小白书上经典DFS题目。
1. 递归实现
// from: https://www.cnblogs.com/huaszjh/p/4686092.html
#include <stdio.h>
#include <string.h>
#define maxn 105
unsigned char data[maxn][maxn];
int m, n, vis[maxn][maxn];
void dfs(int x, int y, int ans) {
if (x < 0 || x >= m || y < 0 || y >= n) return; //出界
if (vis[x][y] > 0 || data[x][y] == '*') return; //非'@'或已经访问
vis[x][y] = ans; //连通分量编号
for (int k = -1; k <= 1; k++) {
for (int t = -1; t <= 1; t++) {
if (k != 0 || t != 0) { //自身格子不需要重复判断
dfs(x + k, y + t, ans);
}
}
}
}
#define DEBUG
int main() {
#ifdef DEBUG
const char* input_txt_pth = "F:/zhangzhuo/debug/OJ/UVA-572.txt";
freopen(input_txt_pth, "r", stdin);
#endif
int i, j;
while (scanf("%d %d", &m, &n) && m &&n) {
int count = 0; //连通块
memset(vis, 0, sizeof(vis));
for (i = 0; i < m; i++) {
scanf("%s", data[i]);
}
for (i = 0; i < m; i++) {
for (j = 0; j < n; j++) {
//对未访问且为`@`的格子进行访问
if (vis[i][j] == 0 && data[i][j] == '@') {
dfs(i, j, ++count);
}
}
}
printf("%d
", count);
#ifdef DEBUG
for (i = 0; i < m; i++) {
for (j = 0; j < n; j++) {
printf("%3d", vis[i][j]);
}
printf("
");
}
printf("
");
#endif
}
return 0;
}
2. 递归dfs函数用迭代实现
每个节点的dfs递归调用，改成用stack容器就地计算，是个while循环，本质上还是栈，但是避免了递归时嵌套产生的开销造成的潜在风险。
C++的stack、vector容器用起来比较顺手。另外就是把坐标简单封装为一个结构体。
#include <stdio.h>
#include <string.h>
#include <iostream>
#include <stack>
#include <vector>
typedef struct Coord {
char x, y;
} Coord;
#define DEBUG
int main() {
#ifdef DEBUG
const char* input_txt_pth = "F:/zhangzhuo/debug/OJ/UVA-572.txt";
freopen(input_txt_pth, "r", stdin);
#endif
int m, n, i, j;
#define maxn 105
unsigned char data[maxn][maxn];
int vis[maxn][maxn];
while (scanf("%d %d", &m, &n) && m &&n) {
int count = 0; //连通块
memset(vis, 0, sizeof(vis));
for (i = 0; i < m; i++) {
scanf("%s", data[i]);
}
std::stack<Coord> stk;
Coord cd;
std::vector<Coord>offset;
cd.x = -1; cd.y = -1; offset.push_back(cd);
cd.x = -1; cd.y = 0; offset.push_back(cd);
cd.x = -1; cd.y = 1; offset.push_back(cd);
cd.x = 0; cd.y = -1; offset.push_back(cd);
cd.x = 0; cd.y = 1; offset.push_back(cd);
cd.x = 1; cd.y = -1; offset.push_back(cd);
cd.x = 1; cd.y = 0; offset.push_back(cd);
cd.x = 1; cd.y = 1; offset.push_back(cd);
for (i = 0; i < m; i++) {
for (j = 0; j < n; j++) {
cd.x = i; cd.y = j;
if (vis[cd.x][cd.y] > 0 || data[cd.x][cd.y] != '@') continue;
count++;
stk.push(cd);
while (!stk.empty()) {
cd = stk.top();
stk.pop();
vis[cd.x][cd.y] = count;
Coord tmp;
for (size_t k = 0; k < offset.size(); k++) {
tmp.x = cd.x + offset[k].x;
tmp.y = cd.y + offset[k].y;
if (tmp.x < 0 || tmp.x >= m || tmp.y < 0 || tmp.y >= n) continue;
if (vis[tmp.x][tmp.y] > 0 || data[tmp.x][tmp.y] != '@') continue;
stk.push(tmp);
}
}
}
}
printf("%d
", count);
#ifdef DEBUG
for (i = 0; i < m; i++) {
for (j = 0; j < n; j++) {
