LeetCode_70. Climbing Stairs

70. Climbing Stairs

Easy

You are climbing a stair case. It takes n steps to reach to the top.

Each time you can either climb 1 or 2 steps. In how many distinct ways can you climb to the top?

Note: Given n will be a positive integer.

Example 1:

Input: 2
Output: 2
Explanation: There are two ways to climb to the top.
1. 1 step + 1 step
2. 2 steps

Example 2:

Input: 3
Output: 3
Explanation: There are three ways to climb to the top.
1. 1 step + 1 step + 1 step
2. 1 step + 2 steps
3. 2 steps + 1 step

package leetcode.easy;

public class ClimbingStairs {
	@org.junit.Test
	public void test() {
		int n1 = 2;
		int n2 = 3;
		System.out.println(climbStairs1(n1));
		System.out.println(climbStairs1(n2));
		System.out.println(climbStairs2(n1));
		System.out.println(climbStairs2(n2));
		System.out.println(climbStairs3(n1));
		System.out.println(climbStairs3(n2));
		System.out.println(climbStairs4(n1));
		System.out.println(climbStairs4(n2));
		System.out.println(climbStairs5(n1));
		System.out.println(climbStairs5(n2));
		System.out.println(climbStairs6(n1));
		System.out.println(climbStairs6(n2));
	}

	public int climbStairs1(int n) {
		return climb_Stairs(0, n);
	}

	public int climb_Stairs(int i, int n) {
		if (i > n) {
			return 0;
		}
		if (i == n) {
			return 1;
		}
		return climb_Stairs(i + 1, n) + climb_Stairs(i + 2, n);
	}

	public int climbStairs2(int n) {
		int[] memo = new int[n + 1];
		return climb_Stairs(0, n, memo);
	}

	public int climb_Stairs(int i, int n, int memo[]) {
		if (i > n) {
			return 0;
		}
		if (i == n) {
			return 1;
		}
		if (memo[i] > 0) {
			return memo[i];
		}
		memo[i] = climb_Stairs(i + 1, n, memo) + climb_Stairs(i + 2, n, memo);
		return memo[i];
	}

	public int climbStairs3(int n) {
		if (n == 1) {
			return 1;
		}
		int[] dp = new int[n + 1];
		dp[1] = 1;
		dp[2] = 2;
		for (int i = 3; i <= n; i++) {
			dp[i] = dp[i - 1] + dp[i - 2];
		}
		return dp[n];
	}

	public int climbStairs4(int n) {
		if (n == 1) {
			return 1;
		}
		int first = 1;
		int second = 2;
		for (int i = 3; i <= n; i++) {
			int third = first + second;
			first = second;
			second = third;
		}
		return second;
	}

	public int climbStairs5(int n) {
		int[][] q = { { 1, 1 }, { 1, 0 } };
		int[][] res = pow(q, n);
		return res[0][0];
	}

	public int[][] pow(int[][] a, int n) {
		int[][] ret = { { 1, 0 }, { 0, 1 } };
		while (n > 0) {
			if ((n & 1) == 1) {
				ret = multiply(ret, a);
			}
			n >>= 1;
			a = multiply(a, a);
		}
		return ret;
	}

	public int[][] multiply(int[][] a, int[][] b) {
		int[][] c = new int[2][2];
		for (int i = 0; i < 2; i++) {
			for (int j = 0; j < 2; j++) {
				c[i][j] = a[i][0] * b[0][j] + a[i][1] * b[1][j];
			}
		}
		return c;
	}

	public int climbStairs6(int n) {
		double sqrt5 = Math.sqrt(5);
		double fibn = Math.pow((1 + sqrt5) / 2, n + 1) - Math.pow((1 - sqrt5) / 2, n + 1);
		return (int) (fibn / sqrt5);
	}
}