CDxxx 从 5 随机到 7 随机及其扩展
/* rand1To5实现等概率随机产生1~7的随机函数rand1To7 */
public int rand1To5()
{
return (int) (Math.random() * 5) + 1;
}
public int rand1To7()
{
int num = 0;
do
{
num = (rand1To5() - 1) * 5 + rand1To5() - 1;
}
while (num > 20);
return num % 7 + 1;
}
/* 用rand01p实现等概率随机产生1~6的随机函数rand1To6。*/
public int rand01p()
{
// 可随意改变 p
double p = 0.83;
return Math.random() < p ? 0 : 1;
}
public int rand01()
{
int num;
do
{
num = rand01p();
}
while (num == rand01p());
return num;
}
public int rand0To3()
{
return rand01() * 2 + rand01();
}
public int rand1To6()
{
int num = 0;
do
{
num = rand0To3() * 4 + rand0To3();
}
while (num > 11);
return num % 6 + 1;
}
/* 用rand1ToM(m)实现等概率随机产生1~n的随机函数rand1ToN。*/
public int rand1ToM(int m)
{
return (int) (Math.random() * m) + 1;
}
public int rand1ToN(int n, int m)
{
int[] nMSys = getMSysNum(n - 1, m);
int[] randNum = getRanMSysNumLessN(nMSys, m);
return getNumFromMSysNum(randNum, m) + 1;
}
// 把 value 转成 m 进制数
public int[] getMSysNum(int value, int m)
{
int[] res = new int[32];
int index = res.length - 1;
while (value != 0)
{
res[index--] = value % m;
value = value / m;
}
return res;
}
// 等概率随机产生一个 0~nMsys 范围的数，只不过是用 m 进制数表达的
public int[] getRanMSysNumLessN(int[] nMSys, int m)
{
int[] res = new int[nMSys.length];
int start = 0;
while (nMSys[start] == 0) start++;
int index = start;
boolean lastEqual = true;
while (index != nMSys.length)
{
res[index] = rand1ToM(m) - 1;
if (lastEqual)
{
if (res[index] > nMSys[index])
{
index = start;
lastEqual = true;
continue;
}
else
lastEqual = res[index] == nMSys[index];
}
index++;
}
return res;
}
// 把 m 进制数转换成十进制数
public int getNumFromMSysNum(int[] mSysNum, int m)
{
int res = 0;
for (int i = 0; i != mSysNum.length; i++)
res = res * m + mSysNum[i];
return res;
}
CD55 一行代码求两个数的最大公约数
public class CD55_1
{
public static int solution(int m, int n)
{
return n == 0 ? m : solution(n, m % n);
}
public static void main(String[] args)
{
Scanner in = new Scanner(System.in);
int n, m;
n = in.nextInt();
m = in.nextInt();
System.out.println(solution(n, m));
}
}
CD56 有关阶乘的两个问题1
/* 因子5的个数 */
public class CD56_1
{
public static long solution(long num)
{
if (num < 0) return 0;
long res = 0;
while (num != 0)
{
res += num / 5;
num /= 5;
}
return res;
}
public static void main(String[] args)
{
Scanner in = new Scanner(System.in);
long n;
n = in.nextLong();
System.out.println(solution(n));
}
}
CD57 有关阶乘的两个问题
public class CD57_1
{
/* 2的因子 */
public static long solution1(long num)
{
if (num < 1) return -1;
long res = 0;
while (num != 0)
{
num >>= 1;
res += num;
}
return res;
}
/*
* 如果把N!的结果中因子2的总个数记为Z,
* 把N的二进制数表达式中1的个数记为m,
* 还存在如下一个关系 Z = N - m，
*/
public static long solution2(long num)
{
if (num < 1) return -1;
long ones = 0;
long tmp = num;
while (tmp != 0)
{
ones += (tmp & 1) != 0 ? 1 : 0;
tmp >>= 1;
}
return num - ones;
}
public static void main(String[] args)
{
Scanner in = new Scanner(System.in);
long n = in.nextLong();
System.out.println(solution1(n));
}
}
CD58 判断一个点是否在矩形内部
public class CD58_1
{
public static boolean solution(double x1, double y1, double x2, double y2,
double x3, double y3, double x4, double y4,
double x, double y)
{
if (y1 == y2) return isInside(x1, y1, x4, y4, x, y);
double l = Math.abs(y4 - y3);
double k = Math.abs(x4 - x3);
double s = Math.sqrt(k * k + l * l);
double sin = l / s;
double cos = k / s;
double x1R = cos * x1 + sin * y1;
double y1R = -x1 * sin + y1 * cos;
double x4R = cos * x4 + sin * y4;
double y4R = -x4 * sin + y4 * cos;
double xR = cos * x + sin * y;