printf("%3d", vis[i][j]);
}
printf("
");
}
printf("
");
#endif
}
return 0;
}
3.纯C，DFS非递归，自定义栈ADT，函数指针
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <string.h>
typedef struct Coord Coord;
struct Coord {
char x, y;
};
typedef struct CoordOffset CoordOffset;
struct CoordOffset {
size_t num;
int* x;
int* y;
};
typedef struct ListNode ListNode;
struct ListNode
{
ListNode* next;
void* data;
};
typedef struct Stack Stack;
struct Stack {
ListNode* head;
size_t len;
void(*push_coord)(Stack* stk, Coord* coord);
void (*pop_coord)(Stack* stk);
void (*top_coord)(Stack* stk, Coord* coord);
};
void stack_push_coord(Stack* stk, Coord* coord) {
ListNode* new_head = (ListNode*)malloc(sizeof(ListNode));
/* new_head->data = coord; */
new_head->data = (Coord*)malloc(sizeof(ListNode));
memcpy(new_head->data, coord, sizeof(Coord));
new_head->next = stk->head;
stk->head = new_head;
stk->len++;
}
void stack_pop_coord(Stack* stk) {
if (stk->head != NULL) {
ListNode* new_head = stk->head->next;
free(stk->head->data);
free(stk->head);
stk->head = new_head;
stk->len--;
}
}
void stack_top_coord(Stack* stk, Coord* coord) {
if (stk->head != NULL) {
Coord* t_coord = (Coord*)(stk->head->data);
coord->x = t_coord->x;
coord->y = t_coord->y;
}
}
void make_stack(Stack** _stk) {
Stack* stk = (Stack*)malloc(sizeof(Stack));
stk->head = NULL;
stk->len = 0;
stk->push_coord = stack_push_coord;
stk->pop_coord = stack_pop_coord;
stk->top_coord = stack_top_coord;
/* write back */
*_stk = stk;
}
void free_stack(Stack* stk) {
ListNode* cur = stk->head;
ListNode* temp;
size_t i;
for (i = 0; i < stk->len; i++) {
temp = cur->next;
free(cur->data);
free(cur);
cur = temp;
}
free(stk);
stk = NULL;
}
void make_8coord_offset(CoordOffset** _offset) {
CoordOffset* offset = (CoordOffset*)malloc(sizeof(CoordOffset));
offset->num = 8;
offset->x = (int*)malloc(sizeof(int)*offset->num);
offset->y = (int*)malloc(sizeof(int)*offset->num);
offset->x[0] = -1; offset->y[0] = -1;
offset->x[1] = -1; offset->y[1] = 0;
offset->x[2] = -1; offset->y[2] = 1;
offset->x[3] = 0; offset->y[3] = -1;
offset->x[4] = 0; offset->y[4] = 1;
offset->x[5] = 1; offset->y[5] = -1;
offset->x[6] = 1; offset->y[6] = 0;
offset->x[7] = 1; offset->y[7] = 1;
/* write back */
*_offset = offset;
}
void free_coord_offset(CoordOffset* offset) {
if (offset) {
if (offset->x) {
free(offset->x);
offset->x = NULL;
}
if (offset->y) {
free(offset->y);
offset->y = NULL;
}
free(offset);
offset = NULL;
}
}
/* #define DEBUG */
int main() {
#ifdef DEBUG
const char* input_txt_pth = "F:/zhangzhuo/debug/OJ/UVA-572.txt";
freopen(input_txt_pth, "r", stdin);
#endif
int m, n, i, j;
size_t k;
#define maxn 105
unsigned char data[maxn][maxn];
int vis[maxn][maxn];
/* here we use 8 neighbours */
