leetcode Paint Fence

最新推荐文章于 2021-01-31 05:48:09 发布

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本文介绍了一种解决围栏涂色问题的动态规划算法。该算法确保相邻栏杆最多只有两个相同颜色，并提供了计算所有可能涂色方案总数的方法。适用于n和k为非负整数的情况。

Problem

There is a fence with n posts, each post can be painted with one of the k colors.

You have to paint all the posts such that no more than two adjacent fence posts have the same color.

Return the total number of ways you can paint the fence.

Note:
n and k are non-negative integers.

Solution

dp[i]表示第 i 个栏杆满足条件的染色方案，那它就等于前一个栏杆颜色不同的方案数量（ dp[ i - 1] * (k -1) ）与

前前一个栏杆颜色不同的方案数量（ dp[ i - 2] * (k -1)）之和

class Solution {
public:
    int numWays(int n, int k) {
        if(n <= 0 || k <= 0) return 0;
        if( n == 1) return k;
        if( n == 2) return k*k;
        
        int num0 = k, num1 = k*k, num2 = 0;
        for( int i = 2; i < n; i++){
            num2 = num0 * (k-1) + num1 *(k-1);
            num0 = num1;
            num1 = num2;
        }
        return num2;
    }
};