Reference: LeetCode

Difficulty: Easy

My Post: Java Solutions Recurrence, DP Bottom-up (easy-understand with comments)

## Problem

On a staircase, the i-th step has some non-negative cost

`cost[i]`

assigned (0 indexed).

Once you pay the cost, you can either climb one or two steps. You need to find minimum cost to reach the top of the floor, and you can either start from the step with index 0, or the step with index 1.

**Note:**

`cost`

will have a length in the range`[2, 1000]`

.- Every
`cost[i]`

will be an integer in the range`[0, 999]`

.

**Example:**

1 | // notice the top is at stair n (not the last element) |

## Analysis

### Recursion

Check out the comment.

1 | // the top stair is at position n, not the last element at (n - 1) |

**Time:** $O(2^N)$**Space:** $O(N)$

### DP (bottom-up)

1 | public int minCostClimbingStairs(int[] cost) { |

**Time:** $O(N)$**Space:** $O(N)$

Optimized Space Complexity:

**Note:** `f1`

is corresponding with `cost[i - 2]`

!

1 | public int minCostClimbingStairs(int[] cost) { |

**Time:** $O(N)$**Space:** $O(1)$