深度优先搜索

 //全排列
 #include <stdio.h>
 int a[10], book[10], n;
 //注意：C语言全局变量在赋值前默认为0； 
 void dfs (int step)
 {
     if (step == n + 1)
     {
         for (int i = 1; i < n + 1; i ++)
         {
             printf("%d", a[i]);
         }
         printf("\n");
         return; 
     }
     for (int i = 1; i <= n; i ++)
     {
         if (book[i] == 0)
         {
             a[step] = i;
             book[i] = 1;
             dfs(step + 1);
             book[i] = 0;
         }   
     }
     return;
 }
 int main ()
 {
     scanf("%d", &n);
     dfs(1);
     getchar();getchar();
     return 0;
 }

 //基本模型
 void dfs (int step)
 {
     //判断边界
     //尝试每一种可能
     for (int i = 1; i < n; i ++)
     {
         //继续下一步
         dsf(step + 1);
     }
     返回
 }

 // ··· + ··· = ···
 #include <stdio.h>
 int a[10], book[10], total;
 void dfs (int step)
 {
     if (step == 10)
     {
         int num1 = a[1] * 100 + a[2] * 10 + a[3];
         int num2 = a[4] * 100 + a[5] * 10 + a[6];
         int num3 = a[7] * 100 + a[8] * 10 + a[9];
         if (num1 + num2 == num3)
         {
             total ++;
             printf("%d + %d = %d\n", num1, num2, num3);
         }
         return;
     }
     for (int i = 1; i < 10; i ++)
     {
         if (book[i] == 0)
         {
             a[step] = i;
             book[i] = 1;
             dfs(step + 1);
             book[i] = 0;
         }
     }
     return;
 }
 int main ()
 {
     dfs(1);
     printf("total = %d", total / 2);
     getchar();getchar();
     return 0;
 }

 //解救小哈
 #include <stdio.h>
 #include <limits.h>
 int next[4][2] = {{0, 1}, {1, 0}, {0, -1}, {-1, 0}};
 int n, m, p, q, min = INT_MAX;
 int a[51][51], book[51][51];
 void dfs (int x, int y, int step)
 {
     if (x == p && y == q)
     {
         if (step < min)
         {
             min = step;
         }
         return;     
     }
     for (int k = 0; k < 4; k ++)
     {
         int tx = x + next[k][0];
         int ty = y + next[k][1];
         if (tx < 1 || tx > n || ty < 1 || ty > m)
         {
             continue;
         }
         if (a[tx][ty] == 0 && book[tx][ty] == 0)
         {
             book[tx][ty] = 1;
             dfs(tx, ty, step + 1);
             book[tx][ty] = 0;
         }
     }
     return;
 }
 int main ()
 {
     int startx, starty;
     scanf ("%d%d", &n, &m);
     for (int i = 1; i <= n; i ++)
         for (int j = 1; j <= m; j ++)
             scanf("%d", &a[i][j]);
     scanf("%d%d%d%d", &startx, &starty, &p, &q);
     book[startx][starty] = 1;
     dfs(startx, starty, 0);
     printf("%d", min);
     return 0;
 } 

P1037 [NOIP2002 普及组] 产生数

 #include <stdio.h>
 #include <string.h>
 #include <math.h>
 int sum;
 int cnt[10];
 int nxt[10][15];
 int book[10];
 int ans[30];
 void dfs (int x) //深度优先搜索
 {
     for (int i = 0; nxt[x][i] != 0; i ++)
     {
         if (book[nxt[x][i]] == 0)
         {
             sum ++;
             book[nxt[x][i]] = 1;
             dfs(nxt[x][i]);
         }   
     }
     return;
 }
 ​
 void mul (int r) // 高精度乘低精度处理
 {
     int up = 0;
     for (int i = 0; i < 30; i ++)
     {
         ans[i] = ans[i] * r + up;
         up = ans[i] / 10;
         ans[i] %= 10;
     }
 } 
 ​
 int main ()
 {
     char s[31];
     scanf("%s", s);
     int len = strlen(s);
     int num[10] = {};
     for (int i = 0; i < len; i ++)
     {
         num[s[i] - '0'] ++;
     }
     int k;
     scanf("%d", &k);
     int x;
     for (int i = 0; i < k; i ++)
     {
         scanf("%d", &x);
         scanf("%d", &nxt[x][cnt[x]++]);
     }
     int cot[10];
     for (int i = 0; i < 10; i ++)
     {
         memset(book, 0, sizeof(book));
         book[i] = 1;
         sum = 1;
         dfs(i);
         if (sum == 0)
         {
             sum = 1;
         }
         cot[i] = sum;
     }
     ans[0] = 1;
     for (int i = 0; i < 10; i ++)
     {
         for (int j = 0; j < num[i]; j ++)
         {
             mul(cot[i]);
         }
     }
     int flag = 0;
     for (int i = 30; i >= 0; i --)
     {
         if (flag == 0 && ans[i] == 0)
         {
             continue;
         } else
         {
             flag = 1;
             printf("%d", ans[i]);
         }
     }
     return 0;
 }

