1. class Solution {
  2.     /**
  3.     there are only two ways to arrive at step i: 
  4.     From step i-1
  5.     From step i-2
  6.  
  7.     Path 1: From i-1
  8.         Cost to reach i-1 is prev1.
  9.         you step on i, so you must pay cost[i].
  10.         total cost: prev1 + cost[i]
  11.     
  12.     Path 2: From i-2
  13.         Cost to reach i-2 is prev2.
  14.         you step on i, so you must pay cost[i].
  15.         total cost: prev2 + cost[i]
  16.  
  17.     best way to reach this ith step = cost of this ith step + the cheapest way to reach the previous reachable step.
  18.     currentCost = cost[i] + Math.min(prev1, prev2)
  19.     And update both prev1 and prev2 accordingly
  20.     */
  21.     public int minCostClimbingStairs(int[] cost) {
  22.         int prev1 = cost[1];
  23.         int prev2 = cost[0];
  24.  
  25.         for(int i=2; i<cost.length; i++)
  26.         {
  27.             int currentCost = cost[i] + Math.min(prev1, prev2);
  28.             prev2 = prev1;
  29.             prev1 = currentCost;
  30.         }
  31.  
  32.         return Math.min(prev1, prev2);
  33.     }
  34. }