上篇博客中 进程管理之死锁 我们讲到了进程管理中死锁的各种问题，其中留下了死锁避免算法中著名的银行家算法没讲，下面就为大家详细解读。
1.安全序列
讲银行家算法之前，我们首先引入安全序列的定义：所谓系统是安全的，是指系统中的所有进程能够按照某一种次序分配资源，并且依次地运行完毕，这种进程序列{P1，P2，...，Pn}就是安全序列。如果存在这样一个安全序列，则系统是安全的；如果系统不存在这样一个安全序列，则系统是不安全的。
安全序列{P1，P2，...，Pn}是这样组成的：若对于每一个进程Pi，它需要的附加资源可以被系统中当前可用资源加上所有进程Pj当前占有资源之和所满足，则{P1，P2，...，Pn}为一个安全序列，这时系统处于安全状态，不会进入死锁状态。
虽然存在安全序列时一定不会有死锁发生，但是系统进入不安全状态（四个死锁的必要条件同时发生）也未必会产生死锁。当然，产生死锁后，系统一定处于不安全状态。
安全序列{P1，P2，...，Pn}是这样组成的：若对于每一个进程Pi，它需要的附加资源可以被系统中当前可用资源加上所有进程Pj当前占有资源之和所满足，则{P1，P2，...，Pn}为一个安全序列，这时系统处于安全状态，不会进入死锁状态。
虽然存在安全序列时一定不会有死锁发生，但是系统进入不安全状态（四个死锁的必要条件同时发生）也未必会产生死锁。当然，产生死锁后，系统一定处于不安全状态。
2.银行家算法
(为了熟悉英语请原谅我借用wiki上的文字来描述)
For the Banker's algorithm to work, it needs to know three things:
(1) 如果Request[j]≤Need[i,j]，则转向（2），否则认为出错。
(2) 如果Request[j]≤Available[j]，则转向（3）；否则表示尚无足够资源，Pi需等待。
(3) 假设进程i的申请已获批准，于是修改系统状态：
Available[j]=Available[j]-Request[i]
Allocation[i,j]=Allocation[i,j]+Request[j]
Need[i,j]=Need[i,j]-Request[j]
(4)系统执行安全性检查，如安全，则分配成立；否则试探险性分配作废，系统恢复原状，进程等待。
(2) 从进程集合中找到一个满足下述条件的进程，
Finish [i]=False;
Need[i,j]≤Work[j];
如找到，执行(3)；否则，执行(4)
(3) 设进程获得资源，可顺利执行，直至完成，从而释放资源。
Work[j]=Work[i]+Allocation[i,j];
Finish[i]=True;
go to step 2;
(4) 如所有的进程Finish[i]=true，则表示安全；否则系统不安全。
下面是java代码实现
参考资料：http://en.wikipedia.org/wiki/Banker's_algorithm#Safe_and_Unsafe_States
- How much of each resource each process could possibly request[CLAIMS]
- How much of each resource each process is currently holding[ALLOCATED]
- How much of each resource the system currently has available[AVAILABLE]
- request ≤ max, else set error condition as process has crossed maximum claim made by it.
- request ≤ available, else process waits until resources are available.
Basic data structures to be maintained to implement the Banker's Algorithm:
- Available: A vector of length m indicates the number of available resources of each type. If Available[j] = k, there are k instances of resource type Rj available.
- Max: An n×m matrix defines the maximum demand of each process. If Max[i,j] = k, then Pi may request at most k instances of resource type Rj.
- Allocation: An n×m matrix defines the number of resources of each type currently allocated to each process. If Allocation[i,j] = k, then process Pi is currently allocated k instance of resource type Rj.
- Need: An n×m matrix indicates the remaining resource need of each process. If Need[i,j] = k, then Pi may need k more instances of resource type Rj to complete task.
Note: Need[i,j] = Max[i,j] - Allocation[i,j].
