> + 2<sup>seq[1]</sup> + ... + 2<sup>seq[m - 1]</sup></code> has `k` **set bits**.
+
+The **array product** of this sequence is defined as `prod(seq) = (nums[seq[0]] * nums[seq[1]] * ... * nums[seq[m - 1]])`.
+
+Return the **sum** of the **array products** for all valid **magical** sequences.
+
+Since the answer may be large, return it **modulo** <code>10<sup>9</sup> + 7</code>.
+
+A **set bit** refers to a bit in the binary representation of a number that has a value of 1.
+
+**Example 1:**
+
+**Input:** m = 5, k = 5, nums = [1,10,100,10000,1000000]
+
+**Output:** 991600007
+
+**Explanation:**
+
+All permutations of `[0, 1, 2, 3, 4]` are magical sequences, each with an array product of 10<sup>13</sup>.
+
+**Example 2:**
+
+**Input:** m = 2, k = 2, nums = [5,4,3,2,1]
+
+**Output:** 170
+
+**Explanation:**
+
+The magical sequences are `[0, 1]`, `[0, 2]`, `[0, 3]`, `[0, 4]`, `[1, 0]`, `[1, 2]`, `[1, 3]`, `[1, 4]`, `[2, 0]`, `[2, 1]`, `[2, 3]`, `[2, 4]`, `[3, 0]`, `[3, 1]`, `[3, 2]`, `[3, 4]`, `[4, 0]`, `[4, 1]`, `[4, 2]`, and `[4, 3]`.
+
+**Example 3:**
+
+**Input:** m = 1, k = 1, nums = [28]
+
+**Output:** 28
+
+**Explanation:**
+
+The only magical sequence is `[0]`.
+
+**Constraints:**
+
+*   `1 <= k <= m <= 30`
+*   `1 <= nums.length <= 50`
+*   <code>1 <= nums[i] <= 10<sup>8</sup></code>
\ No newline at end of file
diff --git a/src/test/kotlin/g3501_3600/s3536_maximum_product_of_two_digits/SolutionTest.kt b/src/test/kotlin/g3501_3600/s3536_maximum_product_of_two_digits/SolutionTest.kt
new file mode 100644
index 000000000..fd6d8d943
--- /dev/null
+++ b/src/test/kotlin/g3501_3600/s3536_maximum_product_of_two_digits/SolutionTest.kt
@@ -0,0 +1,22 @@
+package g3501_3600.s3536_maximum_product_of_two_digits
+
+import org.hamcrest.CoreMatchers.equalTo
+import org.hamcrest.MatcherAssert.assertThat
+import org.junit.jupiter.api.Test
+
+internal class SolutionTest {
+    @Test
+    fun maxProduct() {
+        assertThat<Int>(Solution().maxProduct(31), equalTo<Int>(3))
+    }
+
+    @Test
+    fun maxProduct2() {
+        assertThat<Int>(Solution().maxProduct(22), equalTo<Int>(4))
+    }
+
+    @Test
+    fun maxProduct3() {
+        assertThat<Int>(Solution().maxProduct(124), equalTo<Int>(8))
+    }
+}
diff --git a/src/test/kotlin/g3501_3600/s3537_fill_a_special_grid/SolutionTest.kt b/src/test/kotlin/g3501_3600/s3537_fill_a_special_grid/SolutionTest.kt
new file mode 100644
index 000000000..61faf1519
--- /dev/null
+++ b/src/test/kotlin/g3501_3600/s3537_fill_a_special_grid/SolutionTest.kt
@@ -0,0 +1,38 @@
+package g3501_3600.s3537_fill_a_special_grid
+
+import org.hamcrest.CoreMatchers.equalTo
+import org.hamcrest.MatcherAssert.assertThat
+import org.junit.jupiter.api.Test
+
+internal class SolutionTest {
+    @Test
+    fun specialGrid() {
+        assertThat<Array<IntArray>>(
+            Solution().specialGrid(0),
+            equalTo<Array<IntArray>>(arrayOf<IntArray>(intArrayOf(0))),
+        )
+    }
+
+    @Test
+    fun specialGrid2() {
+        assertThat<Array<IntArray>>(
+            Solution().specialGrid(1),
+            equalTo<Array<IntArray>>(arrayOf<IntArray>(intArrayOf(3, 0), intArrayOf(2, 1))),
+        )
+    }
+
+    @Test
+    fun specialGrid3() {
+        assertThat<Array<IntArray>>(
+            Solution().specialGrid(2),
+            equalTo<Array<IntArray>>(
+                arrayOf<IntArray>(
+                    intArrayOf(15, 12, 3, 0),
+                    intArrayOf(14, 13, 2, 1),
+                    intArrayOf(11, 8, 7, 4),
+                    intArrayOf(10, 9, 6, 5),
+                ),
+            ),
+        )
+    }
+}
diff --git a/src/test/kotlin/g3501_3600/s3538_merge_operations_for_minimum_travel_time/SolutionTest.kt b/src/test/kotlin/g3501_3600/s3538_merge_operations_for_minimum_travel_time/SolutionTest.kt
new file mode 100644
index 000000000..00be368ff
--- /dev/null
+++ b/src/test/kotlin/g3501_3600/s3538_merge_operations_for_minimum_travel_time/SolutionTest.kt
@@ -0,0 +1,31 @@
+package g3501_3600.s3538_merge_operations_for_minimum_travel_time
+
+import org.hamcrest.CoreMatchers.equalTo
+import org.hamcrest.MatcherAssert.assertThat
+import org.junit.jupiter.api.Test
+
+internal class SolutionTest {
+    @Test
+    fun minTravelTime() {
+        assertThat<Int>(
+            Solution()
+                .minTravelTime(10, 4, 1, intArrayOf(0, 3, 8, 10), intArrayOf(5, 8, 3, 6)),
+            equalTo<Int>(62),
+        )
+    }
+
+    @Test
+    fun minTravelTime2() {
+        assertThat<Int>(
+            Solution()
+                .minTravelTime(
+                    5,
+                    5,
+                    1,
+                    intArrayOf(0, 1, 2, 3, 5),
+                    intArrayOf(8, 3, 9, 3, 3),
+                ),
+            equalTo<Int>(34),
+        )
+    }
+}
diff --git a/src/test/kotlin/g3501_3600/s3539_find_sum_of_array_product_of_magical_sequences/SolutionTest.kt b/src/test/kotlin/g3501_3600/s3539_find_sum_of_array_product_of_magical_sequences/SolutionTest.kt
new file mode 100644
index 000000000..dd57b7af2
--- /dev/null
+++ b/src/test/kotlin/g3501_3600/s3539_find_sum_of_array_product_of_magical_sequences/SolutionTest.kt
@@ -0,0 +1,28 @@
+package g3501_3600.s3539_find_sum_of_array_product_of_magical_sequences
+
+import org.hamcrest.CoreMatchers.equalTo
+import org.hamcrest.MatcherAssert.assertThat
+import org.junit.jupiter.api.Test
+
+internal class SolutionTest {
+    @Test
+    fun magicalSum() {
+        assertThat<Int>(
+            Solution().magicalSum(5, 5, intArrayOf(1, 10, 100, 10000, 1000000)),
+            equalTo<Int>(991600007),
+        )
+    }
+
+    @Test
+    fun magicalSum2() {
+        assertThat<Int>(
+            Solution().magicalSum(2, 2, intArrayOf(5, 4, 3, 2, 1)),
+            equalTo<Int>(170),
+        )
+    }
+
+    @Test
+    fun magicalSum3() {
+        assertThat<Int>(Solution().magicalSum(1, 1, intArrayOf(28)), equalTo<Int>(28))
+    }
+}

