分割数组以得最大和的题解

分隔数组以得到最大和

$dp[i]$表示前i个数字的最大和，k种转移。

$$\begin{array}{c}\begin{array}{rl}dp[i]=max\{& \\ & dp[i-1]+1\ast max\{arr[i]\}\\ & dp[i-2]+2\ast max\{arr[i],arr[i-1]\}\\ & ...\\ & k\ast dp[i-k]+max\{arr[i],arr[i-1],...arr[i-k+1]\}\\ \}& \end{array}\end{array}$$
$$\begin{array}{c}\begin{array}{rl}dp[i]& =max(dp[i-j]+j\ast max(arr[i]...arr[i-j+1]))\\ & =max\{dp[i-j]+j\ast max\{arr[t]\}\}\\ & j\in [1,min(k,i)],t\in [i-j+1,i]\end{array}\end{array}$$