Create 15_largestDIvisibleSubset.cpp

11 November Leetcode Challenge 2021/15_largestDIvisibleSubset.cpp

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+class Solution {
+public:
+    vector<int> largestDivisibleSubset(vector<int>& nums) {
+        sort(begin(nums), end(nums));
+        int n = size(nums), max_i = 0;
+		// initially dp[i]=1 since we can always form subset of size=1 ending at i. 
+		// pred[i]=-1 because we havent found any predecessors for any subset yet
+        vector<int> dp(n, 1), pred(n, -1), ans;
+        for(int i = 1; i < n; i++) {          
+            for(int j = 0; j < i; j++)     
+				// nums[i] should divide nums[j] if it is to be included in its subset (i.e dp[j])
+				// only include nums[i] in subset ending at j if resultant subset size (dp[j]+1) is larger than already possible (dp[i])
+                if(nums[i] % nums[j] == 0 && dp[i] < dp[j]+1)
+                    dp[i] = dp[j]+1, pred[i] = j;  // jth element will be predecessor to subset ending at ith element
+            if(dp[i] > dp[max_i]) max_i = i;       // keep track of index where largest subset ends
+        }
+		// start with index where largest subset ended. Reconstruct from that point to the start
+        for(; max_i >= 0; max_i = pred[max_i]) 
+            ans.push_back(nums[max_i]);
+        return ans;
+    }
+};