[DP] Add solutions to Minimum Window Subsequence and Maximum Sum of 3 Non-Overlapping Subarrays

Author: soapyigu

DP/MaximumSumThreeNonOverlappingSubarrays.swift

@@ -0,0 +1,71 @@
+/**
+ * Question Link: https://leetcode.com/problems/maximum-sum-of-3-non-overlapping-subarrays/
+ * Primary idea: Dynamic Programming, find point where sum of [0, i - 1], [i, i + k - 1], [i + k, count - 1] is largest, where k <= i <= count - 2k
+ * Time Complexity: O(n), Space Complexity: O(n)
+ *
+ */
+
+class MaximumSumThreeNonOverlappingSubarrays {
+    func maxSumOfThreeSubarrays(_ nums: [Int], _ k: Int) -> [Int] {
+        let sums = createSums(nums), n = nums.count
+        let leftIndices = createLeftIndices(sums, n, k), rightIndices = createRightIndices(sums, n, k)
+        var total = 0, res = [-1, -1, -1]
+        
+        for i in k...n - 2 * k {
+            let l = leftIndices[i - 1], r = rightIndices[i + k]
+            let currentTotal = (sums[i+k] - sums[i]) + (sums[l + k] - sums[l]) + (sums[r + k] - sums[r]) 
+            
+            if currentTotal > total {
+                total = currentTotal
+                res = [l, i, r]
+            }
+        }
+       
+        return res
+    }
+    
+    fileprivate func createSums(_ nums: [Int]) -> [Int] {
+        var sums = [0], currentSum = 0
+        
+        for num in nums {
+            currentSum += num
+            
+            sums.append(currentSum)
+        }
+        
+        return sums
+    }
+    
+    // DP for starting index of left
+    fileprivate func createLeftIndices(_ sums: [Int], _ n: Int, _ k: Int) -> [Int] {
+        var leftIndices = Array(repeating: 0, count: n), maxSum = sums[k] - sums[0]
+        
+        for i in k..<n {
+            if sums[i + 1] - sums[i + 1 - k] > maxSum {
+                leftIndices[i] = i + 1 - k
+                maxSum = sums[i + 1] - sums[i + 1 - k]
+            } else {
+                leftIndices[i] = leftIndices[i - 1]
+            }
+        }
+        
+        return leftIndices
+    }
+    
+    // DP for starting index of right
+    fileprivate func createRightIndices(_ sums: [Int], _ n: Int, _ k: Int) -> [Int] {
+        var rightIndices = Array(repeating: 0, count: n), maxSum = sums[n] - sums[n - k]
+        rightIndices[n - k] = n - k
+        
+        for i in (0...n - k - 1).reversed() {
+            if sums[i + k] - sums[i] >= maxSum {
+                rightIndices[i] = i
+                maxSum = sums[i + k] - sums[i]
+            } else {
+                rightIndices[i] = rightIndices[i + 1]
+            }
+        }
+        
+        return rightIndices
+    }
+}

DP/MinimumWindowSubsequence.swift

@@ -0,0 +1,39 @@
+/**
+ * Question Link: https://leetcode.com/problems/minimum-window-subsequence/
+ * Primary idea: Dynamic Programming, dp[i][j] = dp[i][j - 1] || dp[i - 1][j - 1]
+ * Time Complexity: O(mn), Space Complexity: O(mn)
+ *
+ */
+
+ class MinimumWindowSubsequence {
+    func minWindow(_ S: String, _ T: String) -> String {
+        let m = T.count, n = S.count, sChars = Array(S), tChars = Array(T)
+        var dp = Array(repeating: Array(repeating: 0, count: n + 1), count: m + 1)
+        var start = 0, len = n + 1
+        
+        for i in 0...n {
+            dp[0][i] = i + 1
+        }
+        
+        for i in 1...m {
+            for j in 1...n {
+                if tChars[i - 1] == sChars[j - 1] {
+                    dp[i][j] = dp[i - 1][j - 1]
+                } else {
+                    dp[i][j] = dp[i][j - 1]
+                }
+            }
+        }
+        
+        for i in 1...n {
+            if dp[m][i] != 0 {
+                if i - dp[m][i] + 1 < len {
+                    len = i - dp[m][i] + 1
+                    start = dp[m][i] - 1
+                }
+            }
+        }
+        
+        return len == n + 1 ? "" : String(sChars[start..<start + len])
+    }
+}

