Algorithms Flowchart for coding interviews

Here’s a practical decision flowchart you can use during interviews and problem solving:

START

  |

  v

Can the problem be solved greedily by making

the best local choice at each step?

  |

  +– YES –> GREEDY ALGORITHM

  |

  +– NO –>

              |

              v

Does the problem ask for:

– All possible solutions?

– Any valid solution?

– Enumerating combinations/permutations/subsets?

– Constraint satisfaction?

              |

              +– YES –>

              |          |

              |          v

              |     Can you prune invalid

              |     partial solutions early?

              |          |

              |          +– YES –> BACKTRACKING

              |          |

              |          +– NO –> BRUTE FORCE

              |

              +– NO –>

                          |

                          v

Does the problem have:

1. Optimal substructure?

2. Overlapping subproblems?

                          |

                          +– YES –>

                          |          |

                          |          v

                          |     Need optimal value,

                          |     counting, or minimum/

                          |     maximum answer?

                          |          |

                          |          +– YES –> DYNAMIC PROGRAMMING

                          |

                          +– NO –>

                                      |

                                      v

Can it be modeled as a graph

(states/nodes + transitions)?

                                      |

                                      +– YES –>

                                      |          |

                                      |          +– Shortest path –> BFS/Dijkstra

                                      |          |

                                      |          +– Reachability –> BFS/DFS

                                      |          |

                                      |          +– DAG ordering –> Topological Sort

                                      |

                                      +– NO –>

                                                  |

                                                  v

Is it primarily about searching

in a sorted/monotonic space?

                                                  |

                                                  +– YES –> BINARY SEARCH

                                                  |

                                                  +– NO –>

                                                              |

                                                              v

Check specialized techniques:

– Divide & Conquer

– Two Pointers

– Sliding Window

– Heap/Priority Queue

– Union-Find

– Segment Tree

– Trie

– Mathematical/Bit Manipulation

Quick Rule of Thumb

If you see…	Use
Generate all combinations/permutations	Backtracking
Optimize (min/max), count ways, repeated states	Dynamic Programming
Best local choice always works	Greedy
State transitions on nodes	Graph Algorithms
Sorted/monotonic answer space	Binary Search
Subarray/substring with contiguous window	Sliding Window
Split into independent halves	Divide & Conquer

Backtracking vs Dynamic Programming

Need to explore choices?

       |

       +– No repeated states –> BACKTRACKING

       |

       +– Same state reached multiple times –>

              DYNAMIC PROGRAMMING

Examples:

• N-Queens → Backtracking
• Sudoku → Backtracking
• Subset Sum (decision) → Backtracking or DP
• Knapsack → DP
• Coin Change → DP
• Longest Common Subsequence → DP
• Generate Parentheses → Backtracking
• Traveling Salesman → DP + Bitmasking (or Backtracking for small inputs)