- 银行家算法:
(1) 如果Request[j]≤Need[i,j]，则转向（2），否则认为出错。
(2) 如果Request[j]≤Available[j]，则转向（3）；否则表示尚无足够资源，Pi需等待。
(3) 假设进程i的申请已获批准，于是修改系统状态：
Available[j]=Available[j]-Request[i]
Allocation[i,j]=Allocation[i,j]+Request[j]
Need[i,j]=Need[i,j]-Request[j]
(4)系统执行安全性检查，如安全，则分配成立；否则试探险性分配作废，系统恢复原状，进程等待。
- 安全性检查
(2) 从进程集合中找到一个满足下述条件的进程，
Finish [i]=False;
Need[i,j]≤Work[j];
如找到，执行(3)；否则，执行(4)
(3) 设进程获得资源，可顺利执行，直至完成，从而释放资源。
Work[j]=Work[i]+Allocation[i,j];
Finish[i]=True;
go to step 2;
(4) 如所有的进程Finish[i]=true，则表示安全；否则系统不安全。
由于时间不早了就借用下wiki上的c语言实现代码，改天用java实现一遍。
/*PROGRAM TO IMPLEMENT BANKER'S ALGORITHM
* --------------------------------------------*/
#include <stdio.h>
int curr[5][5], maxclaim[5][5], avl[5];
int alloc[5] = {0,0,0,0,0};
int maxres[5], running[5], safe=0;
int count = 0, i, j, exec, r, p,k=1;
int main()
{
printf("\nEnter the number of processes: ");
scanf("%d",&p);
for(i=0;i<p;i++)
{
running[i]=1;
count++;
}
printf("\nEnter the number of resources: ");
scanf("%d",&r);
for(i=0;i<r;i++)
{
printf("\nEnter the resource for instance %d: ",k++);
scanf("%d",&maxres[i]);
}
printf("\nEnter maximum resource table:\n");
for(i=0;i<p;i++)
{
for(j=0;j<r;j++)
{
scanf("%d",&maxclaim[i][j]);
}
}
printf("\nEnter allocated resource table:\n");
for(i=0;i<p;i++)
{
for(j=0;j<r;j++)
{
scanf("%d",&curr[i][j]);
}
}
printf("\nThe resource of instances: ");
for(i=0;i<r;i++)
{
printf("\t%d",maxres[i]);
}
printf("\nThe allocated resource table:\n");
for(i=0;i<p;i++)
{
for(j=0;j<r;j++)
{
printf("\t%d",curr[i][j]);
}
printf("\n");
}
printf("\nThe maximum resource table:\n");
for(i=0;i<p;i++)
{
for(j=0;j<r;j++)
{
printf("\t%d",maxclaim[i][j]);
}
printf("\n");
}
for(i=0;i<p;i++)
{
for(j=0;j<r;j++)
{
alloc[j]+=curr[i][j];
}
}
printf("\nAllocated resources:");
for(i=0;i<r;i++)
{
printf("\t%d",alloc[i]);
}
for(i=0;i<r;i++)
{
avl[i]=maxres[i]-alloc[i];
}
printf("\nAvailable resources:");
for(i=0;i<r;i++)
{
printf("\t%d",avl[i]);
}
printf("\n");
//Main procedure goes below to check for unsafe state.