From 619442a8be8363d77908c44548ea20a2cd9d9089 Mon Sep 17 00:00:00 2001
From: Valentyn Kolesnikov <javadev75@gmail.com>
Date: Sun, 4 May 2025 18:03:31 +0300
Subject: [PATCH 2/5] Added tests

---
 .../SolutionTest.kt                               | 15 +++++++++++++++
 1 file changed, 15 insertions(+)

diff --git a/src/test/kotlin/g3501_3600/s3536_maximum_product_of_two_digits/SolutionTest.kt b/src/test/kotlin/g3501_3600/s3536_maximum_product_of_two_digits/SolutionTest.kt
index fd6d8d943..561984792 100644
--- a/src/test/kotlin/g3501_3600/s3536_maximum_product_of_two_digits/SolutionTest.kt
+++ b/src/test/kotlin/g3501_3600/s3536_maximum_product_of_two_digits/SolutionTest.kt
@@ -19,4 +19,19 @@ internal class SolutionTest {
     fun maxProduct3() {
         assertThat<Int>(Solution().maxProduct(124), equalTo<Int>(8))
     }
+
+    @Test
+    fun maxProduct4() {
+        assertThat<Int>(Solution().maxProduct(453), equalTo<Int>(20))
+    }
+
+    @Test
+    fun maxProduct5() {
+        assertThat<Int>(Solution().maxProduct(437), equalTo<Int>(28))
+    }
+
+    @Test
+    fun maxProduct6() {
+        assertThat<Int>(Solution().maxProduct(724), equalTo<Int>(28))
+    }
 }