README.md

@@ -28,7 +28,7 @@
 * [Microsoft](#microsoft)
 
 ## Progress
-[Problem Status](#problem-status) shows the latest progress to all 800+ questions. Currently we have 238 completed solutions. Note: questions with ♥ mark means that you have to **Subscript to premium membership** of LeetCode to unlock them. Thank you for great contributions from [CharleneJiang](https://github.com/CharleneJiang), [ReadmeCritic](https://github.com/ReadmeCritic), [demonkoo](https://github.com/demonkoo), [DaiYue](https://github.com/DaiYue), [Quaggie](https://github.com/Quaggie) and [jindulys](https://github.com/jindulys).
+[Problem Status](#problem-status) shows the latest progress to all 800+ questions. Currently we have 240 completed solutions. Note: questions with ♥ mark means that you have to **Subscript to premium membership** of LeetCode to unlock them. Thank you for great contributions from [CharleneJiang](https://github.com/CharleneJiang), [ReadmeCritic](https://github.com/ReadmeCritic), [demonkoo](https://github.com/demonkoo), [DaiYue](https://github.com/DaiYue), [Quaggie](https://github.com/Quaggie) and [jindulys](https://github.com/jindulys).
 
 
 ## Array
@@ -183,6 +183,7 @@
 [Best Time to Buy and Sell Stock III](https://leetcode.com/problems/best-time-to-buy-and-sell-stock-iii/)| [Swift](./DP/BestTimeBuySellStockIII.swift)| Hard| O(n)| O(n)|
 [Best Time to Buy and Sell Stock IV](https://leetcode.com/problems/https://leetcode.com/problems/best-time-to-buy-and-sell-stock-iv/)| [Swift](./DP/BestTimeBuySellStockIV.swift)| Hard| O(n^2)| O(n)|
 [Best Time to Buy and Sell Stock with Cooldown](https://leetcode.com/problems/best-time-to-buy-and-sell-stock-with-cooldown/)| [Swift](./DP/BestTimeBuySellStockCooldown.swift)| Medium| O(n^2)| O(n)|
+[Maximum Sum of 3 Non-Overlapping Subarrays](https://leetcode.com/problems/maximum-sum-of-3-non-overlapping-subarrays/)| [Swift](./DP/MaximumSumThreeNonOverlappingSubarrays.swift| O(n)| O(n)|
 [Coin Change](https://leetcode.com/problems/coin-change/)| [Swift](./DP/CoinChange.swift)| Medium| O(n^2)| O(n)|
 [Coin Change II](https://leetcode.com/problems/coin-change-ii/)| [Swift](./DP/CoinChangeII.swift)| Medium| O(n^2)| O(n)|
 [Longest Increasing Subsequence](https://leetcode.com/problems/longest-increasing-subsequence/)| [Swift](./DP/LongestIncreasingSubsequence.swift)| Medium| O(n^2)| O(n)|
@@ -199,6 +200,7 @@
 [Triangle](https://leetcode.com/problems/triangle/)| [Swift](./DP/Triangle.swift)| Medium| O(2^n - 1)| O(m)|
 [Wildcard Matching](https://leetcode.com/problems/wildcard-matching/)| [Swift](./DP/WildcardMatching.swift)| Hard| O(mn)| O(mn)|
 [Regular Expression Matching](https://leetcode.com/problems/regular-expression-matching/)| [Swift](./DP/RegularExpressionMatching.swift)| Hard| O(mn)| O(mn)|
+[Minimum Window Subsequence](https://leetcode.com/problems/minimum-window-subsequence/)| [Swift](./DP/MinimumWindowSubsequence.swift)| Hard| O(mn)| O(mn)|
 [Guess Number Higher or Lower II](https://leetcode.com/problems/guess-number-higher-or-lower-ii/)| [Swift](./DP/GuessNumberHigherOrLowerII.swift)| Medium| O(nlogn)| O(n^2)|
 [Burst Ballons](https://leetcode.com/problems/burst-balloons/)| [Swift](./DP/BurstBalloons.swift)| Hard| O(n^3)| O(n)|
 [Frog Jump](https://leetcode.com/problems/frog-jump/)| [Swift](./DP/FrogJump.swift)| Hard| O(n^2)| O(n)|