Merge pull request #14 from Alonza0314/2025/05/09

2025/05/09

Author: Alonza0314

Hard/312 Burst Balloons.md

@@ -0,0 +1,49 @@
+# 312. Burst Balloons
+
+## Intuition
+
+The key insight is to think about the problem in reverse: instead of bursting balloons one by one, we can think about adding balloons back one by one. For each step, we consider which balloon to add last.
+
+## Approach
+
+1. Add two dummy balloons with value 1 at the beginning and end of the array.
+2. Define `dp[left][right]` as the maximum coins that can be collected by bursting all balloons between indices left and right (exclusive).
+3. For each subproblem of length, we try each balloon (at position tmp) as the last one to burst.
+4. The recurrence relation is:
+   `dp[left][right] = max(dp[left][right], dp[left][tmp] + dp[tmp][right] + nums[left] * nums[tmp] * nums[right])`
+5. The final answer is `dp[0][n+1]`, representing the maximum coins obtained by bursting all original balloons.
+
+## Complexity
+
+- Time complexity: O(n³)
+- Space complexity: O(n²)
+
+## Keywords
+
+- Dynamic Programming
+- Interval DP
+
+## Code
+
+```go
+func maxCoins(nums []int) int {
+    nums = append([]int{1}, nums...)
+    nums = append(nums, 1)
+
+    dp := make([][]int, len(nums))
+    for i := range dp {
+        dp[i] = make([]int, len(nums))
+    }
+
+    for length := 2; length < len(nums); length += 1 {
+        for left := 0; left < len(nums) - length; left += 1 {
+            right := left + length
+            for tmp := left + 1; tmp < right; tmp += 1 {
+                dp[left][right] = max(dp[left][right], dp[left][tmp] + dp[tmp][right] + nums[left] * nums[tmp] * nums[right])
+            }
+        }
+    }
+
+    return dp[0][len(nums) - 1]
+}
+```

Hard/887 Super Egg Drop.md

@@ -0,0 +1,46 @@
+# 887. Super Egg Drop
+
+## Intuition
+
+The traditional approach using dynamic programming with states (eggs, floors) leads to O(K*N²) complexity, which is too slow. Instead, we can reformulate the problem: if we have K eggs and can make M moves, what's the maximum number of floors we can cover?
+
+## Approach
+
+For each move, we have two possibilities when dropping an egg from a floor:
+
+1. The egg breaks, so we can only use K-1 eggs for floors below
+2. The egg doesn't break, so we can use K eggs for floors above
+
+We use a mathematical recursion to calculate the maximum floors we can cover with K eggs and M moves:
+
+- Let maxFloor[i] represent the maximum number of floors that can be determined with i eggs and current number of moves
+- For each move, we update maxFloor[i] = 1 + maxFloor[i-1] + maxFloor[i]
+  - maxFloor[i-1]: floors covered if egg breaks
+  - maxFloor[i]: floors covered if egg doesn't break
+  - +1: the current floor we're dropping from
+
+We keep increasing the number of moves until the maximum floor we can check is greater than or equal to N.
+
+## Complexity
+
+- Time complexity: O(K log N)
+- Space complexity: O(K)
+
+## Keywords
+
+- Dynamic Programming
+
+## Code
+
+```go
+func superEggDrop(k int, n int) int {
+    maxFloor := make([]int, k + 1)
+    m := 0
+    for ; maxFloor[k] < n; m += 1 {
+        for i := k; i > 0; i -= 1 {
+            maxFloor[i] = 1 + maxFloor[i - 1] + maxFloor[i]
+        }
+    }
+    return m
+}
+```

Medium/416 Partition Equal Subset Sum.md

@@ -66,4 +66,4 @@ func canPartition(nums []int) bool {
     }
     return dp[sum]
 }
-```
+```

README.md

@@ -28,6 +28,7 @@
 | 210 | Course Schedule II | [go](/Medium/210%20Course%20Schedule%20II.md) | M |
 | 236 | Lowest Common Ancestor of a Binary Tree | [go](/Medium/236%20Lowest%20Common%20Ancestor%20of%20a%20Binary%20Tree.md) | M |
 | 239 | Sliding Window Maximum | [go](/Hard/239%20Sliding%20Window%20Maximum.md) | H |
+| 312 | Burst Balloons | [go](/Hard/312%20Burst%20Balloons.md) | H |
 | 322 | Coin Change | [go](/Medium/322%20Coin%20Change.md) | M |
 | 416 | Partition Equal Subset Sum | [go](/Medium/416%20Partition%20Equal%20Subset%20Sum.md) | M |
 | 435 | Non-overlapping Interval | [go](/Medium/435%20Non-overlapping%20Intervals.md) | M |
@@ -44,6 +45,7 @@
 | 855 | Exam Room | [go](/Medium/855%20Exam%20Room.md) | M |
 | 875 | Koko Eating Bananas | [go](/Medium/875%20Koko%20Eating%20Bananas.md) | M |
 | 881 | Boats to Save People | [go](/Medium/881%20Boats%20to%20Save%20People.md) | M |
+| 887 | Super Egg Drop | [go](/Hard/887%20Super%20Egg%20Drop.md) | H |
 | 912 | Sort an Array | [go](/Medium/912%20Sort%20an%20Array.md) | M |
 | 948 | Bag of Tokens | [go](/Medium/948%20Bag%20Of%20Tokens.md) | M |
 | 1395 | Count Number of Trams | [go](/Medium/1395%20Count%20Number%20of%20Teams.md) | M |

