Create Maximum Number in C++

Suppose we have two arrays of length m and n with digits 0-9 representing two numbers. We have to create the maximum number of length k that is less than m + n from digits of the two. We have to keep in mind that the relative order of the digits from the same array must be preserved. We have to find the array of the k digits. So if the inputs are like [3,4,7,5] and [9,1,3,5,8,4], and k = 5, then the answer will be [9,8,7,5,4].

To solve this, we will follow these steps −

  • Define a function mergeThem(), this will take an array nums1, an array nums2,
  • Define an array ret
  • i := 0, j := 0, n := size of nums1, m := size of nums2
  • while (i < n or j < m), do −
    • if call the function greater(nums1, nums2, i, j) is true, then −
      • insert nums1[i] at the end of ret
      • (increase i by 1)
    • Otherwise
      • insert nums2[j] at the end of ret
      • (increase j by 1)
  • return ret
  • Define a function modify(), this will take an array v, k,
  • Define one stack st
  • Define an array ret
  • for initialize i := 0, when i < size of v, update (increase i by 1), do −
    • x := v[i]
    • while (st is not empty and top element of st < x and size of st + size of v – i – 1 >= k), do −
      • delete element from st
    • if size of st < k, then −
      • insert x into st
  • while (st is not empty), do −
    • insert top element of st at the end of ret
    • delete element from st
  • reverse the array ret
  • return ret
  • Define a function greater(), this will take an array a, an array b, i, j,
  • while (i < size of a and j < size of b and a[i] is same as b[j]), do −
    • increase i by 1 and increase j by 1
  • return true when j == size of b or i < size of a and a[i] > b[j]
  • From the main method do the following:
  • Define an array ret
  • n := size of nums1
  • m := size of nums2
  • for initialize i := 0, when i <= k, update (increase i by 1), do −
    • if i <= n and (k - i) <= m, then −
      • Define an array candidate = mergeThem(modify(nums1, i), modify(nums2, k - i))
      • if greater(candidate, ret, 0, 0) is true, then −
      • ret := candidate
  • return ret

Let us see the following implementation to get better understanding −

Example

 Live Demo

#include <bits/stdc++.h>
using namespace std;
void print_vector(vector<auto> v){
   cout << "[";
   for(int i = 0; i<v.size(); i++){
      cout << v[i] << ", ";
   }
   cout << "]"<<endl;
}
class Solution {
public:
   vector<int> mergeThem(vector<int> nums1, vector<int> nums2)
   {
      vector<int> ret;
      int i = 0;
      int j = 0;
      int n = nums1.size();
      int m = nums2.size();
      while (i < n || j < m) {
         if (greater(nums1, nums2, i, j)) {
            ret.push_back(nums1[i]);
            i++;
         }
         else {
            ret.push_back(nums2[j]);
            j++;
         }
      }
      return ret;
   }
   vector<int> modify(vector<int>& v, int k)
   {
      stack<int> st;
      vector<int> ret;
      for (int i = 0; i < v.size(); i++) {
         int x = v[i];
         while (!st.empty() && st.top() < x && st.size() + (v.size() - i) - 1 >= k) {
            st.pop();
         }
         if (st.size() < k)
            st.push(x);
         }
         while (!st.empty()) {
            ret.push_back(st.top());
            st.pop();
         }
         reverse(ret.begin(), ret.end());
         return ret;
      }
      bool greater(vector<int>& a, vector<int>& b, int i, int j)
      {
         while (i < a.size() && j < b.size() && a[i] == b[j])
         i++, j++;
         return j == b.size() || (i < a.size() && a[i] > b[j]);
      }
      vector<int> maxNumber(vector<int>& nums1, vector<int>& nums2, int k)
      {
         vector<int> ret;
         int n = nums1.size();
         int m = nums2.size();
         for (int i = 0; i <= k; i++) {
            if (i <= n && (k - i) <= m) {
               vector<int> candidate = mergeThem(modify(nums1, i), modify(nums2, k - i));
               if (greater(candidate, ret, 0, 0)) {
                  ret = candidate;
               }
            }
         }
         return ret;
     }
};
main() {
   Solution ob;
   vector<int> v = { 3, 4, 7, 5 }, v1 = { 9, 1, 3, 5, 8, 4 };
   print_vector(ob.maxNumber(v, v1, 5));
}

Input

{ 3, 4, 7, 5 }
{ 9, 1, 3, 5, 8, 4 }
5

Output

[9, 8, 7, 5, 4, ]

Updated on: 01-Jun-2020

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