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理论基础

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509. 斐波那契数

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普通递归：

class Solution {public int fib(int n) {if (n < 2) {return n;}return fib(n - 1) + fib(n - 2);}
}

动态规划：

class Solution {public int fib(int n) {if (n < 2) {return n;}int a = 0, b = 1, sum = 0;for (int i = 2; i <= n; i++) {sum = a + b;a = b;b = sum;}return sum;}
}

70. 爬楼梯

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dp 数组：

class Solution {public int climbStairs(int n) {if (n <= 2) {return n;}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];}
}

状态压缩：

class Solution {public int climbStairs(int n) {if (n <= 2) {return n;}int first = 1;  // dp[i-2]int second = 2; // dp[i-1]int current = 0; // dp[i]for (int i = 3; i <= n; i++) {current = first + second;first = second;second = current;}return second; // dp[n]}
}

746. 使用最小花费爬楼梯

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视频讲解：动态规划开更了！| LeetCode：746. 使用最小花费爬楼梯_哔哩哔哩_bilibili

class Solution {public int minCostClimbingStairs(int[] cost) {int n = cost.length;if (n <= 2) {return Math.min(cost[0], cost[1]);}int first = 0;int second = 0;int current = 0;for (int i = 2; i <= n; i++) {current = Math.min(first + cost[i - 2], second + cost[i - 1]);first = second;second = current;}return current;}
}