The best replacement for dynamic programming is divide and conquer.

The best alternatives to dynamic programming are rated as following:
★★★★★  divide and conquer
★★★★  recursion
★★★★  memoization
★★★  linear programming
★★★  greedy
★★★  branch and bound
★★★  greedy method
★★★  static programming
★★  greedy algorithm
★  greedy technique
★  dijkstra
★  optimal control
  branch bound

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Speaking about dynamic programming, one probably shouldn't forget about knapsack problem.

Other search terms related to dynamic programming and their ratings are:
★★★★★ knapsack problem
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dynamic programming
divide and conquer
recursion