From 9abc5aa3a3294b223fc75cfac672b93544a29724 Mon Sep 17 00:00:00 2001
From: Valentyn Kolesnikov <javadev75@gmail.com>
Date: Tue, 6 May 2025 08:47:02 +0300
Subject: [PATCH 3/5] Updated tags

---
 .../g3501_3600/s3536_maximum_product_of_two_digits/Solution.kt | 2 +-
 .../kotlin/g3501_3600/s3537_fill_a_special_grid/Solution.kt    | 3 ++-
 .../s3538_merge_operations_for_minimum_travel_time/Solution.kt | 3 ++-
 .../Solution.kt                                                | 3 ++-
 4 files changed, 7 insertions(+), 4 deletions(-)

diff --git a/src/main/kotlin/g3501_3600/s3536_maximum_product_of_two_digits/Solution.kt b/src/main/kotlin/g3501_3600/s3536_maximum_product_of_two_digits/Solution.kt
index 01dfff875..ca91a3beb 100644
--- a/src/main/kotlin/g3501_3600/s3536_maximum_product_of_two_digits/Solution.kt
+++ b/src/main/kotlin/g3501_3600/s3536_maximum_product_of_two_digits/Solution.kt
@@ -1,6 +1,6 @@
 package g3501_3600.s3536_maximum_product_of_two_digits
 
-// #Easy #2025_05_04_Time_1_ms_(100.00%)_Space_40.93_MB_(100.00%)
+// #Easy #Math #Sorting #2025_05_04_Time_1_ms_(100.00%)_Space_40.93_MB_(100.00%)
 
 class Solution {
     fun maxProduct(n: Int): Int {
diff --git a/src/main/kotlin/g3501_3600/s3537_fill_a_special_grid/Solution.kt b/src/main/kotlin/g3501_3600/s3537_fill_a_special_grid/Solution.kt
index a5ff7d47e..a2612ba3c 100644
--- a/src/main/kotlin/g3501_3600/s3537_fill_a_special_grid/Solution.kt
+++ b/src/main/kotlin/g3501_3600/s3537_fill_a_special_grid/Solution.kt
@@ -1,6 +1,7 @@
 package g3501_3600.s3537_fill_a_special_grid
 
-// #Medium #2025_05_04_Time_2_ms_(100.00%)_Space_88.71_MB_(61.54%)
+// #Medium #Array #Matrix #Divide_and_Conquer
+// #2025_05_04_Time_2_ms_(100.00%)_Space_88.71_MB_(61.54%)
 
 import kotlin.math.pow
 
diff --git a/src/main/kotlin/g3501_3600/s3538_merge_operations_for_minimum_travel_time/Solution.kt b/src/main/kotlin/g3501_3600/s3538_merge_operations_for_minimum_travel_time/Solution.kt
index 30fdabcdf..8d84a2522 100644
--- a/src/main/kotlin/g3501_3600/s3538_merge_operations_for_minimum_travel_time/Solution.kt
+++ b/src/main/kotlin/g3501_3600/s3538_merge_operations_for_minimum_travel_time/Solution.kt
@@ -1,6 +1,7 @@
 package g3501_3600.s3538_merge_operations_for_minimum_travel_time
 
-// #Hard #2025_05_04_Time_10_ms_(100.00%)_Space_46.96_MB_(100.00%)
+// #Hard #Array #Dynamic_Programming #Prefix_Sum
+// #2025_05_04_Time_10_ms_(100.00%)_Space_46.96_MB_(100.00%)
 
 import kotlin.math.min
 
diff --git a/src/main/kotlin/g3501_3600/s3539_find_sum_of_array_product_of_magical_sequences/Solution.kt b/src/main/kotlin/g3501_3600/s3539_find_sum_of_array_product_of_magical_sequences/Solution.kt
index 23efcf986..9ec80549d 100644
--- a/src/main/kotlin/g3501_3600/s3539_find_sum_of_array_product_of_magical_sequences/Solution.kt
+++ b/src/main/kotlin/g3501_3600/s3539_find_sum_of_array_product_of_magical_sequences/Solution.kt
@@ -1,6 +1,7 @@
 package g3501_3600.s3539_find_sum_of_array_product_of_magical_sequences
 
