Memory 在 c++ 中分配动态二维布尔数组时超出限制

Question

I have tried to allocate a dynamic 2D array of booleans for implementing graph in C++. Even though I have declared the graph globally and have done dynamic allocation using new operator yet I am getting memory limit exceeded error on codeforces. I have gone through segmentation fault answers already but all answers ask for dynamic allocation to avoid this error which I have already done.

#include<bits/stdc++.h>
using namespace std;
bool ** g;
bool dfs_h(int n,int k,int src,int *vis){
vis[src]=1;
if(src==k) return true;
for(int i=1;i<=n;i++){
    if(g[src][i]&&!vis[i]){
        if(dfs_h(n,k,i,vis)) return true;
    }
}
return false;
}
bool dfs(int n,int k,int src){
int *vis=new int[n+1]{0};
bool ans=dfs_h(n,k,src,vis);
return ans;
}

main(){
int n,k;
cin>>n>>k;
g=new bool *[n+1];
for(int i=0;i<=n;i++) g[i]=new bool [n+1];
for(int i=1;i<=n;i++){
    for(int j=1;j<=n;j++) g[i][j]=false;
}
int buf;
for(int i=1;i<n;i++){
    cin>>buf;
    g[i][i+buf]=true;
}
bool ans=dfs(n,k,1);
for(int i=0;i<=n;i++) delete g[i];
delete [] g;
if(ans) cout<<"YES\n";
else cout<<"NO\n";
}

Answer 1

Let's think about this for the case of n=10000:

g=new bool *[n+1];

That will allocate 640064 bits on a 64-bit system. Then:

for(int i=0;i<=n;i++)
    g[i]=new bool [n+1];

That will allocate 800160008 bits (10001*10001*8).

In total this is more than 95 GB of allocation to store 10001*10001 bits which is fundamentally only 12 GB.

So the first thing you should do is change your storage strategy to use every bit, instead of just one bit per byte, and perhaps a single allocation instead of 10002 allocations. Using a single std::vector<bool> bits(10001*10001) will accomplish this easily, you just need to write an indexing function like bool get(int x, int y) { return bits[x + y * 10001]; } bool get(int x, int y) { return bits[x + y * 10001]; } .