# Minimal sparse ruler problem minimum ruler scale problem

Source: Internet
Author: User

A ruler of length 13, if the 1-bit point can be 1 and 12, 133 kinds of scale. So at least a few points, you can directly measure the length of 1-13, which are engraved in which positions?

Note: Must be a direct quantity. That is, the ruler can find a 1-13 arbitrary integer length.

Wrote a no-tech solution to DFS violence. A viable solution is 1, 2, 6, 10.

`1#include <iostream>2#include <vector>3#include <unordered_map>4 using namespacestd;5 6 classSolution {7  Public:8vector<vector<int>> Ruler (intN, vector<int> &Minpath) {9Dfs0, N, Minpath);Ten         returnresult; One     } Avector<vector<int>>result; -vector<int>path; -     voidDfsintStartintN, vector<int> &Minpath) { the         if(Start = = n +1) { -             if(Fullscale (path)) { - result.push_back (path); -                 if(Path.size () <Minlen) { +Minlen =path.size (); -Minpath =path; +                 } A             } at             return; -         } -          for(inti = start; I <= N; i++) { - Path.push_back (i); -DFS (i +1, N, Minpath); - Path.pop_back (); in         } -     } to     BOOLFullscale (vector<int>path) { +         if(Path.size () <4) { -             return false; the         } *unordered_map<int,int>Umap; \$umap[ -]++;Panax Notoginsengumap[0]++; -          for(inti =0; I < path.size (); i++) { the              for(intj =0; J < I; J + +) { +                 if(Path[i]-PATH[J] < -) { AUmap[path[i]-path[j]]++; theumap[path[j]]++; +umap[path[i]]++; -umap[ --path[i]]++; \$umap[ --path[j]]++; \$                 } -                 if(Umap.size () >= -) { -                     return true; the                 } -             }Wuyi         } the         return false; -     } Wu Private: -     intMinlen = -; About }; \$  - intMain () { -     intn = -; - solution Solu; Avector<int>Minpath; +vector<vector<int>> res =Solu.ruler (n, minpath); the      for(Auto X:minpath) { -cout << x <<", "; \$     } the}`

Ref:https://en.wikipedia.org/wiki/sparse_ruler

Minimal sparse ruler problem minimum ruler scale problem

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