-// #Hard #2025_05_04_Time_58_ms_(_%)_Space_49.73_MB_(_%)
+// #Hard #Array #Dynamic_Programming #Math #Bit_Manipulation #Bitmask #Combinatorics
+// #2025_05_04_Time_58_ms_(_%)_Space_49.73_MB_(_%)
 
 class Solution {
     fun magicalSum(m: Int, k: Int, nums: IntArray): Int {

From c0f06b1f0ed432883528361eaf1119391fe9d47a Mon Sep 17 00:00:00 2001
From: Valentyn Kolesnikov <javadev75@gmail.com>
Date: Tue, 6 May 2025 08:59:37 +0300
Subject: [PATCH 4/5] Improved task

---
 .../Solution.kt                               | 54 +++++++++----------
 1 file changed, 26 insertions(+), 28 deletions(-)

diff --git a/src/main/kotlin/g3501_3600/s3539_find_sum_of_array_product_of_magical_sequences/Solution.kt b/src/main/kotlin/g3501_3600/s3539_find_sum_of_array_product_of_magical_sequences/Solution.kt
index 9ec80549d..b2c990054 100644
--- a/src/main/kotlin/g3501_3600/s3539_find_sum_of_array_product_of_magical_sequences/Solution.kt
+++ b/src/main/kotlin/g3501_3600/s3539_find_sum_of_array_product_of_magical_sequences/Solution.kt
@@ -1,16 +1,20 @@
 package g3501_3600.s3539_find_sum_of_array_product_of_magical_sequences
 
 // #Hard #Array #Dynamic_Programming #Math #Bit_Manipulation #Bitmask #Combinatorics
-// #2025_05_04_Time_58_ms_(_%)_Space_49.73_MB_(_%)
+// #2025_05_06_Time_60_ms_(100.00%)_Space_48.98_MB_(100.00%)
 
 class Solution {
+    private val mod = 1000000007
+    private val c: Array<IntArray> = precomputeBinom(31)
+    private val p: IntArray = precomputePop(31)
+
     fun magicalSum(m: Int, k: Int, nums: IntArray): Int {
         val n = nums.size
         val pow = Array<LongArray>(n) { LongArray(m + 1) }
         for (j in 0..<n) {
             pow[j][0] = 1L
             for (c in 1..m) {
-                pow[j][c] = pow[j][c - 1] * nums[j] % MOD
+                pow[j][c] = pow[j][c - 1] * nums[j] % mod
             }
         }
         var dp = Array<Array<LongArray>>(m + 1) { Array<LongArray>(k + 1) { LongArray(m + 1) } }
@@ -38,12 +42,12 @@ class Solution {
                                     (
                                         next[t + cc][o + (total and 1)][total ushr 1] +
                                             dp[t][o][c] *
-                                            C[m - t][cc] %
-                                            MOD
+                                            this@Solution.c[m - t][cc] %
+                                            mod
                                             * pow[i][cc] %
-                                            MOD
+                                            mod
                                         ) %
-                                        MOD
+                                        mod
                                     )
                         }
                     }
@@ -56,37 +60,31 @@ class Solution {
         var res: Long = 0
         for (o in 0..k) {
             for (c in 0..m) {
-                if (o + P[c] == k) {
-                    res = (res + dp[m][o][c]) % MOD
+                if (o + p[c] == k) {
+                    res = (res + dp[m][o][c]) % mod
                 }
             }
         }
         return res.toInt()
     }
 
-    companion object {
-        private const val MOD = 1000000007
-        private val C: Array<IntArray> = precomputeBinom(31)
-        private val P: IntArray = precomputePop(31)
-
-        private fun precomputeBinom(max: Int): Array<IntArray> {
-            val res = Array<IntArray>(max) { IntArray(max) }
-            for (i in 0..<max) {
-                res[i][i] = 1
-                res[i][0] = res[i][i]
-                for (j in 1..<i) {
-                    res[i][j] = (res[i - 1][j - 1] + res[i - 1][j]) % MOD
-                }
+    private fun precomputeBinom(max: Int): Array<IntArray> {
+        val res = Array<IntArray>(max) { IntArray(max) }
+        for (i in 0..<max) {
+            res[i][i] = 1
+            res[i][0] = res[i][i]
+            for (j in 1..<i) {
+                res[i][j] = (res[i - 1][j - 1] + res[i - 1][j]) % mod
             }
-            return res
         }
+        return res
+    }
 
