为了方便显示，我们假定拥有以下函数以供调用：
public static void print(int[] seq) {
System.out.println(Arrays.toString(seq));
}
public static void print(double[] seq) {
System.out.println(Arrays.toString(seq));
}
public static void print(int val) {
System.out.println(val);
}
public static void print(String str) {
System.out.println(str);
}InsertionSort:
int[] seq = {10,4,5};
InsertionSort is = new InsertionSort(seq,InsertionSort.InsertionSortType.ascending);
print(is.sort());
print("InsertionSortWithRecursion: " + is.sortWithRecursion());LinearQuery:
int[] lq_A = {1,4,6,13};
int v = 6;
LineQuery lq = new LineQuery(lq_A,v);
print("lineQuery: " + lq.query());
int[] lq_B = {1,2,3,14};
int v_d = 16;
LineQuery lq_d = new LineQuery(lq_B,v_d);
print("dichotomy: " + lq_d.queryWithDichotomy());BinaryAddition
int[] _A = {1,1,0,1,1,0,1,1,1,0};
int[] B = {1,0,0,0,1,0,0,1,0,1};
BinaryAddition ba = BinaryAddition.create(_A,B);
ba.add();
print(ba.A);
print(ba.B);
print(ba.C);SelectionSort
int[] ss_A = {1,4,7,9,10,3,20,8,3,2,4,4};
SelectionSort ss = new SelectionSort(ss_A);
print(ss_A);
print(ss.sort());MergeSort
int[] ms_A = {6,5,4,3,2,7};
MergeSort ms = new MergeSort(ms_A);
print("MergeSort: ");
print(ms_A);
print(ms.sort(false));
print("Inversion: " + ms.inversion);BubbleSort
int[] bs_A = {1,4,2,9,5,18,15,17,12};
BubbleSort bs = new BubbleSort(bs_A);
print("BubbleSort: ");
print(bs_A);
print(bs.sort());Horner
int[] hornerA = {20,20,3,6,9,12};
int x = 8;
Horner h = new Horner(hornerA,x);
print("Horner: ");
print("Normal: " + h.normalCal());
print("Special: " + h.specialCal());FindMaximumSubArray
int[] fmsa_B = {0,1,-5,6};
FindMaximumSubArray.SubSeq recursion = FindMaximumSubArray.recursionFind(fmsa_B);
FindMaximumSubArray.SubSeq violentFind = FindMaximumSubArray.violentFind(fmsa_B);
FindMaximumSubArray.SubSeq lineFind = FindMaximumSubArray.LinearFind(fmsa_B);
print("FindMaximumSubArray: ");
print(fmsa_A);
print("recursion: [low: " + recursion.low + ", high: " + recursion.high + ", sum: " + recursion.sum + "]");
print("violentFind: [low: " + violentFind.low + ", high: " + violentFind.high + ", sum: " + violentFind.sum + "]") ;
print("lineFind: [low: " + lineFind.low + ", high: " + lineFind.high + ", sum: " + lineFind.sum + "]");Strassen
Square-Matrix-Multyply-Recursive
int[][] mA = {
{1,1,1,1},
{1,1,1,1},
{1,1,1,1},
{2,10,1,5}
};
int[][] mB = {
{1,1,1,1},
{1,1,1,1},
{1,1,1,1},
{1,1,1,1}
};
int[][] strassen = SquareMatrixMultiply.multi(mA,mB);
for (int i = 0; i < strassen.length; i++) {
print(strassen[i]);
}HireAssistant
HireAssistant hire = new HireAssistant();
print("HireAssistant: ");
print("Directly: ");
hire.hireDirectly(1,2,3,4,5);
print("Randomly: ");
hire.hireRandomly(1,2,3,4,5);HeapSort
int[] hps_A = {6,1,5,3,2,4};
print("HeapSort: ");
print(hps_A);
HeapSort.sort(hps_A);
print(hps_A);PriorityQueue
int[] pq_A = {1,3,2,5,4};
PriorityQueue pq = new PriorityQueue(pq_A);
print("PriorityQueue:");
System.out.print("Raws:"); pq.printRaw();
System.out.print("Heap:"); pq.printHeap();
print("Maximum:" + pq.maximum());
pq.extractMax();