 // 再解炸弹人
 #include <stdio.h>
 char a[51][51];
 bool book[51][51];
 int nxt[4][2] = {{0, 1}, {1, 0}, {0, -1}, {-1, 0}};
 int max = -1;
 int n, m;
 int getnum (int i, int j)
 {
     int sum = 0;
     int x = i;
     int y = j;
     while (a[x][y] != '#')
     {
         if (a[x][y] == 'G')
         {
             sum ++;
         }
         x --;
     }
     x = i;
     y = j;
     while (a[x][y] != '#')
     {
         if (a[x][y] == 'G')
         {
             sum ++;
         }
         x ++;
     }
     x = i;
     y = j;
     while (a[x][y] != '#')
     {
         if (a[x][y] == 'G')
         {
             sum ++;
         }
         y --;
     }
     x = i;
     y = j;
     while (a[x][y] != '#')
     {
         if (a[x][y] == 'G')
         {
             sum ++;
         }
         y ++;
     }
     return sum;
 }
 void dfs (int x, int y)
 {
     int sum = getnum(x, y);
     if (sum > max)
     {
         max = sum;
     }
     for (int k = 0; k < 4; k ++)
     {
         int tx = x + nxt[k][0];
         int ty = y + nxt[k][1];
         if (tx < 1 || tx > n - 2 || ty < 1 || ty > m - 2)
         {
             continue;
         }
         if (a[tx][ty] == '.' && book[tx][ty] == 0)
         {
             book[tx][ty] = 1;
             dfs(tx, ty);
         }
     }
     return;
 }
 int main ()
 {
     int startx, starty;
     scanf("%d%d%d%d", &n, &m, &startx, &starty);
     for (int i = 0; i < n; i ++)
     {
         scanf("%s", a[i]);
     }
     book[startx][starty] = 1;
     dfs(startx, starty);
     printf("%d", max);
     return 0;
 }

 // 宝岛探险
 #include <stdio.h>
 int a[101][101];
 bool book[101][101];
 int n, m, sum;
 int nxt[4][2] = {{0, 1}, {1, 0}, {0, -1}, {-1, 0}};
 void dfs (int x, int y)
 {
     int tx, ty;
     for (int k = 0; k < 4; k ++)
     {
         tx = x + nxt[k][0];
         ty = y + nxt[k][1];
         if (tx < 1 || tx > n || ty < 1 || ty > m)
         {
             continue;
         } 
         if (a[tx][ty] > 0 && book[tx][ty] == 0)
         {
             sum ++;
             book[tx][ty] = 1;
             dfs(tx, ty);
         }
     }
     return;
 }
 int main ()
 {
     int startx, starty;
     scanf("%d%d%d%d", &n, &m, &startx, &starty);
     for (int i = 1; i <= n; i ++)
     {
         for (int j = 1; j <= m; j ++)
         {
             scanf("%d", &a[i][j]);
         }
     }
     book[startx][starty] = 1;
     sum = 1;
     dfs(startx, starty);
     printf("%d", sum);
     return 0;
 }

cout&cin优化

 using namespace std;
 ios::sync_with_stdio(false);
 cin.tie(NULL),cout.tie(NULL);

此段代码可优化cout、cin的效率

广度优先搜索

//解救小哈
#include <stdio.h>
struct note
{
	int x;
	int y;
	int f;
	int s;
};
int main ()
{
	struct note que[10001];
	int nxt[4][2] = {{0, 1}, {1, 0}, {0, -1}, {-1, 0}};
	int book[101][101] = {};
	
	//read
	int n, m;
	scanf("%d%d", &n, &m);
	int a[101][101];
	for (int i = 1; i <= n; i ++)
	{
		for (int j = 1; j <= m; j ++)
		{
			scanf("%d", &a[i][j]);	
		}
	}
	int startx, starty, p, q;
	scanf("%d%d%d%d", &startx, &starty, &p, &q);
	int head = 1;
	int tail = 1;
	que[tail].x = startx;
	que[tail].y = starty;
	que[tail].s = 0;
	que[tail].f = 0;
	tail ++;
	book[startx][starty] = 1;
	int flag = 0;
	while (head < tail)
	{
		for (int k = 0; k < 4; k ++)
		{
			int tx = que[head].x + nxt[k][0];
			int ty = que[head].y + nxt[k][1];
			if (tx < 1 || tx > n || ty > m || ty < 1)
			{
				continue;
			}
			if (a[tx][ty] == 0 && book[tx][ty] == 0)
			{
				book[tx][ty] = 1;
				que[tail].x = tx;
				que[tail].y = ty;
				que[tail].f = head;
				que[tail].s = que[head].s + 1;
				tail ++;		
			}
			if (tx == p && ty == q)
			{
				flag = 1;
				break;
			}
		}
		if (flag)
		{
			break;
		}
		head ++;
	}
	if (flag)
	{
		printf("%d", que[tail - 1].s);	
	} else
	{
		printf("No Way!");
	}
	getchar();getchar();
	return 0;
}

