#Is there any other transition out there that can be optimised using DnC optimization

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fallow ingot
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Is there any other transition out there that can be optimised using DnC optimization

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Currently i'm learning about DnC optimization for dynamic programming

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and i have found in many Source that the transition needs to be in this form

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dp[i][j] = min1≤k<j (dp[i-1][k-1] + cost[k][j])

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does it have to be in that form for the problem to be optimized by DnC

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or Do i only have to check the cost function for quadrangle inequality