double yR = -x * sin + y * cos;
return isInside(x1R, y1R, x4R, y4R, xR, yR);
}
public static boolean isInside(double x1, double y1, double x4, double y4, double x, double y)
{
if (x <= x1 || x >= x4 || y >= y1 || y <= y4)
return false;
else return true;
}
public static void main(String[] args)
{
Scanner in = new Scanner(System.in);
double[][] points = new double[5][2];
for (int i = 0; i < points.length; i++)
{
points[i][0] = in.nextDouble();
points[i][1] = in.nextDouble();
}
System.out.println(solution(points[0][0], points[0][1], points[1][0], points[1][1],
points[2][0], points[2][1], points[3][0], points[3][1],
points[4][0], points[4][1]) ? "Yes" : "No");
}
}
CD59 判断一个点是否在三角形内部
/* 如果点O在三角形ABC中,
* 那么从三角形的一点出发,
* 逆时针走过所有边的过程中,
* 点O始终都在走过边的左侧。
*/
public class CD59_1
{
public static boolean solution(double x1, double y1, double x2, double y2,
double x3, double y3, double x, double y)
{
if (crossProduct(x3 - x1, y3 - y1, x2 - x1, y2 - y1) >= 0)
{
double tmpx = x2;
double tmpy = y2;
x2 = x3;
y2 = y3;
x3 = tmpx;
y3 = tmpy;
}
if (crossProduct(x2 - x1, y2 - y1, x - x1, y - y1) < 0)
return false;
if (crossProduct(x3 - x2, y3 - y2, x - x2, y - y2) < 0)
return false;
if (crossProduct(x1 - x3, y1 - y3, x - x3, y - y3) < 0)
return false;
return true;
}
public static double crossProduct(double x1, double y1, double x2, double y2)
{
return x1 * y2 - x2 * y1;
}
public static void main(String[] args)
{
Scanner in = new Scanner(System.in);
double[][] points = new double[4][2];
for (int i = 0; i < points.length; i++)
{
points[i][0] = in.nextDouble();
points[i][1] = in.nextDouble();
}
System.out.println(solution(points[0][0], points[0][1], points[1][0], points[1][1],
points[2][0], points[2][1], points[3][0], points[3][1]) ? "Yes" : "No");
}
}
CD60 折纸问题
public class CD60_1
{
public static PrintWriter out = new PrintWriter(System.out);
public static void solution(int n)
{
process(1, n, true);
}
public static void process(int i, int N, boolean down)
{
if (i > N) return;
process(i + 1, N, true);
out.println(down ? "down " : "up ");
process(i + 1, N, false);
}
public static void main(String[] args)
{
Scanner in = new Scanner(System.in);
int n = in.nextInt();
solution(n);
out.flush();
}
}
CD61 能否完美地拼成矩形
/*
* 1. 大矩形面积 = 小矩形面积之和
* 2. 除大矩形的四个顶点只出现 1 次之外，其他任何小矩形的顶点都必须出现偶数次
*/
public class CD61_1
{
public static boolean solution(int[][] arr)
{
int ldx = Integer.MAX_VALUE, ldy = Integer.MAX_VALUE, rux = Integer.MIN_VALUE, ruy = Integer.MIN_VALUE;
int area = 0;
HashSet<String> set = new HashSet<>();
for (int[] rec : arr)
{
if (ldx > rec[0] || (ldx == rec[0] && ldy > rec[1]))
{
ldx = rec[0];
ldy = rec[1];
}
if (rux < rec[2] || (rux == rec[2] && ruy < rec[3]))
{
rux = rec[2];
ruy = rec[3];
}
area += (rec[2] - rec[0]) * (rec[3] - rec[1]);
String leftDown = rec[0] + "_" + rec[1];
String leftUp = rec[0] + "_" + rec[3];
String rightDown = rec[2] + "_" + rec[1];
String rightUp = rec[2] + "_" + rec[3];
if (!set.add(leftDown)) set.remove(leftDown);
if (!set.add(leftUp)) set.remove(leftUp);
if (!set.add(rightDown)) set.remove(rightDown);
if (!set.add(rightUp)) set.remove(rightUp);
}
if (!set.contains(ldx + "_" + ldy) || !set.contains(ldx + "_" + ruy) || !set.contains(rux + "_" + ruy) || !set.contains(rux + "_" + ldy) || set.size() != 4)
return false;
else
return area == (rux - ldx) * (ruy - ldy);
}
public static void main(String[] args)
{
Scanner in = new Scanner(System.in);
int n = in.nextInt();
int[][] arr = new int[n][4];
for (int i = 0; i < n; i++)
for (int j = 0; j < arr[0].length; j++)
