2012

第一题

时间复杂度:$O(n)$
空间复杂度:$O(n)$

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const int N = 100010;
int n;
int a[N];
int temp[N];

void print()
{
for(int i = 1; i <= n; i ++ ) cout << a[i] << " ";
cout << endl;
}

void solve()
{
int idx = 0;
for(int i = 1; i <= n; i ++ )
if(a[i] % 2 != 0)
temp[ ++ idx] = a[i];

for(int i = 1; i <= n; i ++ )
if(a[i] % 2 == 0)
temp[ ++ idx] = a[i];

for(int i = 1; i <= n; i ++ )
a[i] = temp[i];
}

int main()
{
cin >> n;
for(int i = 1; i <= n; i ++ ) cin >> a[i];
solve();
print();

return 0;
}

第二题

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#include <iostream>
#include <cstring>
#include <cstdio>
#include <algorithm>

using namespace std;

const int N = 100010;

char t[N], s[N], temp[N];
int idx;
int pos;
int n, m;

// char *function(){} 用于返回字符数组
void insert(char *t,char *s, int pos)
{
int n = 0, m = 0; // n记录t的长度,m记录s的长度
char *tt = t, *ts = s;
while(*t != '\0') // 计算t的长度
{
n ++ ;
t ++ ;
}

while(*s != '\0') // 计算s的长度
{
m ++ ;
s ++ ;
}

t = tt, s = ts;

// 将t中[0, pos - 1]插入temp中
for(int i = 0; i < pos; i ++ )
temp[idx ++ ] = t[i];

// 将 s插入temp中
for(int i = 0; i < m; i ++ )
temp[idx ++ ] = s[i];

// 将t中剩下的插入
for(int i = pos; i < n; i ++ )
temp[idx ++ ] = t[i];

// 将temp赋值给t
for(int i = 0; i < idx; i ++ )
t[i] = temp[i];
}

int main()
{
cin >> t >> s >> pos;

insert(t, s, pos);

cout << t << endl;

return 0;
}

第三题

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#include <iostream>
#include <cstring>
#include <cstdio>
#include <algorithm>

using namespace std;

const int N = 100010;
int n;

struct Node
{
int val;
Node *left, *right;

Node(): left(NULL), right(NULL) {}
Node(int _val): val(_val), left(NULL), right(NULL) {}
};

// 传参的时候一定要用 Node* &root,如果用 Node* root 那么传入的指针就变为形参了
void create(Node* &root, int x)
{
// 如果左右满足条件并且有子树
if(root->val > x && root->left != NULL) create(root->left, x);
if(root->val < x && root->right != NULL) create(root->right, x);

// 如果左右满足条件并且无子树
if(root->val > x && root->left == NULL)
{
root->left = new Node(x);
return;
}
if(root->val < x && root->right == NULL)
{
root->right = new Node(x);
return;
}
}

void print(Node *root) // 先序遍历
{
cout << root->val << " ";
if(root->left) print(root->left);
if(root->right) print(root->right);
}

int find(Node *root ,int x, int d)
{
if(root->val == x)
{
return d;
}

// 满足条件且左子树或右子树不为空
// 注意要链式返回return
if(root->val > x && root->left) return find(root->left, x, ++ d);
if(root->val < x && root->right) return find(root->right, x, ++ d);

return -1; // 说明没有这个值
}

int main()
{
cin >> n;
int x;
cin >> x;
Node *root = new Node(x); // 创建树根

for(int i = 1; i < n; i ++ ) // 创建二叉排序树
{
int x;
cin >> x;
create(root, x);
}

// print(root);

int d = 1;
cin >> x;
cout << find(root, x, d) << endl;

return 0;
}

2013

第一题

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#include <iostream>
#include <cstring>
#include <cstdio>
#include <algorithm>

using namespace std;

const int N = 100010;

char stk[N], q[N]; // stk:栈,q:队列
char a[N];

