Russian Dolls Envelopes

RussianDollsEnvelopes.cpp

@@ -0,0 +1,71 @@
+Problem statement
+You are given a set of ‘N’ rectangular envelopes. 
+The height and width of each envelope are given by arrays,
+ ‘height’ and ‘width’ respectively, each consisting of ‘N’ 
+ positive integers. The height, width of the ith envelope is 
+ given by ‘height[i]’ and ‘width[i]’ respectively.
+
+You can put one envelope inside another envelope if and only if 
+both the height and width of one envelope is strictly greater than 
+the height and width of the other envelope.
+
+What is the maximum number of envelopes you can Russian doll? 
+(put one inside other)
+Note:
+Rotation of envelope is not allowed, that is, height and width 
+can’t be exchanged
+
+//code
+
+#include<algorithm>
+#include<climits>
+
+int LIS(vector<int>& arr, int n){
+    vector<int> tail(n);
+    tail[0] = arr[0];
+    int length = 1;
+
+    for(int i = 1;i<n;i++){
+
+        int j = lower_bound(tail.begin(), tail.begin()+ length, arr[i]) - tail.begin();
+
+        if(j == length){
+            tail[length++] = arr[i];
+        }
+        else{
+            tail[j] = arr[i];
+        }
+
+    }
+
+    return length;
+
+}
+
+
+
+int findMaxEnvelopes(vector<int> &height, vector<int> &width, int n) {
+
+    vector<vector<int>> envelopes(n, vector<int> (2));
+
+    for(int i =0;i<n;i++){
+        envelopes[i][0] = height[i];
+        envelopes[i][1] = width[i];
+    }
+
+    sort(envelopes.begin(), envelopes.end(), [](vector<int>& v1, vector<int>& v2) -> bool{
+        if(v1[0] < v2[0] or (v1[0] == v2[0] and v1[1] > v2[1])){
+            return true;
+        }
+
+        return false;
+    });
+
+    vector<int> arr(n);
+    for(int i=0;i<n;i++){
+        arr[i] = envelopes[i][1];
+    }
+
+    return LIS(arr,n);
+
+}