arr[i][j] = in.nextInt();
System.out.println(solution(arr) ? "Yes" : "No");
}
}
CDxxx 蓄水池算法
public int rand(int max)
{
return (int) (Math.random() * max) + 1;
}
public int[] getKNumsRand(int k, int max)
{
if (max < 1 || k < 1)
return null;
int[] res = new int[Math.min(k, max)];
for (int i = 0; i != res.length; i++)
res[i] = i + 1; // 前 k 个数直接进袋子
for (int i = k + 1; i < max + 1; i++)
{
if (rand(i) <= k) // 决定 i 进不进袋子
res[rand(k) - 1] = i; // i 随机替掉袋子中的一个
}
return res;
}
CD62 设计有 setAll 功能的哈希表
public class CD62_1
{
public static class MyValue
{
private Integer value;
private long time;
public MyValue(Integer value, long time)
{
this.value = value;
this.time = time;
}
public Integer getValue()
{
return this.value;
}
public long getTime()
{
return this.time;
}
}
public static class MyHashMap
{
private HashMap<Integer, MyValue> baseMap;
private long time;
private MyValue setAll;
public MyHashMap()
{
this.baseMap = new HashMap<Integer, MyValue>();
this.time = 0;
this.setAll = new MyValue(null, -1);
}
public boolean containsKey(Integer key)
{
return this.baseMap.containsKey(key);
}
public void put(Integer key, Integer value)
{
this.baseMap.put(key, new MyValue(value, this.time++));
}
public void setAll(Integer value)
{
this.setAll = new MyValue(value, this.time++);
}
public int get(Integer key)
{
if (this.containsKey(key))
{
if (this.baseMap.get(key).getTime() > this.setAll.getTime())
return this.baseMap.get(key).getValue();
else
return this.setAll.getValue();
}
else
return -1;
}
}
public static void main(String[] args)
{
MyHashMap myMap = new MyHashMap();
Scanner in = new Scanner(System.in);
int op, num1, num2, n;
n = in.nextInt();
while (n-- > 0)
{
op = in.nextInt();
switch (op)
{
case 1:
num1 = in.nextInt();
num2 = in.nextInt();
myMap.put(num1, num2);
break;
case 2:
num1 = in.nextInt();
System.out.println(myMap.get(num1));
break;
case 3:
num1 = in.nextInt();
myMap.setAll(num1);
break;
}
}
}
}
CD63 最大的 leftMax 与 rightMax 之差的绝对值
public class CD63_1
{
public static int solution(int[] arr)
{
int[] lArr = new int[arr.length];
int[] rArr = new int[arr.length];
lArr[0] = arr[0];
rArr[arr.length - 1] = arr[arr.length - 1];
for (int i = 1; i < arr.length; i++)
lArr[i] = Math.max(lArr[i - 1], arr[i]);
for (int i = arr.length - 2; i > -1; i--)
rArr[i] = Math.max(rArr[i + 1], arr[i]);
int ans = 0;
for (int i = 0; i < arr.length - 1; i++)
ans = Math.max(ans, Math.abs(lArr[i] - rArr[i + 1]));
return ans;
}
public static void main(String[] args)
{
Scanner in = new Scanner(System.in);
int n = in.nextInt();
int[] arr = new int[n];
for (int i = 0; i < n; i++)
arr[i] = in.nextInt();
System.out.println(solution(arr));
}
}
public class CD63_2
{
public static int solution(int[] arr)
{
int ans = Integer.MIN_VALUE;
for (int num : arr) ans = Math.max(num, ans);
return ans - Math.min(arr[0], arr[arr.length - 1]);
}
public static void main(String[] args)
{
Scanner in = new Scanner(System.in);
int n = in.nextInt();
int[] arr = new int[n];
for (int i = 0; i < n; i++)
arr[i] = in.nextInt();
System.out.println(solution(arr));
}
}
CD64 设计 LRU 缓存结构
public class CD64_1
{
public static class Node
{
public Integer value;
public Node last;
public Node next;
public Node(Integer value)
{
this.value = value;
}
}
public static class NodeDoubleLinkedList
{
private Node head;
private Node tail;
public NodeDoubleLinkedList()
{
this.head = null;
this.tail = null;
}
public void addNode(Node newNode)
{
if (newNode == null)
return;
if (this.head == null)
{
this.head = newNode;
this.tail = newNode;
}