CoordOffset* offset = NULL;
make_8coord_offset(&offset);
while (scanf("%d %d", &m, &n) && m &&n) {
int count = 0; /* 连通块 */
memset(vis, 0, sizeof(vis));
for (i = 0; i < m; i++) {
scanf("%s", data[i]);
}
/* std::stack<Coord> stk; */
Stack* stk;
make_stack(&stk);
Coord cd;
for (i = 0; i < m; i++) {
for (j = 0; j < n; j++) {
cd.x = i; cd.y = j;
if (vis[cd.x][cd.y] > 0 || data[cd.x][cd.y] != '@') continue;
count++;
/* stk.push(cd); */
stack_push_coord(stk, &cd);
/* while (!stk.empty()) { */
while(stk->len!=0) {
/* cd = stk.top(); */
/* stack_top_coord(stk, &cd); */
stk->top_coord(stk, &cd);
/* stk.pop(); */
/* stack_pop_coord(stk); */
stk->pop_coord(stk);
vis[cd.x][cd.y] = count;
Coord tmp;
for (k = 0; k < offset->num; k++) {
tmp.x = cd.x + offset->x[k];
tmp.y = cd.y + offset->y[k];
if (tmp.x < 0 || tmp.x >= m || tmp.y < 0 || tmp.y >= n) continue;
if (vis[tmp.x][tmp.y] > 0 || data[tmp.x][tmp.y] != '@') continue;
/* stk.push(tmp); */
/* stack_push_coord(stk, &tmp); */
stk->push_coord(stk, &tmp);
}
}
}
}
free_stack(stk);
printf("%d
", count);
#ifdef DEBUG
for (i = 0; i < m; i++) {
for (j = 0; j < n; j++) {
printf("%3d", vis[i][j]);
}
printf("
");
}
printf("
");
#endif
}
free_coord_offset(offset);
return 0;
}
4.DFS+并查集实现
#include <stdio.h>
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
int fa[10500];
int m, n, cnt, vis[105][105];
char mp[105][105];
int find(int x) {
if (fa[x] == x) return x;
fa[x] = find(fa[x]);
return fa[x];
}
void merge(int x, int y) {
int fx = find(x);
int fy = find(y);
if (fx == fy) return;
fa[fx] = fy;
}
void dfs(int x, int y, int fx, int fy) {
if (x < 0 || x >= m || y < 0 || y >= n) return;
if (vis[x][y] || mp[x][y] == '*') return;
vis[x][y] = 1;
/* cout<<"x || y || fx || fy : "<<x<<" || "<<y<<" || "<<fx<<" || "<<fy<<endl; */
if (fx != -1) {
merge(x*m + y, fx*m + fy);
}
int i, j;
for (i = -1; i < 2; i++) {
for (j = -1; j < 2; j++) {
if (!i && !j) continue;
dfs(x + i, y + j, x, y);
}
}
}
/* #define LOCAL */
int main() {
#ifdef LOCAL
const char* input_txt = "F:/zhangzhuo/debug/OJ/UVA-572.txt";
freopen(input_txt, "r", stdin);
#endif
int i, j;
while (scanf("%d%d", &m, &n) == 2 && m && n) {
cnt = 0;
memset(vis, 0, sizeof(vis));
for (i = 0; i < m; i++) {
scanf("%s", mp[i]);
}
for (i = 0; i < 10500; i++) {
fa[i] = i;
}
for (i = 0; i < m; i++) {
for (j = 0; j < n; j++) {
if (!vis[i][j] && mp[i][j] == '@') {
dfs(i, j, -1, -1);
cnt++;
}
}
}
printf("%d
", cnt);
#ifdef LOCAL
for (i = 0; i < m; i++) {
for (j = 0; j < n; j++) {
printf("%3d", vis[i][j]);
}
printf("
");
}
printf("
");
#endif
}
return 0;
}
5.DFS+并查集+不使用全局变量+简单封装为结构体
修改自 UVA572 (并查集解法) 。这种写法有点问题：已经用了dfs，dfs里用并查集多此一举，如果用并查集就不应该递归调用dfs。
#include <stdio.h>
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