System.out.print("ExtractMax:");pq.printHeap();
pq.insert(10);
System.out.print("Insert:");pq.printHeap();
pq.increaseKey(1,15);
System.out.print("IncreseKey:");pq.printHeap();QuickSort
int[] qs_A = {3,7,6,5,4,4};
print("QuickSort:");
print(qs_A);
QuickSort.isAscending = false;
QuickSort.sort(qs_A);
print(qs_A);CountingSort
int[] cs_A = {6,8,4,2,2,1,4,7,5,13,16,18,20,14,15};
int[] cs_B = CountingSort.sort(cs_A);
print("CountingSort:");
print(cs_A);
print(cs_B);RadixSort
String[] rs_A = {"Irelia","Trundle","Ezreal","Alistar",
"Garen","Graves","Jayce","Katarina",
"LeBlanc","lulu","Lux"};
String[] rs_B = RadixSort.sort(rs_A);
for (String str : rs_B) {
print("[" + str + "]");
}BucketSort
double[] bucket_A = {0.14,0.13,0.2,0.11,0.99,0.88,0.7,0.6,0.5,0.4,0.3,0.2,0.1,0.898,0.875};
double[][]bucket_B = BucketSort.sort(bucket_A);
for (double[] list : bucket_B) {
print(list);
}RandomizeSelect
int[] randomizeSelect_A = {1,3,4,2};
int val = RandomizedSelect.select(randomizeSelect_A,2);
print(randomizeSelect_A);
print(val);Stack
print("Stack:");
Integer[] array = new Integer[100];
Stack<Integer> stack = new Stack(array);
stack.push(3);stack.push(4);stack.push(5);
stack.push(8);stack.push(20);
stack.pop();
ArrayList<Integer> raw = stack.raw();
for (Integer integer : raw)
System.out.print(integer.intValue() + ",");
print("");Queue
print("Queue:");
Queue queue = new Queue(50);
queue.in(3);queue.in(4);queue.in(5);
queue.out();
print(queue.raw());Linklist
print("LinkList:");
LinkList head = new LinkList(LinkList.head,null);
Random r = new Random();
LinkList node = head;
for (int i = 0; i < 10; i++) {
node.next = new LinkList(r.nextInt(100), null);
node = node.next;
System.out.print("[+" + node.value + "]");
}
print("");
print(head.array());BinaryTree
print("BinaryTree:");
Tree.BinaryTree root = new Tree.BinaryTree(100);
root.setLeftChild(new Tree.BinaryTree(50));
root.setRightChild(new Tree.BinaryTree(110));
root.leftChild.setLeftChild(new Tree.BinaryTree(35));
root.leftChild.leftChild.setRightChild(new Tree.BinaryTree(40));
root.leftChild.leftChild.rightChild.setLeftChild(new Tree.BinaryTree(37));
root.leftChild.leftChild.rightChild.setRightChild(new Tree.BinaryTree(45));
root.rightChild.setRightChild(new Tree.BinaryTree(150));
root.rightChild.setLeftChild(new Tree.BinaryTree(105));
print(root.allValue(true, Tree.BinaryTree.WalkType.inorder));
print(root.find(105).key);
print(root.maximum_Recursion().key);
print(root.rightChild.rightChild.predecessor().key);
root.insert(new Tree.BinaryTree(60));
root.insert_recursion(new Tree.BinaryTree(160));
print(root.allValue(true, Tree.BinaryTree.WalkType.inorder));
Tree.BinaryTree del = root.find(105);
root.deleteFromTree();
print(del.allValue(true, Tree.BinaryTree.WalkType.inorder));RedBlackTree
print("RedBlackTree:");
Tree.RedBlackTree rbroot = new Tree.RedBlackTree(100);
rbroot = (Tree.RedBlackTree) rbroot.insert(new Tree.RedBlackTree(20));
rbroot = (Tree.RedBlackTree) rbroot.insert(new Tree.RedBlackTree(21));
rbroot = (Tree.RedBlackTree) rbroot.insert(new Tree.RedBlackTree(150));
