From c00ec984ce19c59a9d275d9f117f7c469c1102fa Mon Sep 17 00:00:00 2001 From: Alonza0314 <dufengplus@gmail.com> Date: Wed, 14 May 2025 13:26:45 +0800 Subject: [PATCH 1/4] feat: 416 --- Medium/416 Partition Equal Subset Sum.md | 2 +- Week12/416 AC.png | Bin 0 -> 127852 bytes Week12/416 Partition Equal Subset Sum.md | 69 +++++++++++++++++++++++ 3 files changed, 70 insertions(+), 1 deletion(-) create mode 100644 Week12/416 AC.png create mode 100644 Week12/416 Partition Equal Subset Sum.md diff --git a/Medium/416 Partition Equal Subset Sum.md b/Medium/416 Partition Equal Subset Sum.md index 1c011fb..58b5fed 100644 --- a/Medium/416 Partition Equal Subset Sum.md +++ b/Medium/416 Partition Equal Subset Sum.md @@ -66,4 +66,4 @@ func canPartition(nums []int) bool { } return dp[sum] } -``` \ No newline at end of file +``` diff --git a/Week12/416 AC.png b/Week12/416 AC.png new file mode 100644 index 0000000000000000000000000000000000000000..a661b48cd76521377f96c4c921510be52cc2870a GIT binary patch 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zW2pj+fKauYnfgKs-ICtq0vm7CD`P}(@{XO0>sqMsA{U+gYbpxFDr3f&oa;hIOmA>0 zp<J)5xwzs7y}K)af_xQa>(tlB(dHLi>RUa|<OPD#Vs8&RsC*L|&Kzq8jVk{&O(hPn zc6tnF|CMC{H0H?5o0WGx_+j{nuEFCBDn~9%j!{1;4S3E-gao8iy8`+z+%pjxDj?qN z=c+a9PD+=@jpU6t{|wFkF9I8l>0;}mG6vY$p4B&sGbIC4Q8Ay<JH?fv2odkgD8M@A zyZ?r)MS*jFso0iID8^NPPyg0;d**z~8_o%tTx?GwIki0waCqd>m0B6TZ~Sw!C;@*b z>97vNfF+HJdn-=>c0u_XB-pDN08&-tl2gGqt+!49NvyW!xLQDtAinHx&}Y8KWI*g% zP~Y~<)n1LyF9XsdaBkyrGWbv;<q_1ogQw5DPH)9b=@a@VASK}U3Pi}S7!Kk>n#NwC zGtU8^@E+fdJiIb=8A{92{dqNzU{aH;^byqEnU|r*^lrK#DA4j&hTPA~!E%|CSCXsl z82u#>_T2%evjEIo5P8G$pO^ff;s4VnfBu*Mo7yDu8%vH?Ev?2jA&ddIj4qq$zd|}b F_#eV32JZj> literal 0 HcmV?d00001 diff --git a/Week12/416 Partition Equal Subset Sum.md b/Week12/416 Partition Equal Subset Sum.md new file mode 100644 index 0000000..58b5fed --- /dev/null +++ b/Week12/416 Partition Equal Subset Sum.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] +} +``` From f0af139c5190fca5699a82e01cba675753820612 Mon Sep 17 00:00:00 2001 From: Alonza0314 <dufengplus@gmail.com> Date: Wed, 14 May 2025 13:32:05 +0800 Subject: [PATCH 2/4] feat: basic setup --- Hard/312 Burst Balloons.md | 18 ++++++++++++++++++ Hard/887 Super Egg Drop.md | 18 ++++++++++++++++++ README.md | 2 ++ 3 files changed, 38 insertions(+) create mode 100644 Hard/312 Burst Balloons.md create mode 100644 Hard/887 Super Egg Drop.md diff --git a/Hard/312 Burst Balloons.md b/Hard/312 Burst Balloons.md new file mode 100644 index 0000000..58c9743 --- /dev/null +++ b/Hard/312 Burst Balloons.md @@ -0,0 +1,18 @@ +# 312. Burst Balloons + +## Intuition + +## Approach + +## Complexity + +- Time complexity: +- Space complexity: + +## Keywords + +## Code + +```go + +``` diff --git a/Hard/887 Super Egg Drop.md b/Hard/887 Super Egg Drop.md new file mode 100644 index 0000000..b93ffc6 --- /dev/null +++ b/Hard/887 Super Egg Drop.md @@ -0,0 +1,18 @@ +# 887. Super