class Solution {
    /**
    there are only two ways to arrive at step i: 
    From step i-1
    From step i-2

    Path 1: From i-1
        Cost to reach i-1 is prev1.
        you step on i, so you must pay cost[i].
        total cost: prev1 + cost[i]
    
    Path 2: From i-2
        Cost to reach i-2 is prev2.
        you step on i, so you must pay cost[i].
        total cost: prev2 + cost[i]

    best way to reach this ith step = cost of this ith step + the cheapest way to reach the previous reachable step.
    currentCost = cost[i] + Math.min(prev1, prev2)
    And update both prev1 and prev2 accordingly
    */
    public int minCostClimbingStairs(int[] cost) {
        int prev1 = cost[1];
        int prev2 = cost[0];

        for(int i=2; i<cost.length; i++)
        {
            int currentCost = cost[i] + Math.min(prev1, prev2);
            prev2 = prev1;
            prev1 = currentCost;
        }

        return Math.min(prev1, prev2);
    }
}