-        private fun precomputePop(max: Int): IntArray {
-            val res = IntArray(max)
-            for (i in 1..<max) {
-                res[i] = res[i shr 1] + (i and 1)
-            }
-            return res
+    private fun precomputePop(max: Int): IntArray {
+        val res = IntArray(max)
+        for (i in 1..<max) {
+            res[i] = res[i shr 1] + (i and 1)
         }
+        return res
     }
 }

From 94e4a9919b32c6437ef34879e9ecba57b06dc904 Mon Sep 17 00:00:00 2001
From: Valentyn Kolesnikov <javadev75@gmail.com>
Date: Tue, 6 May 2025 09:03:09 +0300
Subject: [PATCH 5/5] Improved task

---
 .../Solution.kt                               | 52 ++++++++++---------
 1 file changed, 27 insertions(+), 25 deletions(-)

diff --git a/src/main/kotlin/g3501_3600/s3539_find_sum_of_array_product_of_magical_sequences/Solution.kt b/src/main/kotlin/g3501_3600/s3539_find_sum_of_array_product_of_magical_sequences/Solution.kt
index b2c990054..255af8e89 100644
--- a/src/main/kotlin/g3501_3600/s3539_find_sum_of_array_product_of_magical_sequences/Solution.kt
+++ b/src/main/kotlin/g3501_3600/s3539_find_sum_of_array_product_of_magical_sequences/Solution.kt
@@ -4,17 +4,13 @@ package g3501_3600.s3539_find_sum_of_array_product_of_magical_sequences
 // #2025_05_06_Time_60_ms_(100.00%)_Space_48.98_MB_(100.00%)
 
 class Solution {
-    private val mod = 1000000007
-    private val c: Array<IntArray> = precomputeBinom(31)
-    private val p: IntArray = precomputePop(31)
-
     fun magicalSum(m: Int, k: Int, nums: IntArray): Int {
         val n = nums.size
         val pow = Array<LongArray>(n) { LongArray(m + 1) }
         for (j in 0..<n) {
             pow[j][0] = 1L
             for (c in 1..m) {
-                pow[j][c] = pow[j][c - 1] * nums[j] % mod
+                pow[j][c] = pow[j][c - 1] * nums[j] % MOD
             }
         }
         var dp = Array<Array<LongArray>>(m + 1) { Array<LongArray>(k + 1) { LongArray(m + 1) } }
@@ -42,12 +38,12 @@ class Solution {
                                     (
                                         next[t + cc][o + (total and 1)][total ushr 1] +
                                             dp[t][o][c] *
-                                            this@Solution.c[m - t][cc] %
-                                            mod
+                                            C[m - t][cc] %
+                                            MOD
                                             * pow[i][cc] %
-                                            mod
+                                            MOD
                                         ) %
-                                        mod
+                                        MOD
                                     )
                         }
                     }
@@ -60,31 +56,37 @@ class Solution {
         var res: Long = 0
         for (o in 0..k) {
             for (c in 0..m) {
-                if (o + p[c] == k) {
-                    res = (res + dp[m][o][c]) % mod
+                if (o + P[c] == k) {
+                    res = (res + dp[m][o][c]) % MOD
                 }
             }
         }
         return res.toInt()
     }
 
-    private fun precomputeBinom(max: Int): Array<IntArray> {
-        val res = Array<IntArray>(max) { IntArray(max) }
-        for (i in 0..<max) {
-            res[i][i] = 1
-            res[i][0] = res[i][i]
-            for (j in 1..<i) {
-                res[i][j] = (res[i - 1][j - 1] + res[i - 1][j]) % mod
+    companion object {
+        private const val MOD = 1000000007
+        private val C: Array<IntArray> = precomputeBinom(31)
+        private val P: IntArray = precomputePop(31)
+
+        private fun precomputeBinom(max: Int): Array<IntArray> {
+            val res = Array<IntArray>(max) { IntArray(max) }
+            for (i in 0..<max) {
+                res[i][i] = 1
+                res[i][0] = res[i][i]
+                for (j in 1..<i) {
+                    res[i][j] = (res[i - 1][j - 1] + res[i - 1][j]) % MOD
+                }
             }
+            return res
         }
-        return res
-    }
 
-    private fun precomputePop(max: Int): IntArray {
-        val res = IntArray(max)
-        for (i in 1..<max) {
-            res[i] = res[i shr 1] + (i and 1)
+        private fun precomputePop(max: Int): IntArray {
+            val res = IntArray(max)
+            for (i in 1..<max) {
+                res[i] = res[i shr 1] + (i and 1)
+            }
+            return res
         }
-        return res
     }
 }