Merge pull request soapyigu#195 from soapyigu/DP

[DP] Add a solution to DP

Author: soapyigu

DP/FrogJump.swift

@@ -0,0 +1,47 @@
+/**
+ * Question Link: https://leetcode.com/problems/frog-jump/
+ * Primary idea: Dynamic Programming, a dictionary to keep all steps that the position 
+ *               can jump, and a dp array to keep max step that the position can take
+ * Time Complexity: O(n^2), Space Complexity: O(1)
+ *
+ */
+
+class FrogJump {
+    func canCross(_ stones: [Int]) -> Bool {
+        guard stones.count > 1 else {
+            return true
+        }
+    
+        var indexSteps = [Int: Set<Int>](), maxStep = Array(repeating: 0, count: stones.count)
+        var k = 0
+        
+        insert(&indexSteps, 0, 0)
+        
+        for i in 1 ..< stones.count {
+            while maxStep[k] + 1 < stones[i] - stones[k] {
+                k += 1
+            }
+            for j in k ..< i {
+                let distance = stones[i] - stones[j]
+                
+                if let steps = indexSteps[j], steps.contains(distance - 1) || steps.contains(distance) || steps.contains(distance + 1) {
+                
+                    insert(&indexSteps, distance, i)
+                    maxStep[i] = max(maxStep[i], distance)
+                }
+            }
+        }
+        
+        return maxStep.last! > 0
+    }
+    
+    private func insert(_ dict: inout [Int: Set<Int>], _ num: Int, _ index: Int) {
+        if dict[index] != nil {
+            dict[index]!.insert(num)
+        } else {
+            var set = Set<Int>()
+            set.insert(num)
+            dict[index] = set
+        }
+    }
+}