Climbing_70.java

public class Climbing_70 {
    // Standard solution #3 (Dynamic Programming)
    // Time O(n) Space O(n)
    // If we use two pointers instead of array, we can make Space O(1)
    public int climbStairs(int n) {
        int[] dp = new int[n + 2];
        dp[1] = 1;
        dp[2] = 2;
        for (int i = 3; i <= n; i++)
            dp[i] = dp[i - 1] + dp[i - 2];
        return dp[n];
    }

    // Standard solution #2 (Recursion with memorization)
    // Time O(n) Space O(n)
    /*
    public int climbStairs(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];
    }
    */

    // Standard solution #5 (Binets Method)
    // Use matrix multiplication to get Fibonacci Number
    // Time O(logn) Space O(1)
    /*
    public int climbStairs(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;
    }
    */
}