备忘录方法(自顶向下的动态规划)
public class Solution {
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;
}
//如果计算过,就直接返回
if (memo[i] > 0) {
return memo[i];
}
//如果没有计算过,就现计算,然后return
memo[i] = climb_Stairs(i + 1, n, memo) + climb_Stairs(i + 2, n, memo);
return memo[i];
}
}
自底向上的动态规划
public class Solution {
public int climbStairs(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];
}
}