Given a non-negative integer numRows, generate the first numRows of Pascal’s triangle.

n Pascal’s triangle, each number is the sum of the two numbers directly above it.

Example:

Input: 5
Output:
[
     [1],
    [1,1],
   [1,2,1],
  [1,3,3,1],
 [1,4,6,4,1]
]

Solution analysis:

In each row, the first and last element are 1. And the other element is the sum of the two elements in the previous row. e.g.

   1 3 3 1   Previous row
1 1+3 3+3 3+1 1   Next row

   1 4 6 4 1 Previous row
1 1+4 4+6 6+4 4+1 1 Next row

Hence this problem can be solved directly as shown in the code below:

Solution in C++

/*
* File     : pascals_triangle.cpp
*/
    

#include<iostream>
#include<string>
#include<vector>

using namespace std;


vector<vector<int>> generate(int numRows) 
{
  vector<vector<int>> result;
  for(auto i=0;i<numRows;++i)
  {
      result.push_back(vector<int>(i+1,1));
    for(auto j=1; j<i; ++j) 
    {
      result[i][j] = result[i-1][j-1] + result[i-1][j];
    }
    }
    return result;
}

int main()
{
  int numRows = 4;

  vector<vector<int> > result = generate (numRows);

  for (int i = 0; i < result.size(); i++)
    {
      for (int j = 0; j < result[i].size(); j++)
      {
        cout<< result[i][j]<<" ";
      }
      cout<<endl;
    }
}