bool judge_stack(char *a, int len) // 用栈进行判断
{
int half = len / 2; // 折半
int tt = 0;
for(int i = 0; i < half; i ++ )
{
stk[ ++ tt] = *a;
a ++ ;
}

if(len % 2 != 0) a ++ ; // 如果字符长度为奇数,下标就要往后移动一位

for(int i = 0; i < half; i ++ )
{
char top = stk[tt -- ]; // 取出栈顶
if(top != *a) return false; // 如果不匹配,则匹配失败

a ++ ; // 否则移动一位继续匹配
}

return true;
}

bool judge_queue(char *a, int len) // 用队列判断
{
char *t = a;

int hh = 0, tt = -1;
int half = len / 2;
for(int i = 0; i < half; i ++ )
{
q[ ++ tt] = *a;
a ++ ;
}

int flag = 0;
if(len % 2 != 0) flag = 1 ; // 判断是否为奇数

a = t;

for(int i = len - 1; i > len / 2 + flag; i -- )
{
char val = q[hh ++ ];
if(val != a[i]) return false;
}

return true;
}

int main()
{
char t;
int len = 0;
while(cin >> t, t != '@')
{
a[len ++ ] = t;
}

cout << judge_stack(a, len) << endl;

cout << judge_queue(a, len) << endl;

return 0;
}

第二题

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#include <iostream>
#include <cstring>
#include <cstdio>
#include <algorithm>

using namespace std;

const int N = 10010;

int n;
int x;
struct Node
{
int val;
Node *left, *right;

Node(): left(NULL), right(NULL) {}
Node(int _val): val(_val), left(NULL), right(NULL) {}
};

void insert(Node* &root, int x)
{
if(root->val > x && root->left != NULL) insert(root->left, x);
if(root->val < x && root->right != NULL) insert(root->right, x);

if(root->val > x && root->left == NULL)
{
Node *node = new Node(x);
root->left = node;
}

if(root->val < x && root->right == NULL)
{
Node *node = new Node(x);
root->right = node;
}
}

bool find(Node *root, int x)
{
if(root->val == x) return true;
if(root->val > x && root->left != NULL) return find(root->left, x);
if(root->val < x && root->right != NULL) return find(root->right, x);

return false;
}

int main()
{
cin >> n;
cin >> x;
Node *root = new Node(x);
for(int i = 1; i < n; i ++ )
{
cin >> x;
insert(root, x);
}

cin >> x;
if(find(root, x)) puts("YES");
else puts("NO");

return 0;
}

第三题

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#include <iostream>
#include <cstring>
#include <cstdio>
#include <algorithm>

using namespace std;

const int N = 1010;

int n, m, v;
int g[N][N];
int dist[N];
bool st[N];

void dijkstra(int v)
{
memset(dist, 0x3f, sizeof dist);
dist[v] = 0;

for(int i = 0; i < n; i ++ )
{
int t = -1;
for(int j = 1; j <= n; j ++ )
if(!st[j] && (t == -1 || dist[t] > dist[j]))
t = j;

st[t] = true;

for(int j = 1; j <= n; j ++ )
if(dist[j] > dist[t] + g[t][j])
dist[j] = dist[t] + g[t][j];
}
}

int main()
{
cin >> n >> m >> v;

memset(g, 0x3f, sizeof g);

while(m -- )
{
int a, b, c;
cin >> a >> b >> c;
g[a][b] = min(g[a][b], c);
}

dijkstra(v);

long long sum = 0;
for(int i = 1; i <= n; i ++ ) sum += dist[i];
cout << sum << endl;

return 0;
}

2014

第一题

1

第二题

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#include <iostream>
#include <cstring>
#include <cstdio>
#include <algorithm>

using namespace std;

int n;
int x;

struct Node
{
int val;
Node *left, *right;

