how to solve problems like mixture in medium level

please help

how to solve problems like mixture in medium level

please help

this is a dynamic programming problem. Can be solved similar to the classical matrix multiplication problem where you need to place brackets to minimize the number of multiplications.

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its similiar to the standard matrix multiplication problem

you need to mantain two auxiliary table

1.) dp[n][n] //stores maximum smoke for subarry ai to aj is in dp[i][j]

2.) color[n][n] // stores color of all subarray ai to aj