Week12/312 AC.png

@@ -0,0 +1,49 @@
+# 312. Burst Balloons
+
+## Intuition
+
+The key insight is to think about the problem in reverse: instead of bursting balloons one by one, we can think about adding balloons back one by one. For each step, we consider which balloon to add last.
+
+## Approach
+
+1. Add two dummy balloons with value 1 at the beginning and end of the array.
+2. Define `dp[left][right]` as the maximum coins that can be collected by bursting all balloons between indices left and right (exclusive).
+3. For each subproblem of length, we try each balloon (at position tmp) as the last one to burst.
+4. The recurrence relation is:
+   `dp[left][right] = max(dp[left][right], dp[left][tmp] + dp[tmp][right] + nums[left] * nums[tmp] * nums[right])`
+5. The final answer is `dp[0][n+1]`, representing the maximum coins obtained by bursting all original balloons.
+
+## Complexity
+
+- Time complexity: O(n³)
+- Space complexity: O(n²)
+
+## Keywords
+
+- Dynamic Programming
+- Interval DP
+
+## Code
+
+```go
+func maxCoins(nums []int) int {
+    nums = append([]int{1}, nums...)
+    nums = append(nums, 1)
+
+    dp := make([][]int, len(nums))
+    for i := range dp {
+        dp[i] = make([]int, len(nums))
+    }
+
+    for length := 2; length < len(nums); length += 1 {
+        for left := 0; left < len(nums) - length; left += 1 {
+            right := left + length
+            for tmp := left + 1; tmp < right; tmp += 1 {
+                dp[left][right] = max(dp[left][right], dp[left][tmp] + dp[tmp][right] + nums[left] * nums[tmp] * nums[right])
+            }
+        }
+    }
+
+    return dp[0][len(nums) - 1]
+}
+```

Week12/312 Burst Balloons.md

@@ -0,0 +1,69 @@
+# 416. Partition Equal Subset Sum
+
+## Intuition
+
+The problem can be transformed into finding if we can select some numbers from the array that sum up to half of the total sum. This is essentially a 0/1 knapsack problem where we need to determine if we can fill a knapsack of capacity sum/2 using the given numbers.
+
+## Approach
+
+1. First, calculate the total sum of the array
+2. If the sum is odd, return false as equal partition is impossible
+3. Divide the sum by 2 to get our target sum
+4. Use dynamic programming to solve:
+   - Create a dp array where dp[j] represents if we can make sum j using the numbers
+   - For each number, we can either include it or not include it
+   - Use a temporary array to avoid affecting previous calculations
+   - If at any point we can make the target sum, return true
+5. As an optimization, we also:
+   - Sort the array first
+   - Use binary search to check if target sum exists directly in array
+
+## Complexity
+
+- Time complexity: O(n * sum)
+- Space complexity: O(sum)
+
+## Keywords
+
+- Dynamic Programming
+- 0/1 Knapsack
+- Binary Search
+
+## Code
+
+```go
+func canPartition(nums []int) bool {
+    sum := 0
+    for _, num := range nums {
+        sum += num
+    }
+    if sum & 1 == 1 {
+        return false
+    }
+    sum >>= 1
+    sort.Ints(nums)
+    _, flag := slices.BinarySearch(nums, sum)
+    if flag {
+        return true
+    }
+    dp := make([]bool, sum + 1)
+    dp[0] = true
+    for _, num := range nums {
+        tmp := make([]bool, sum + 1)
+        tmp[0] = true
+        for j := 1; j <= sum ; j += 1 {
+            tmp[j] = dp[j]
+            if j >= num {
+                tmp[j] = (tmp[j] || dp[j - num])
+            }
+        }
+
+        if tmp[sum] {
+            return true
+        }
+
+        copy(dp, tmp)
+    }
+    return dp[sum]
+}
+```

Week12/416 AC.png

@@ -0,0 +1,46 @@
+# 887. Super Egg Drop
+
+## Intuition
+
+The traditional approach using dynamic programming with states (eggs, floors) leads to O(K*N²) complexity, which is too slow. Instead, we can reformulate the problem: if we have K eggs and can make M moves, what's the maximum number of floors we can cover?
+
+## Approach
+
+For each move, we have two possibilities when dropping an egg from a floor:
+
+1. The egg breaks, so we can only use K-1 eggs for floors below
+2. The egg doesn't break, so we can use K eggs for floors above
+
+We use a mathematical recursion to calculate the maximum floors we can cover with K eggs and M moves:
+
+- Let maxFloor[i] represent the maximum number of floors that can be determined with i eggs and current number of moves
+- For each move, we update maxFloor[i] = 1 + maxFloor[i-1] + maxFloor[i]
+  - maxFloor[i-1]: floors covered if egg breaks
+  - maxFloor[i]: floors covered if egg doesn't break
+  - +1: the current floor we're dropping from
+
+We keep increasing the number of moves until the maximum floor we can check is greater than or equal to N.
+
+## Complexity
+
+- Time complexity: O(K log N)
+- Space complexity: O(K)
+
+## Keywords
+
+- Dynamic Programming
+
+## Code
+
+```go
+func superEggDrop(k int, n int) int {
+    maxFloor := make([]int, k + 1)
+    m := 0
+    for ; maxFloor[k] < n; m += 1 {
+        for i := k; i > 0; i -= 1 {
+            maxFloor[i] = 1 + maxFloor[i - 1] + maxFloor[i]
+        }
+    }
+    return m
+}
+```