Node(): left(NULL), right(NULL) {}
Node(int _val): val(_val), left(NULL), right(NULL) {}
};

void insert(Node* &root, int x)
{
if(root->val > x && root->left != NULL) insert(root->left, x);
if(root->val < x && root->right != NULL) insert(root->right, x);

if(root->val > x && root->left == NULL)
{
Node *root = new Node(x);
root->left = root;
}

if(root->val < x && root->right == NULL)
{
Node *root = new Node(x);
root->right = root;
}
}

Node *find(Node *root, int x)
{
if(root->val == x) return root;

if(root->val > x && root->left != NULL) return find(root->left, x);
if(root->val < x && root->right != NULL) return find(root->right, x);

if(root->val > x && root->left == NULL) return NULL;
if(root->val < x && root->right == NULL) return NULL;
}

int main()
{
cin >> n;
cin >> x;
Node *root = new Node(x);
for(int i = 1; i < n; i ++ )
{
cin >> x;
insert(root, x);
}

cin >> x;
Node *res = find(root, x);

if(res == NULL) puts("NULL");
else cout << res->val << endl;

return 0;
}

第三题

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#include <iostream>
#include <cstring>
#include <cstdio>
#include <algorithm>

using namespace std;

const int N = 100010;

int n;
int tree[N]; // -1表示空节点

// 前序遍历
void preorder(int u)
{
cout << tree[u] << " ";
if(tree[2 * u] != -1 && 2 * u <= n) preorder(2 * u);
if(tree[2 * u + 1] != -1 && 2 * u + 1 <= n) preorder(2 * u + 1);
}

// 中序遍历
void inorder(int u)
{
if(tree[2 * u] != -1 && 2 * u <= n) inorder(2 * u);
cout << tree[u] << " ";
if(tree[2 * u + 1] != -1 && 2 * u + 1 <= n) inorder(2 * u + 1);
}

// 后序遍历
void postorder(int u)
{
if(tree[2 * u] != -1 && 2 * u <= n) postorder(2 * u);
if(tree[2 * u + 1] != -1 && 2 * u + 1 <= n) postorder(2 * u + 1);
cout << tree[u] << " ";
}

// 查找x在第几层
int find(int u, int x)
{
int t = 0;
for(int i = 1; i <= n; i ++ )
if(tree[i] == x)
{
t = i;
break;
}

if(t == 0) return -1;

int floor = 1;
while(t / 2)
{
floor ++ ;
t /= 2;
}

return floor;
}

int main()
{
cin >> n;
memset(tree, -1, sizeof tree);
for(int i = 1; i <= n; i ++ ) cin >> tree[i];

preorder(1);
cout << endl;

inorder(1);
cout << endl;

postorder(1);
cout << endl;

int x;
cin >> x;
cout << find(1, x) << endl;

return 0;
}

2015

第一题

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#include <iostream>
#include <cstring>
#include <cstdio>
#include <algorithm>

using namespace std;

const int N = 100010;

int stk[N], tt; // tt表示栈顶,为-1时栈为空

void init()
{
tt = -1;
}

bool Is_empty()
{
return tt == -1;
}

void Push(int x)
{
stk[ ++ tt] = x;
}

int Get()
{
return stk[tt -- ];
}

void Transform(int x)
{
init(); // 将栈初始化
while(x / 8)
{
int t = x % 8;
Push(t);
x /= 8;
}

if(x % 8 != 0) Push(x);
}

int main()
{
int x;
cin >> x;

Transform(x);

while(!Is_empty())
{
cout << Get();
}
cout << endl;

return 0;
}

第二题

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#include <iostream>
#include <cstring>
#include <cstdio>
#include <algorithm>

using namespace std;

struct Node
{
int val;
Node *left, *right;

Node(): left(NULL), right(NULL) {}
Node(int _val): val(_val), left(NULL), right(NULL){}
};

void build(Node* &root, int deep)
{
cout << "当前在第:" << deep << "层" << endl;
Node *left_node = new Node();
Node *right_node = new Node();

cout << "输入左、右的值(输入-1则置为空节点)" << endl;
int left_val, right_val;
cin >> left_val >> right_val;

if(left_val != -1)
{
left_node->val = left_val;
root->left = left_node;
build(left_node, ++ deep);
deep -- ;
}

if(right_val != -1)
{
right_node->val = right_val;
root->right = right_node;
build(right_node, ++ deep);
deep -- ;
}
}