else
{
this.tail.next = newNode;
newNode.last = this.tail;
this.tail = newNode;
}
}
public void moveNodeToTail(Node node)
{
if (this.tail == node) return;
if (this.head == node)
{
this.head = node.next;
this.head.last = null;
}
else
{
node.last.next = node.next;
node.next.last = node.last;
}
node.last = this.tail;
node.next = null;
this.tail.next = node;
this.tail = node;
}
public Node removeHead()
{
if (this.head == null) return null;
Node res = this.head;
if (this.head == this.tail)
{
this.head = null;
this.tail = null;
}
else
{
this.head = res.next;
res.next = null;
this.head.last = null;
}
return res;
}
}
public static class MyCache
{
private HashMap<Integer, Node> keyNodeMap;
private HashMap<Node, Integer> nodeKeyMap;
private NodeDoubleLinkedList nodeList;
private int capacity;
public MyCache(int capacity)
{
if (capacity < 1)
throw new RuntimeException("should be more than 0.");
this.keyNodeMap = new HashMap<>();
this.nodeKeyMap = new HashMap<>();
this.nodeList = new NodeDoubleLinkedList();
this.capacity = capacity;
}
public Integer get(Integer key)
{
if (this.keyNodeMap.containsKey(key))
{
Node res = this.keyNodeMap.get(key);
this.nodeList.moveNodeToTail(res);
return res.value;
}
return -1;
}
public void set(Integer key, Integer value)
{
if (this.keyNodeMap.containsKey(key))
{
Node node = this.keyNodeMap.get(key);
node.value = value;
this.nodeList.moveNodeToTail(node);
}
else
{
Node newNode = new Node(value);
this.keyNodeMap.put(key, newNode);
this.nodeKeyMap.put(newNode, key);
this.nodeList.addNode(newNode);
if (this.keyNodeMap.size() == this.capacity + 1)
this.removeMostUnusedCache();
}
}
private void removeMostUnusedCache()
{
Node removeNode = this.nodeList.removeHead();
Integer removeKey = this.nodeKeyMap.get(removeNode);
this.nodeKeyMap.remove(removeNode);
this.keyNodeMap.remove(removeKey);
}
}
public static void main(String[] args)
{
Scanner in = new Scanner(System.in);
int op, num1, num2, n, k;
n = in.nextInt();
k = in.nextInt();
MyCache myCache = new MyCache(k);
while (n-- > 0)
{
op = in.nextInt();
switch (op)
{
case 1:
num1 = in.nextInt();
num2 = in.nextInt();
myCache.set(num1, num2);
break;
case 2:
num1 = in.nextInt();
System.out.println(myCache.get(num1));
break;
}
}
}
}
CD65 LFU 缓存结构设计
public class CD65_1
{
public static class Node
{
public Integer key;
public Integer value;
public Integer times; // 发生get或set的次数总和
public Node up;
public Node down;
public Node(int key, int value, int times)
{
this.key = key;
this.value = value;
this.times = times;
}
}
public static class NodeList
{
public Node head;
public Node tail;
public NodeList last;
public NodeList next;
public NodeList(Node node)
{
head = node;
tail = node;
}
public void addNodeFromHead(Node newHead)
{
newHead.down = head;
head.up = newHead;
head = newHead;
}
public boolean isEmpty()
{
return head == null;
}
public void deleteNode(Node node)
{
if (head == tail)
{
head = null;
tail = null;
}
else
{
if (node == head)
{
head = node.down;
head.up = null;
}
else if (node == tail)
{
tail = node.up;
tail.down = null;
}
else
{
node.up.down = node.down;
node.down.up = node.up;
}
}
node.up = null;
node.down = null;
}
}
public static class LFUCache
{
private int capacity; // 缓存的大小限制
private int size; // 缓存目前有多少个节点
private HashMap<Integer, Node> records;// 表示节点(Node)在哪个桶(NodeList)里
private HashMap<Node, NodeList> heads;
private NodeList headList; // 整个结构中位于最左的桶
public LFUCache(int K)
{
this.capacity = K;
this.size = 0;
this.records = new HashMap<>();
this.heads = new HashMap<>();