typedef struct FSU_Node {
int p; /* parent id */
int rank;
int vis; /* group(connected component) id */
} FSU_Node;
/*
get node's root id
@param x: node id
@param nodes: all nodes in map
*/
int fus_find(int x, FSU_Node* nodes) {
if (nodes[x].p == x) return x;
nodes[x].p = fus_find(nodes[x].p, nodes);
return nodes[x].p;
}
/*
merge two node groups
@param a: a node from one node group
@param b: a node from another node group
*/
void fus_union(int a, int b, FSU_Node* nodes)
{
int ra = fus_find(a, nodes); /* ra: root id of a */
int rb = fus_find(b, nodes); /* rb: root id of b */
if (ra == rb) {
return;
}
if (nodes[ra].rank > nodes[rb].rank)
{
nodes[rb].p = ra;
}
else {
if (nodes[ra].rank == nodes[rb].rank)
{
nodes[rb].rank++;
}
nodes[ra].p = rb;
}
}
typedef struct ImageSize {
int w, h;
} ImageSize;
typedef struct Coord {
int row, col;
} Coord;
void fus_dfs(const Coord* pt, const Coord* f_pt, FSU_Node* nodes, ImageSize* sz, unsigned char* mp) {
int row = pt->row;
int col = pt->col;
int f_row = f_pt->row;
int f_col = f_pt->col;
if (row < 0 || row >= sz->h || col < 0 || col >= sz->w) return;
int id = row * sz->w + col;
int fid = f_row * sz->w + f_col;
/* if (vis[id] || mp[id] == '*') return; */
if (nodes[id].vis || mp[id] == '*') return;
/* vis[id] = 1; */
nodes[id].vis = 1;
if (f_row != -1) {
fus_union(id, fid, nodes);
}
int i, j;
Coord neighbor;
for (i = -1; i < 2; i++) {
for (j = -1; j < 2; j++) {
if (!i && !j) continue;
neighbor.row = row + i;
neighbor.col = col + j;
fus_dfs(&neighbor, pt, nodes, sz, mp);
}
}
}
/*#define LOCAL*/
int main() {
#ifdef LOCAL
const char* input_txt = "F:/zhangzhuo/debug/OJ/UVA-572.txt";
freopen(input_txt, "r", stdin);
#endif
#define MAXN 105
int m, n, cnt, i, j;
/* int vis[MAXN*MAXN]; */
unsigned char mp[MAXN*MAXN];
FSU_Node nodes[MAXN*MAXN];
int idx;
while (scanf("%d%d", &m, &n) == 2 && m && n) {
cnt = 0;
/* memset(vis, 0, sizeof(int)*MAXN*MAXN); */
for (i = 0; i < m; i++) {
for (j = 0; j < n; j++) {
idx = i * n + j;
scanf(" %c", &mp[idx]);
/* printf("! %c !", mp[idx]); */
}
}
for (i = 0; i < m*n; i++) {
nodes[i].p = idx;
nodes[i].rank = 1;
nodes[i].vis = 0;
}
ImageSize im_sz;
im_sz.h = m;
im_sz.w = n;
Coord pt;
Coord f_pt;
f_pt.row = -1;
f_pt.col = -1;
for (i = 0; i < m; i++) {
for (j = 0; j < n; j++) {
idx = i * n + j;
/* if (!vis[idx] && mp[idx] == '@') { */
if (!nodes[idx].vis && mp[idx] == '@') {
/* dfs(i, j, -1, -1); */
pt.row = i;
pt.col = j;
/* fus_dfs(&pt, &f_pt, nodes, &im_sz, vis, mp); */
fus_dfs(&pt, &f_pt, nodes, &im_sz, mp);
cnt++;
}
}
}
printf("%d
", cnt);
#ifdef LOCAL
for (i = 0; i < m; i++) {
for (j = 0; j < n; j++) {
idx = i * m + j;
/* printf("%3d", vis[idx]); */
printf("%c", mp[idx]);
}
printf("
");
}
printf("
");
#endif
}
