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70. Climbing Stairs 👍

Approach 1: 2D DP

  • Time: $O(n)$
  • Space: $O(n)$
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class Solution {
 public:
  int climbStairs(int n) {
    // dp[i] := the number of ways to climb to the i-th stair
    vector<int> dp(n + 1);
    dp[0] = 1;
    dp[1] = 1;

    for (int i = 2; i <= n; ++i)
      dp[i] = dp[i - 1] + dp[i - 2];

    return dp[n];
  }
};

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class Solution {
  public int climbStairs(int n) {
    // dp[i] := the number of ways to climb to the i-th stair
    int[] dp = new int[n + 1];
    dp[0] = 1;
    dp[1] = 1;

    for (int i = 2; i <= n; ++i)
      dp[i] = dp[i - 1] + dp[i - 2];

    return dp[n];
  }
}

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class Solution:
  def climbStairs(self, n: int) -> int:
    # dp[i] := the number of ways to climb to the i-th stair
    dp = [1, 1] + [0] * (n - 1)

    for i in range(2, n + 1):
      dp[i] = dp[i - 1] + dp[i - 2]

    return dp[n]

Approach 2: 1D DP

  • Time: $O(n)$
  • Space: $O(1)$
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class Solution {
 public:
  int climbStairs(int n) {
    int prev1 = 1;  // dp[i - 1]
    int prev2 = 1;  // dp[i - 2]

    for (int i = 2; i <= n; ++i) {
      const int dp = prev1 + prev2;
      prev2 = prev1;
      prev1 = dp;
    }

    return prev1;
  }
};

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class Solution {
  public int climbStairs(int n) {
    int prev1 = 1; // dp[i - 1]
    int prev2 = 1; // dp[i - 2]

    for (int i = 2; i <= n; ++i) {
      final int dp = prev1 + prev2;
      prev2 = prev1;
      prev1 = dp;
    }

    return prev1;
  }
}

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class Solution:
  def climbStairs(self, n: int) -> int:
    prev1 = 1  # dp[i - 1]
    prev2 = 1  # dp[i - 2]

    for _ in range(2, n + 1):
      dp = prev1 + prev2
      prev2 = prev1
      prev1 = dp

    return prev1