headList = null;
}
// removeNodeList：刚刚减少了一个节点的桶
private boolean modifyHeadList(NodeList removeNodeList)
{
if (removeNodeList.isEmpty())
{
if (headList == removeNodeList)
{
headList = removeNodeList.next;
if (headList != null)
headList.last = null;
}
else
{
removeNodeList.last.next = removeNodeList.next;
if (removeNodeList.next != null)
removeNodeList.next.last = removeNodeList.last;
}
return true;
}
return false;
}
// node 这个节点的次数+1 了，这个节点原来在 oldNodeList 里。
// 把 node 从 oldNodeList 删掉，然后放到次数+1 的桶中
private void move(Node node, NodeList oldNodeList)
{
oldNodeList.deleteNode(node);
NodeList preList = modifyHeadList(oldNodeList) ? oldNodeList.last : oldNodeList;
NodeList nextList = oldNodeList.next;
if (nextList == null)
{
NodeList newList = new NodeList(node);
if (preList != null)
preList.next = newList;
newList.last = preList;
if (headList == null)
headList = newList;
heads.put(node, newList);
}
else
{
if (nextList.head.times.equals(node.times))
{
nextList.addNodeFromHead(node);
heads.put(node, nextList);
}
else
{
NodeList newList = new NodeList(node);
if (preList != null) preList.next = newList;
newList.last = preList;
newList.next = nextList;
nextList.last = newList;
if (headList == nextList)
headList = newList;
heads.put(node, newList);
}
}
}
public void set(int key, int value)
{
if (records.containsKey(key))
{
Node node = records.get(key);
node.value = value;
node.times++;
NodeList curNodeList = heads.get(node);
move(node, curNodeList);
}
else
{
if (size == capacity)
{
Node node = headList.tail;
headList.deleteNode(node);
modifyHeadList(headList);
records.remove(node.key);
heads.remove(node);
size--;
}
Node node = new Node(key, value, 1);
if (headList == null)
headList = new NodeList(node);
else
{
if (headList.head.times.equals(node.times))
headList.addNodeFromHead(node);
else
{
NodeList newList = new NodeList(node);
newList.next = headList;
headList.last = newList;
headList = newList;
}
}
records.put(key, node);
heads.put(node, headList);
size++;
}
}
public Integer get(int key)
{
if (!records.containsKey(key)) return -1;
Node node = records.get(key);
node.times++;
NodeList curNodeList = heads.get(node);
move(node, curNodeList);
return node.value;
}
}
public static void main(String[] args)
{
Scanner in = new Scanner(System.in);
int op, num1, num2, n, k;
n = in.nextInt();
k = in.nextInt();
LFUCache lfuCache = new LFUCache(k);
while (n-- > 0)
{
op = in.nextInt();
switch (op)
{
case 1:
num1 = in.nextInt();
num2 = in.nextInt();
lfuCache.set(num1, num2);
break;
case 2:
num1 = in.nextInt();
System.out.println(lfuCache.get(num1));
break;
}
}
}
}
CDxxx 设计 RandomPool 结构
public class Pool<K>
{
private HashMap<K, Integer> keyIndexMap;
private HashMap<Integer, K> indexKeyMap;
private int size;
public Pool()
{
this.keyIndexMap = new HashMap<K, Integer>();
this.indexKeyMap = new HashMap<Integer, K>();
this.size = 0;
}
public void insert(K key)
{
if (!this.keyIndexMap.containsKey(key))
{
this.keyIndexMap.put(key, this.size);
this.indexKeyMap.put(this.size++, key);
}
}
public void delete(K key)
{
if (this.keyIndexMap.containsKey(key))
{
int deleteIndex = this.keyIndexMap.get(key);
int lastIndex = --this.size;
K lastKey = this.indexKeyMap.get(lastIndex);
this.keyIndexMap.put(lastKey, deleteIndex);
this.indexKeyMap.put(deleteIndex, lastKey);
this.keyIndexMap.remove(key);
this.indexKeyMap.remove(lastIndex);
}
}
public K getRandom()
{
if (this.size == 0) return null;
int randomIndex = (int) (Math.random() * this.size);
return this.indexKeyMap.get(randomIndex);
}
}