Egg Drop + +## Intuition + +## Approach + +## Complexity + +- Time complexity: +- Space complexity: + +## Keywords + +## Code + +```go + +``` diff --git a/README.md b/README.md index 7a65001..e28e619 100644 --- a/README.md +++ b/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 | From d039f664552611dfbc908edae470c0fe250a8bca Mon Sep 17 00:00:00 2001 From: Alonza0314 <dufengplus@gmail.com> Date: Wed, 14 May 2025 13:49:06 +0800 Subject: [PATCH 3/4] feat: 887 --- Hard/887 Super Egg Drop.md | 34 +++++++++++++++++++++++--- Week12/887 AC.png | Bin 0 -> 125889 bytes Week12/887 Super Egg Drop.md | 46 +++++++++++++++++++++++++++++++++++ 3 files changed, 77 insertions(+), 3 deletions(-) create mode 100644 Week12/887 AC.png create mode 100644 Week12/887 Super Egg Drop.md diff --git a/Hard/887 Super Egg Drop.md b/Hard/887 Super Egg Drop.md index b93ffc6..0c95249 100644 --- a/Hard/887 Super Egg Drop.md +++ b/Hard/887 Super Egg Drop.md @@ -2,17 +2,45 @@ ## 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: -- Space 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 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z^I7)WW&F)t8w(kA9*Aa{JksGZy={V9SGPdIzi_t)%DaxOsM)4_dz#V_z2D1h_v1=V z3XO`K8b|m%Zx?&wDyyO=H8{PQ=2Mm*g{#bz0I8U;#dbO_TQ;ZyEy+8X@_iYuj5+EI gl>9(Mq#XFqtUs%=qLnY{9s>|~y85}Sb4q9e079@T8vp<R literal 0 HcmV?d00001 diff --git a/Week12/887 Super Egg Drop.md b/Week12/887 Super Egg Drop.md new file mode 100644 index 0000000..0c95249 --- /dev/null +++ b/Week12/887 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 +} +``` From 4d719386b3519e0f7039594528f06836fd934b4b Mon Sep 17 00:00:00 2001 From: Alonza0314 <dufengplus@gmail.com> Date: Wed, 14 May 2025 15:00:32 +0800 Subject: [PATCH 4/4] feat: 312 --- Hard/312 Burst Balloons.md | 37 +++++++++++++++++++++++--- Week12/312 AC.png | Bin 0 -> 125143 bytes Week12/312 Burst Balloons.md | 49 +++++++++++++++++++++++++++++++++++ 3 files changed, 83 insertions(+), 3 deletions(-) create mode 100644 Week12/312 AC.png create mode 100644 Week12/312 Burst Balloons.md diff --git a/Hard/312 Burst Balloons.md b/Hard/312 Burst Balloons.md index 58c9743..45474c8 100644 --- a/Hard/312 Burst Balloons.md +++ b/Hard/312 Burst Balloons.md @@ -2,17 +2,48 @@ ## 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: -- Space 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] +} ``` diff --git a/Week12/312 AC.png b/Week12/312 AC.png new file mode 100644 index 0000000000000000000000000000000000000000..010c0ae4b6d971a17ff82a143ea9f6a253953660 GIT binary patch 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z$Y@n$<)8Zgm&f3AK)zl#*zWZGFMs_9kXeKOrwJ7~$iY<>JUqN=)w}X1>7OTY`u`uh btRLStCK?)9zV8bR0Z&y?^KPkv)sz1Pjg{2u literal 0 HcmV?d00001 diff --git a/Week12/312 Burst Balloons.md b/Week12/312 Burst Balloons.md new file mode 100644 index 0000000..45474c8 --- /dev/null +++ b/Week12/312 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] +} +```