Language: C++

#include<stdio.h>
#include<iostream>
#include<cmath>
#include<string>
#include<cassert>
using namespace std;
#define N 4
#define N2 16
#define LIMIT 100

struct Puzzle{
  int f[N2], space, MD;
};

static const int dx[4] = {0,-1,0,1};
static const int dy[4] = {1,0,-1,0};
static const char dir[4] = {'r','u','l','d'};
int MDT[N2][N2];
Puzzle state;
int limit;
int path[LIMIT];

int get(Puzzle pz){
  int sum = 0, i;
  for(i = 0; i < N2; i++){
    if(pz.f[i] == N2) continue;
    sum += MDT[i][pz.f[i] -1];
  }
  return sum;
}
bool isSolved(){
  for(int i = 0; i < N2; i++)
    if(state.f[i] != i + 1) return false;
  return true;
}

bool dfs(int depth, int prev){
  if(state.MD == 0) return true;
  if(depth + state.MD > limit) return false;
  int sx = state.space / N;
  int sy = state.space % N;
  Puzzle tmp;
  for(int r = 0; r < 4; r++){
    int tx = sx + dx[r];
    int ty = sy + dy[r];
    if(tx < 0 || ty < 0 || tx >= N || ty >= N) continue;
    if(max(prev, r) - min(prev, r) == 2) continue;
    tmp = state;
    state.MD -= MDT[tx * N + ty][state.f[tx * N + ty] - 1];
    state.MD += MDT[sx * N + sy][state.f[tx * N + ty] - 1];
    swap(state.f[tx * N + ty], state.f[sx * N + sy]);
    state.space = tx * N + ty;
    if(dfs(depth + 1, r)){
      path[depth] = r;
      return true;
    }
    state = tmp;
  }
  return false;
}

string iterdeep(Pazzle in){
  in.MD = get(in);

  for(limit = in.MD; limit <= LIMIT; limit++){
    state = in;
    if(dfs(0, -100)){
      string ans = "";
      for(int i = 0; i <limit; i++)
        ans += dir[path[i]];
      return ans;
    }
  }
  return "unsolvable";
}
int main(){
  for(int i = 0; i < N2; i++){
    for(int j = 0; j < N2; j++){
      MDT[i][j] = abs(i / N - j / N) + abs(i % N - j % N);
    }
  }
  Puzzle in;
  for(int i = 0; i < N2; i++){
    cin >> in.f[i];
    if(in.f[i] == 0){
      in.f[i] = N2;
      in.space = i;
    }
  }
  string ans = iterdeep(in);
  cout << ans.size() << endl;

  return 0;
}
int main(){
  for(int i = 0; i < N2; i++){
    for(int j = 0; j < N2; j++){
      MDT[i][j] = abs(i / N - j / N) + abs(i % N - j % N);
    }
  }
  Puzzle in;
  for(int i = 0; i < N2; i++){
    cin >> in.f[i];
    if(in.f[i] == 0){
      in.f[i] = N2;
      in.space = i;
    }
  }
  string ans = iterdeep(in);
  cout << ans.size() << endl;

  return 0;
}

Compiler output:
a.cc:62:17: error: 'Pazzle' was not declared in this scope; did you mean 'Puzzle'?
   62 | string iterdeep(Pazzle in){
      |                 ^~~~~~
      |                 Puzzle
a.cc:62:27: error: expected ',' or ';' before '{' token
   62 | string iterdeep(Pazzle in){
      |                           ^
a.cc: In function 'int main()':
a.cc:90:24: error: no match for call to '(std::string {aka std::__cxx11::basic_string<char>}) (Puzzle&)'
   90 |   string ans = iterdeep(in);
      |                ~~~~~~~~^~~~
a.cc: At global scope:
a.cc:95:5: error: redefinition of 'int main()'
   95 | int main(){
      |     ^~~~
a.cc:76:5: note: 'int main()' previously defined here
   76 | int main(){
      |     ^~~~
a.cc: In function 'int main()':
a.cc:109:24: error: no match for call to '(std::string {aka std::__cxx11::basic_string<char>}) (Puzzle&)'
  109 |   string ans = iterdeep(in);
      |                ~~~~~~~~^~~~