while(count!=0)
{
safe=0;
for(i=0;i<p;i++)
{
if(running[i])
{
exec=1;
for(j=0;j<r;j++)
{
if(maxclaim[i][j] - curr[i][j] > avl[j]){
exec=0;
break;
}
}
if(exec)
{
printf("\nProcess%d is executing\n",i+1);
running[i]=0;
count--;
safe=1;
for(j=0;j<r;j++) {
avl[j]+=curr[i][j];
}
break;
}
}
}
if(!safe)
{
printf("\nThe processes are in unsafe state.\n");
break;
}
else
{
printf("\nThe process is in safe state");
printf("\nSafe sequence is:");
for(i=0;i<r;i++)
{
printf("\t%d",avl[i]);
}
printf("\n");
}
}
}
/*SAMPLE OUTPUT
-----------------
Enter the number of resources:4
Enter the number of processes:5
Enter Claim Vector:8 5 9 7
Enter Allocated Resource Table:
2 0 1 1
0 1 2 1
4 0 0 3
0 2 1 0
1 0 3 0
Enter Maximum Claim table:
3 2 1 4
0 2 5 2
5 1 0 5
1 5 3 0
3 0 3 3
The Claim Vector is: 8 5 9 7
The Allocated Resource Table:
2 0 1 1
0 1 2 1
4 0 0 3
0 2 1 0
1 0 3 0
The Maximum Claim Table:
3 2 1 4
0 2 5 2
5 1 0 5
1 5 3 0
3 0 3 3
Allocated resources: 7 3 7 5
Available resources: 1 2 2 2
Process3 is executing
The process is in safe state
Available vector: 5 2 2 5
Process1 is executing
The process is in safe state
Available vector: 7 2 3 6
Process2 is executing
The process is in safe state
Available vector: 7 3 5 7
Process4 is executing
The process is in safe state
Available vector: 7 5 6 7
Process5 is executing
The process is in safe state
Available vector: 8 5 9 7
---------------------------------------------------------*/import java.util.Scanner;
public class Bankers{
private int need[][],allocate[][],max[][],avail[][],np,nr;
private void input(){
Scanner sc=new Scanner(System.in);
System.out.print("Enter no. of processes and resources : ");
np=sc.nextInt(); //no. of process
nr=sc.nextInt(); //no. of resources
need=new int[np][nr]; //initializing arrays
max=new int[np][nr];
allocate=new int[np][nr];
avail=new int[1][nr];
System.out.println("Enter allocation matrix -->");
for(int i=0;i<np;i++)
for(int j=0;j<nr;j++)
allocate[i][j]=sc.nextInt(); //allocation matrix
System.out.println("Enter max matrix -->");
for(int i=0;i<np;i++)
for(int j=0;j<nr;j++)
max[i][j]=sc.nextInt(); //max matrix
System.out.println("Enter available matrix -->");
for(int j=0;j<nr;j++)
avail[0][j]=sc.nextInt(); //available matrix
sc.close();
}
private int[][] calc_need(){
for(int i=0;i<np;i++)
for(int j=0;j<nr;j++) //calculating need matrix
need[i][j]=max[i][j]-allocate[i][j];
return need;
}
private boolean check(int i){
//checking if all resources for ith process can be allocated
for(int j=0;j<nr;j++)
if(avail[0][j]<need[i][j])
return false;
return true;
}
public void isSafe(){
input();
calc_need();
boolean done[]=new boolean[np];
int j=0;
while(j<np){ //until all process allocated
boolean allocated=false;
for(int i=0;i<np;i++)
if(!done[i] && check(i)){ //trying to allocate
for(int k=0;k<nr;k++)
avail[0][k]=avail[0][k]-need[i][k]+max[i][k];
System.out.println("Allocated process : "+i);
allocated=done[i]=true;
j++;
}
if(!allocated) break; //if no allocation
}
if(j==np) //if all processes are allocated
System.out.println("\nSafely allocated");
else
System.out.println("All proceess cant be allocated safely");
}
public static void main(String[] args) {
new Bankers().isSafe();
}
}
--------------------------------------------------------------------------------------------------------------------------
Output
--------------------------------------------------------------------------------------------------------------------------
Enter no. of processes and resources : 3 4
Enter allocation matrix -->
1 2 2 1
1 0 3 3
1 2 1 0
Enter max matrix -->
3 3 2 2
1 1 3 4
1 3 5 0
Enter available matrix -->
3 1 1 2
Allocated process : 0
Allocated process : 1
Allocated process : 2
Safely allocated参考资料：http://en.wikipedia.org/wiki/Banker's_algorithm#Safe_and_Unsafe_States
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