rbroot = (Tree.RedBlackTree) rbroot.insert(new Tree.RedBlackTree(89));
rbroot = (Tree.RedBlackTree) rbroot.insert(new Tree.RedBlackTree(201));
rbroot = (Tree.RedBlackTree) rbroot.insert(new Tree.RedBlackTree(12));
rbroot = (Tree.RedBlackTree) rbroot.insert(new Tree.RedBlackTree(101));
print(rbroot.allValue(true, Tree.BinaryTree.WalkType.inorder));
rbroot.find(201).deleteFromTree();
rbroot.find(12).deleteFromTree();
print(rbroot.allValue(true, Tree.BinaryTree.WalkType.inorder));OrderStaticTree
print("OrderStaticTree:");
Tree.OrderStaticTree OSRoot = new Tree.OrderStaticTree(999);
OSRoot = (Tree.OrderStaticTree) OSRoot.insert(new Tree.OrderStaticTree(80));
OSRoot = (Tree.OrderStaticTree) OSRoot.insert(new Tree.OrderStaticTree(1004));
OSRoot = (Tree.OrderStaticTree) OSRoot.insert(new Tree.OrderStaticTree(99));
OSRoot = (Tree.OrderStaticTree) OSRoot.insert(new Tree.OrderStaticTree(200));
OSRoot = (Tree.OrderStaticTree) OSRoot.insert(new Tree.OrderStaticTree(50));
OSRoot = (Tree.OrderStaticTree) OSRoot.insert(new Tree.OrderStaticTree(44));
print(OSRoot.allValue(true, Tree.BinaryTree.WalkType.inorder));
Tree.OrderStaticTree t = (Tree.OrderStaticTree) OSRoot.find(44);
print(t.rank());
t = (Tree.OrderStaticTree) OSRoot.find(1004);
print(t.rank());
print(OSRoot.select(0).key);
print(OSRoot.select(10).key);CutRod
print("CutRod:");
int[] price = {1,5,8,9,10,17,17,20,24,30};
print(CutRod.cut(price,10));
CutRod.cut_memoized(price,7).printSolution();
CutRod.cut_bottom_up(price,7).printSolution();
System.out.println(997.0/1000.0);Gauss and Cholesky and QR
print("Gauss:");
double[][] Gauss_R = {
{1,4,7},
{2,5,8},
{3,6,10}
};
Matrix Gauss_A = Matrix.create(Gauss_R);
Gauss_A = GaussianElimination.Eliminate(Gauss_A);
Gauss_A.print();
print("Cholesky:");
double[][] Cholesky_R = {
{4,-2,4,2},
{-2,10,-2,-7},
{4,-2,8,4},
{2,-7,4,7}
};
Matrix Cholesky_A = Matrix.create(Cholesky_R);
Cholesky_A = CholeskyFactorization.Eliminate(Cholesky_A);
Cholesky_A.print();
print("QR:");
double[][] QR_A = {
{4,-2,4,2},
{-2,10,-2,-7},
{4,-2,8,4},
{2,-7,4,7},
{8,-5,3,13}
};
Matrix QR_M = Matrix.create(QR_A);
Householder.House[] houses = QRDecomposition.decompose(QR_M);
QR_M.print();MatrixChainOrder
MatrixChainOrder.Result re = MatrixChainOrder.cal(30,35,15,5,10,20,25);
re.printOptimalParens(1,re.n);
print(re.m.get(2,5));
MatrixChainOrder.Result re2 = MatrixChainOrder.memoizedCal(30,35,15,5,10,20,25);
re2.printOptimalParens(1,re2.n);
print(re2.m.get(2,5));LCS
求最长公共子序列，属于求最优解问题，该问题适合使用动态规划来解决。
动态规划类似于分治法，需要将问题分割为多个子问题进行求解。然而分治法只关注问题的分割，没有关注重复计算的问题，有可能导致相同子问题大量重复计算
动态规划也将问题分为多个子问题，但是，它会选择缓存子问题的结果，重复计算问题得到解决
对于求最长公共子序列，其属于求最优解问题，且可以分割为子问题，所以可以使用动态规划来解决
其子问题可以归结为：
print("LCS:");
String[] LCS_X = {"A","B","C","B","D","A","B"};
String[] LCS_Y = {"B","D","C","A","B","A"};
LCS.Result LCS_re = LCS.getLCS(LCS_X,LCS_Y);
LCS_re.printLCS();OptimalBST
print("OptimalBST:");
double[] p = {0,0.15,0.10,0.05,0.10,0.20};
double[] q = {0.05,0.10,0.05,0.05,0.05,0.10};
OptimalBST.Result OBST_re = OptimalBST.cal(p,q);
OBST_re.printOptimalBST();