// 前序
void preorder(Node* &root)
{
cout << root->val << " ";
if(root->left != NULL) preorder(root->left);
if(root->right != NULL) preorder(root->right);
}

// 中序
void inorder(Node* &root)
{
if(root->left != NULL) inorder(root->left);
cout << root->val << " ";
if(root->right != NULL) inorder(root->right);
}

// 后序
void postorder(Node* &root)
{
if(root->left != NULL) postorder(root->left);
if(root->right != NULL) postorder(root->right);
cout << root->val << " ";
}

// 清除
bool delete_tree(Node* &root)
{
if(root->left != NULL) delete_tree(root->left);
if(root->right != NULL) delete_tree(root->right);

delete root;
}

/*
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*/

int main()
{
cout << "输入根节点的值" << endl;
int x;
cin >> x;
Node *root = new Node(x);
build(root, 2);

if(root != NULL) preorder(root);
cout << endl;

if(root != NULL) inorder(root);
cout << endl;

if(root != NULL) postorder(root);
cout << endl;

delete_tree(root);
root = NULL;

return 0;
}

第三题

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#include <iostream>
#include <cstring>
#include <cstdio>
#include <algorithm>

using namespace std;

const int N = 200010;

int n, m, Size;
int a[N];

void down(int u)
{
int t = u;
if(2 * u <= Size && a[t] < a[2 * u]) t = 2 * u;
if(2 * u + 1 <= Size && a[t] < a[2 * u + 1]) t = 2 * u + 1;

if(t != u)
{
swap(a[t], a[u]);
down(t);
}
}

int main()
{
cin >> n >> m;
Size = n;
for(int i = 1; i <= n; i ++ ) cin >> a[i];

for(int i = n / 2; i >= 1; i -- ) down(i);

while(m -- )
{
cout << a[1] << " ";
swap(a[1], a[Size]);
Size -- ;
down(1);
}
cout << endl;
return 0;
}

2016

第一题

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#include <iostream>
#include <cstring>
#include <cstdio>
#include <algorithm>

using namespace std;

const int N = 100010;

// ¶¨Òå˳ÐòÕ»£¬topΪջ¶¥£¬top == -1ʱΪ¿Õ
char stk[N];
int top = -1;

struct Node
{
char val;
Node *next;

Node(): next(NULL) {}
Node(char _val): val(_val), next(NULL) {}
};


// Õ»Ïà¹Ø
void Init_stack()
{
top = -1;
}

void Push_stack(char x)
{
stk[ ++ top] = x;
}

char Top_stack()
{
char t = stk[top];
top -- ;
return t;
}

bool Is_empty_stack()
{
return top == -1;
}

bool Judge_stack(char str[])
{
int len = strlen(str);
int mid = len / 2;
int flag = 0;
if(len % 2 == 0) flag = 0;
else flag = 1;

Init_stack();
for(int i = 0; i < mid; i ++ ) Push_stack(str[i]);

for(int i = mid + flag; i < len; i ++ )
if(Top_stack() != str[i])
return false;

return true;
}


// ¶ÓÁÐÏà¹Ø
void Init_queue(Node* &front, Node* &rear)
{
Node* t;
while(front->next != NULL)
{
t = front;
front = front->next;
delete t;
}
front = new Node();
rear = front;
}

void Print_queue(Node *front)
{
if(front->next != NULL) front = front->next;
else return;
while(front != NULL)
{
cout << front->val << " ";
front = front->next;
}
cout << endl;
}

void Push_queue(Node* &rear, char x)
{
Node *node = new Node(x);
rear->next = node;
rear = rear->next;
}

char Front_queue(Node* &front, Node* &rear)
{
if(front == NULL) return '-1';

char res = front->val;
Node* t = front;
if(front->next != NULL)
{
front = front->next;
delete t;
}
else Init_queue(front, rear);

return res;
}

bool Judge_queue(Node* &front, Node* &rear, char str[])
{
int len = strlen(str);
int mid = len / 2;
int flag = 0;
if(len % 2 == 0) flag = 0;
else flag = 1;