// 再解炸弹人
#include <stdio.h>
struct note 
{
	int x;
	int y;
};
char a[51][51];
int getnum (int i, int j)
{
	int sum = 0;
	int x = i;
	int y = j;
	while (a[x][y] != '#')
	{
		if (a[x][y] == 'G')
		{
			sum ++;
		}
		x --;
	}
	x = i;
	y = j;
	while (a[x][y] != '#')
	{
		if (a[x][y] == 'G')
		{
			sum ++;
		}
		x ++;
	}
	x = i;
	y = j;
	while (a[x][y] != '#')
	{
		if (a[x][y] == 'G')
		{
			sum ++;
		}
		y --;
	}
	x = i;
	y = j;
	while (a[x][y] != '#')
	{
		if (a[x][y] == 'G')
		{
			sum ++;
		}
		y ++;
	}
	return sum;
}
int main ()
{
	struct note que[2501];
	int nxt[4][2] = {{0, 1}, {1, 0}, {0, -1}, {-1, 0}};
	int n, m, startx, starty;
	scanf("%d%d%d%d/n", &n, &m, &startx, &starty);
	for (int i = 0; i < n; i ++)
	{
		scanf("%s", a[i]);
	}
	int head = 1;
	int tail = 1;
	que[tail].x = startx;
	que[tail].y = starty;
	tail ++;
	bool book[51][51];
	book[startx][starty] = 1;
	int max = getnum(startx, starty);
	while (head < tail)
	{
		int tx, ty;
		for (int k = 0; k < 4; k ++)
		{
			tx = que[head].x + nxt[k][0];
			ty = que[head].y + nxt[k][1];
			if (tx < 1 || tx > n - 2 || ty < 1 || ty > m - 2)
			{
				continue;
			}
			if (a[tx][ty] == '.' && book[tx][ty] == 0)
			{
				book[tx][ty] = 1;
				que[tail].x = tx;
				que[tail].y = ty;
				tail ++;
				int sum = getnum(tx, ty);
				if (sum > max)
				{
					max = sum;
				}
			}
		}
		head ++;
	}
	printf("%d", max);
	return 0;
}

// 宝岛探险
#include <stdio.h>
struct note
{
	int x;
	int y;
};
int main ()
{
	struct note que[10001];
	int nxt[4][2] = {{0, 1}, {1, 0}, {0, -1}, {-1, 0}};
	int n, m, startx, starty;
	scanf("%d%d%d%d", &n, &m, &startx, &starty);
	int a[101][101];
	bool book[101][101] = {};
	for (int i = 1; i <= n; i ++)
	{
		for (int j = 1; j <= m; j ++)
		{
			scanf("%d", &a[i][j]);
		}
	}
	int head = 1;
	int tail = 1;
	que[tail].x = startx;
	que[tail].y = starty;
	tail ++;
	book[startx][starty] = 1;
	int sum = 1;
	while (head < tail)
	{
		int tx, ty;
		for (int k = 0; k < 4; k ++)
		{
			tx = que[head].x + nxt[k][0];
			ty = que[head].y + nxt[k][1];
			if (tx < 1 || tx > n || ty < 1 || ty > m)
			{
				continue;
			}
			if (a[tx][ty] > 0 && book[tx][ty] == 0)
			{
				sum ++;
				book[tx][ty] = 1;
				que[tail].x = tx;
				que[tail].y = ty;
				tail ++;
			}
		}
		head ++;
	}
	printf("%d", sum);
	return 0;
}

Floodfill

漫水填充法(也称种子填充法)

求一个图中独立子图的个数

即查找周围与选中种子点相近(设置阈值)的种子点，并且将其入队，并进行扩展操作

多用于计算机图形学，图像分割识别，自动选中以及更改周围颜色相近的区域

// 宝岛探险 -- 小岛个数，以及染色
#include <stdio.h>
int a[101][101];
bool book[101][101];
int n, m;
int nxt[4][2] = {{0, 1}, {1, 0}, {0, -1}, {-1, 0}};
void dfs (int x, int y, int color)
{
	a[x][y] = color; //染色 
	int tx, ty;
	for (int k = 0; k < 4; k ++)
	{
		tx = x + nxt[k][0];
		ty = y + nxt[k][1];
		if (tx < 1 || tx > n || ty < 1 || ty > m)
		{
			continue;
		} 
		if (a[tx][ty] > 0 && book[tx][ty] == 0)
		{
			book[tx][ty] = 1;
			dfs(tx, ty, color);
		}
	}
	return;
}
int main ()
{
	scanf("%d%d", &n, &m);
	for (int i = 1; i <= n; i ++)
	{
		for (int j = 1; j <= m; j ++)
		{
			scanf("%d", &a[i][j]);
		}
	}
	int num = 0;
	for (int i = 1; i <= n; i ++)
	{
		for (int j = 1; j <= m; j ++)
		{
			if (a[i][j] > 0)
			{
				num --;
				book[i][j] = 1;
				dfs(i, j, num);
			}
		}
	}
	for (int i = 1; i <= n; i ++)
	{
		for (int j = 1; j <= m; j ++)
		{
			printf("%2d", a[i][j]);
		}
		printf("\n");
	}
	printf("有%d个小岛！", -num);
	return 0;
}