矩阵中 1 的 Groups/Islands 个数:定义说明
Number of Groups/Islands of 1's in a Matrix: Definition clarification
我正在研究 Number of Groups (or "islands") of 1's in a Matrix 的各种解决方案,虽然以下清晰简洁的 Java 解决方案看起来方向正确,但对我来说它也不完整:
/*
* Given a matrix of 0's and 1's,
* find the number of groups of 1's in the matrix.
*
* A group of 1's is defined as all ADJACENT 1's
* vertically or horizontally but not diagonally.
*/
public class Islands {
/**
* main entry point
*/
public static void main(String[] args) {
int[][] A = new int[4][4];
int totalNumGroups = 0;
int curCnt = 0;
/*
* Initialize 2-dimensional array with 1's and 0's (randomly!)
* For testing/verification purpose only
*/
for(int x=0; x<A.length; x++) {
for(int y=0; y<A[x].length; y++) {
A[x][y] = (int) Math.round(Math.random());
System.out.print(A[x][y] + " ");
}
System.out.println(" ");
}
/*
* The crux of the solution: iterate through all (x,y):
* If encountered a 1,
* reset current count and
* increase total number of groups by what clean_block returns.
*/
for(int x=0; x<A.length; x++) {
for(int y=0; y<A[x].length; y++) {
if (A[x][y] == 1) {
curCnt = 0;
totalNumGroups = totalNumGroups + cleanBlock(A, x,y, curCnt);
}
// else (0), keep curCnt and totalNumGroups as are.
}
}
System.out.println("\nTotal # of groups: " + totalNumGroups);
}
/*
* Recursively clean found 1 and its adjacent 1's.
*/
public static int cleanBlock(int[][] A, int x, int y, int cnt) {
A[x][y] = 0;
if (inMatrix(x-1,y ,A.length,A[0].length) == 1 && A[x-1][y] == 1) {
cleanBlock(A, x-1,y ,cnt);
cnt = 1;
}
if (inMatrix(x+1,y ,A.length,A[0].length) == 1 && A[x+1][y] == 1) {
cleanBlock(A, x+1,y ,cnt);
cnt = 1;
}
if (inMatrix(x,y-1 ,A.length,A[0].length) == 1 && A[x][y-1] == 1) {
cleanBlock(A, x,y-1 ,cnt);
cnt = 1;
}
if (inMatrix(x,y+1 ,A.length,A[0].length) == 1 && A[x][y+1] == 1) {
cleanBlock(A, x,y+1 ,cnt);
cnt = 1;
}
return cnt;
}
public static int inMatrix(int x, int y, int lenX, int lenY) {
if ( (x >= 0 && x <= (lenX-1)) && (y >= 0 && y <= (lenY-1)) )
return 1;
else
return 0;
}
}
那是因为它不将单个 1(被 0 包围)计为一个组。例如此 4x4 矩阵的输出仅产生一个组:
1 1 0 1
1 0 0 0
1 1 0 1
1 0 0 0
Total # of groups: 1
所以,我的问题是:被 0 包围的单个 1 是否被视为一个组?
是正确的,因为根据问题:
A group of 1's can be formed if a 1 is present either vertically or
horizontally to the adjacent 1
所以在你的情况下,一个单独的 1 不能算作一个组,因为没有其他 1 水平或垂直相邻。
countgroup=1
countgroup_of_one_array=[]
def check_to_search(p_i,p_j,matrix):
allow=True
if p_j <0:
allow=False
if p_j >len(matrix[0])-1:
allow=False
if p_i<0:
allow=False
if p_i>len(matrix)-1:
allow=False
return allow
def looking_for1(p_i,p_j,matrix,countgroup):
# global countgroup
if matrix[p_i][p_j]==1:
matrix[p_i][p_j]=0
if check_to_search(p_i,p_j+1,matrix):
if matrix[p_i][p_j+1] == 1:
countgroup =countgroup+1
countgroup = looking_for1(p_i,p_j+1,matrix,countgroup)
if check_to_search(p_i,p_j-1,matrix):
if matrix[p_i][p_j-1] == 1:
countgroup =countgroup+1
countgroup = looking_for1(p_i,p_j-1,matrix,countgroup)
if check_to_search(p_i+1,p_j,matrix):
if matrix[p_i+1][p_j] == 1:
countgroup =countgroup+1
countgroup = looking_for1(p_i+1,p_j,matrix,countgroup)
if check_to_search(p_i-1,p_j,matrix):
if matrix[p_i-1][p_j] == 1:
countgroup =countgroup+1
countgroup = looking_for1(p_i-1,p_j,matrix,countgroup)
return countgroup
myarray=[[0,0,1,0,1],
[1,1,0,1,0],
[1,1,0,1,0],
[0,0,0,0,0],
[1,1,0,1,0]]
for i in range (0, len(myarray)):
for j in range (0, len(myarray[i])):
a= looking_for1(i,j,myarray,countgroup)
if a >=2 :
countgroup_of_one_array.append(a)
print("number of group of 1 is : "+format(len(countgroup_of_one_array)) )
print((countgroup_of_one_array))
答案:
3个
[4,2,2]
我正在研究 Number of Groups (or "islands") of 1's in a Matrix 的各种解决方案,虽然以下清晰简洁的 Java 解决方案看起来方向正确,但对我来说它也不完整:
/*
* Given a matrix of 0's and 1's,
* find the number of groups of 1's in the matrix.