return 0;
}
这里的教训是，如果在双重for循环中使用变量x、y来表示坐标，容易把2维度坐标->1维坐标的计算算错。使用row,col能减少犯错可能；
另外就是数据读取，这里改成%c，则需要过滤掉换行符
，方法是scanf时的格式串首部添加空格：scanf(" %c", &xx)
6. 并查集，去掉了DFS
思路：遍历每个像素点，每个像素点用并查集算法合并周边8邻域中为'@'的像素点。再次遍历，统计每个'@'像素对应的等价类（root节点）的值。第三次遍历，把第二次统计的值当中cnt数大于0的累计，就是区域个数。在统计连通域个数的时候顺带把每个连通域id（像素的parent值）修改为从1开始严格单调增的序列，开启LOCAL和LOCAL_DEBUG宏可以看到。
和通常用的模板写法略有差别，比如返回root的递归终止条件，比如root初值。
不得不说，uDebug是个好东西。
#include <stdio.h>
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
typedef struct FSU_Node {
int p; /* parent id */
int rank;
} FSU_Node;
/*
get node's root id
@param x: node id
@param nodes: all nodes in map
*/
int fus_find(int x, FSU_Node* nodes) {
if (nodes[x].p == x) {
return x;
}
nodes[x].p = fus_find(nodes[x].p, nodes);
return nodes[x].p;
}
/*
merge two node groups
@param a: a node from one node group
@param b: a node from another node group
*/
void fus_union(int a, int b, FSU_Node* nodes)
{
int ra = fus_find(a, nodes); /* ra: root id of a */
int rb = fus_find(b, nodes); /* rb: root id of b */
if (ra == rb) {
return;
}
if (nodes[ra].rank > nodes[rb].rank) {
nodes[rb].p = ra;
}
else {
if (nodes[ra].rank == nodes[rb].rank) {
nodes[rb].rank++;
}
nodes[ra].p = rb;
}
}
/* #define LOCAL */
/* #define LOCAL_DEBUG */
int main() {
#ifdef LOCAL
const char* input_txt = "F:/zhangzhuo/debug/OJ/UVA-572.txt";
freopen(input_txt, "r", stdin);
#endif
#define MAXN 105
int m, n, cnt, i, j, k;
int shift_x[8] = { -1, -1, -1, 0, 0, 1, 1, 1 };
int shift_y[8] = { -1, 0, 1, -1, 1, -1, 0, 1 };
unsigned char mp[MAXN*MAXN];
FSU_Node nodes[MAXN*MAXN];
int idx;
while (scanf("%d%d", &m, &n) == 2 && m && n) {
cnt = 0;
for (i = 0; i < m; i++) {
for (j = 0; j < n; j++) {
idx = i * n + j;
scanf(" %c", &mp[idx]);
}
}
for (i = 0; i < m; i++) {
for (j = 0; j < n; j++) {
idx = i * n + j;
nodes[idx].p = idx;
nodes[idx].rank = 1;
}
}
for (i = 0; i < m; i++) {
for (j = 0; j < n; j++) {
idx = i * n + j;
if (mp[idx] != '@') continue;
for (k = 0; k < 8; k++) {
int row = i + shift_x[k];
int col = j + shift_y[k];
int neighbor_idx = row * n + col;
if (row < 0 || row >= m || col < 0 || col >= n || mp[neighbor_idx] != '@') continue;
fus_union(idx, neighbor_idx, nodes);
}
}
}
int bowl[MAXN*MAXN] = { 0 };
int label_cnt = 0;
for (i = 0; i < m*n; i++) {
if (mp[i] != '@') continue;
int t = fus_find(i, nodes);
nodes[i].p = t;
if (bowl[t] == 0) {
label_cnt++;
bowl[t] = label_cnt;
}
}
printf("%d
", label_cnt);
#ifdef LOCAL_DEBUG
/* print out debug info */
for (i = 0; i < m; i++) {
for (j = 0; j < n; j++) {
idx = i * n + j ;
if (mp[idx] == '@') {
/* printf("%3d", fus_find(idx, nodes)); */
/* printf("%3d", nodes[idx].p); */
printf("%3d", bowl[nodes[idx].p]);
}
else {
printf("%3c", '*');
}
}
printf("
");
}
printf("
");
#endif
}
return 0;
}