Init_queue(front, rear);

for(int i = 0; i < mid; i ++ )
Push_queue(rear, str[i]);

if(front->next != NULL) front = front->next;
// ʹµÃfrontÍùºóÒƶ¯Ò»Î»
// ÒòΪ³õʼ»¯µÄʱºòfrontµÈÓÚÒ»¸ö¿Õ½Úµã

for(int i = len - 1; i >= mid + flag; i -- )
{
char t = Front_queue(front, rear);
if(t != str[i])
return false;
}

return true;
}

int main()
{
Node *front = new Node();
Node *rear = front;

char str[N];
cin >> str;
cout << Judge_stack(str) << endl;
cout << Judge_queue(front, rear, str) << endl;

}

第二题

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#include <iostream>
#include <string>
#include <cstdio>
#include <algorithm>

using namespace std;

struct Node
{
int val;
Node *left, *right;

Node(): left(NULL), right(NULL) {}
Node(int _val): val(_val), left(NULL), right(NULL) {}
};

void build(Node* &root, int deep)
{
cout << "输入第" << deep << "层的左右节点值(-1表示为空):" << endl;
int left_val, right_val;
cin >> left_val >> right_val;

if(~left_val)
{
Node *left_node = new Node(left_val);
root->left = left_node;
build(root->left, ++ deep);
deep -- ;
}
if(~right_val)
{
Node *right_node = new Node(right_val);
root->right = right_node;
build(root->right, ++ deep);
deep -- ;
}
}

void preorder(Node *root)
{
cout << root->val << " ";
if(root->left != NULL) preorder(root->left);
if(root->right != NULL) preorder(root->right);
}

void inorder(Node *root)
{
if(root->left != NULL) inorder(root->left);
cout << root->val << " ";
if(root->right != NULL) inorder(root->right);
}

void postorder(Node *root)
{
if(root->left != NULL) postorder(root->left);
if(root->right != NULL) postorder(root->right);
cout << root->val << " ";
}

// flag表示当前节点为父节点的左/右儿子,1为左,2为右
// last表示上一层的节点
void delete_tree(Node* &last, Node* &root, int flag)
{
if(root->left != NULL) delete_tree(root, root->left, 1);
if(root->right != NULL) delete_tree(root, root->right, 2);

// 由于是递归处理,执行到此句时一定是根节点往父节点走
if(flag == 1) delete last->left; // 如果当前节点为父节点的左儿子,从父节点删除此节点
else delete last->right;
}

int main()
{
int x;
cout << "输入树根节点的值:" << endl;
cin >> x;
Node *root = new Node(x);

build(root, 2);

preorder(root);
puts("");

inorder(root);
puts("");

postorder(root);
puts("");

delete_tree(root, root, 0);
delete root;

return 0;
}

第三题

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#include <iostream>
#include <cstring>
#include <cstdio>
#include <algorithm>

using namespace std;

const int N = 80010;

int a[N], Size;
int n, m;

void down(int u)
{
int t = u;
if(u * 2 <= Size && a[t] < a[u * 2]) t = u * 2;
if(u * 2 + 1 <= Size && a[t] < a[u * 2 + 1]) t = u * 2 + 1;
if(t != u)
{
swap(a[t], a[u]);
down(t);
}
}

int main()
{
cin >> n >> m;
Size = n;
for(int i = 1; i <= n; i ++ ) cin >> a[i];

for(int i = n / 2; i >= 1; i -- ) down(i);

while(m -- )
{
cout << a[1] << " ";
a[1] = a[Size];
Size -- ;
down(1);
}

return 0;
}