*
* A group of 1's is defined as all ADJACENT 1's
* vertically or horizontally but not diagonally.
*/
public class Islands {
/**
* main entry point
*/
public static void main(String[] args) {
int[][] A = new int[4][4];
int totalNumGroups = 0;
int curCnt = 0;
/*
* Initialize 2-dimensional array with 1's and 0's (randomly!)
* For testing/verification purpose only
*/
for(int x=0; x<A.length; x++) {
for(int y=0; y<A[x].length; y++) {
A[x][y] = (int) Math.round(Math.random());
System.out.print(A[x][y] + " ");
}
System.out.println(" ");
}
/*
* The crux of the solution: iterate through all (x,y):
* If encountered a 1,
* reset current count and
* increase total number of groups by what clean_block returns.
*/
for(int x=0; x<A.length; x++) {
for(int y=0; y<A[x].length; y++) {
if (A[x][y] == 1) {
curCnt = 0;
totalNumGroups = totalNumGroups + cleanBlock(A, x,y, curCnt);
}
// else (0), keep curCnt and totalNumGroups as are.
}
}
System.out.println("\nTotal # of groups: " + totalNumGroups);
}
/*
* Recursively clean found 1 and its adjacent 1's.
*/
public static int cleanBlock(int[][] A, int x, int y, int cnt) {
A[x][y] = 0;
if (inMatrix(x-1,y ,A.length,A[0].length) == 1 && A[x-1][y] == 1) {
cleanBlock(A, x-1,y ,cnt);
cnt = 1;
}
if (inMatrix(x+1,y ,A.length,A[0].length) == 1 && A[x+1][y] == 1) {
cleanBlock(A, x+1,y ,cnt);
cnt = 1;
}
if (inMatrix(x,y-1 ,A.length,A[0].length) == 1 && A[x][y-1] == 1) {
cleanBlock(A, x,y-1 ,cnt);
cnt = 1;
}
if (inMatrix(x,y+1 ,A.length,A[0].length) == 1 && A[x][y+1] == 1) {
cleanBlock(A, x,y+1 ,cnt);
cnt = 1;
}
return cnt;
}
public static int inMatrix(int x, int y, int lenX, int lenY) {
if ( (x >= 0 && x <= (lenX-1)) && (y >= 0 && y <= (lenY-1)) )
return 1;
else
return 0;
}
}
那是因为它不将单个 1(被 0 包围)计为一个组。例如此 4x4 矩阵的输出仅产生一个组:
1 1 0 1
1 0 0 0
1 1 0 1
1 0 0 0
Total # of groups: 1
所以,我的问题是:被 0 包围的单个 1 是否被视为一个组?
是正确的,因为根据问题:
A group of 1's can be formed if a 1 is present either vertically or horizontally to the adjacent 1
所以在你的情况下,一个单独的 1 不能算作一个组,因为没有其他 1 水平或垂直相邻。
countgroup=1
countgroup_of_one_array=[]
def check_to_search(p_i,p_j,matrix):
allow=True
if p_j <0:
allow=False
if p_j >len(matrix[0])-1:
allow=False
if p_i<0:
allow=False
if p_i>len(matrix)-1:
allow=False
return allow
def looking_for1(p_i,p_j,matrix,countgroup):
# global countgroup
if matrix[p_i][p_j]==1:
matrix[p_i][p_j]=0
if check_to_search(p_i,p_j+1,matrix):
if matrix[p_i][p_j+1] == 1:
countgroup =countgroup+1
countgroup = looking_for1(p_i,p_j+1,matrix,countgroup)
if check_to_search(p_i,p_j-1,matrix):
if matrix[p_i][p_j-1] == 1:
countgroup =countgroup+1
countgroup = looking_for1(p_i,p_j-1,matrix,countgroup)
if check_to_search(p_i+1,p_j,matrix):
if matrix[p_i+1][p_j] == 1:
countgroup =countgroup+1
countgroup = looking_for1(p_i+1,p_j,matrix,countgroup)
if check_to_search(p_i-1,p_j,matrix):
if matrix[p_i-1][p_j] == 1:
countgroup =countgroup+1
countgroup = looking_for1(p_i-1,p_j,matrix,countgroup)
return countgroup
myarray=[[0,0,1,0,1],
[1,1,0,1,0],
[1,1,0,1,0],
[0,0,0,0,0],
[1,1,0,1,0]]
for i in range (0, len(myarray)):
for j in range (0, len(myarray[i])):
a= looking_for1(i,j,myarray,countgroup)
if a >=2 :
countgroup_of_one_array.append(a)
print("number of group of 1 is : "+format(len(countgroup_of_one_array)) )
print((countgroup_of_one_array))
答案: 3个 [4,2,2]