PART17 一维动态规划

锅包一切2026-02-19 16:45

第N个泰波那契数

cpp 复制代码

class Solution {
public:
    int tribonacci(int n) {
        if (n == 0) {
            return 0;
        }
        if (n <= 2) {
            return 1;
        }
        int dp[n + 1];
        dp[0] = 0;
        dp[1] = 1;
        dp[2] = 1;
        for (int i = 3; i <= n; i++) {
            dp[i] = dp[i - 1] + dp[i - 2] + dp[i - 3];
        }
        return dp[n];
    }
};

使用最小花费爬楼梯

lc.746

cpp 复制代码

class Solution {
public:
    int minCostClimbingStairs(vector<int>& cost) {
        int cLen = cost.size();
        int minCost[cLen + 1];
        minCost[0] = 0;
        minCost[1] = 0;
        for (int i = 2; i <= cLen; i++) {
            minCost[i] = min(minCost[i - 1] + cost[i - 1], minCost[i - 2] + cost[i - 2]);
        }
        return minCost[cLen];
    }
};

打家劫舍

lc.198

cpp 复制代码

class Solution {
public:
    int rob(vector<int>& nums) {
        int n = nums.size();
        if (n == 1) {
            return nums[0];
        }
        if (n == 2) {
            return max(nums[0], nums[1]);
        }
        int dp[n];
        dp[0] = nums[0];
        dp[1] = max(nums[0],nums[1]);
        for (int i = 2; i < n; i++) {
            dp[i] = max(dp[i - 1], dp[i - 2] + nums[i]);
        }
        return dp[n - 1];
    }
};

多米诺和托米诺平铺

cpp 复制代码

class Solution {
public:
    int numTilings(int n) {
        if (n <= 2) {
            return n;
        }
        vector<long long> f(n + 1);
        f[0] = 1;
        f[1] = 1;
        f[2] = 2;
        long long y = f[0];
        for (int i = 3; i <= n; i++) {
            f[i] = (f[i - 1] + f[i - 2] + 2 * y) % (1000000007);
            y += f[i - 2];
        }
        return f[n];
    }
};