Digit Matrix vs CLRS.Helper[Lite]

Digit Matrix is a collection of interesting mathematics exercises. This APP can improve the ability of calculation and logical reasoning, and cultivate mathematical thinking. It includes topics ranging from simple to very difficult. It is a good helper in learning mathematics or training the brain. Feature: Computing and Logical Reasoning Fifteen types. Infinite exercises Different Difficulties Easy to get started Five themes Contents: 1. Arithmetic Square Place the numbers from 1 to 9 into the cells (a different single number in each cell) so that the indicated equations are correct. Evaluate from left-to-right and top-to-bottom (ignore the usual precedence of the operators). 2. Chains Enter the numbers from 1 to X in the squares, once each, so that the given equations are correct. (Each equation begins at one square and ends at the next square; X is the total number of squares.) 3. SUMS Place a number from 1 to N into each cell. (N is the total number of cells in the grid.) Every cell must contain a different number. The numbers outside the grid, when given, indicate the sum of the numbers in the corresponding row, column, or diagonal. 4. Coins Place one coin into each cell such that the sum of the coins in each row and column matches the number to the left and the top. the same denomination may be used multiple times in each row or column. 5. Hundred A square grid whose cells are to be filled by some digits. The task is to fill additional digits in required cells such that the sum of numbers in each row and each column equals to 100. 6. Antimagic Square Place numbers from 1 to 2*N (N is the number of cells per side) into the cells so that there are exactly two numbers in each row, column and main diagonal. The sums of the two numbers are shown around the grid. 7. Products Place numbers from 1 to 2*N (N is the number of cells per side) into some cells so that each number is in exactly one cell, and no cell has more than one number. Each row and each column must contain exactly two numbers. Numbers outside the grid are the product of the two numbers in that row or column. 8. Products (Off-by-One) Place numbers from 1 to 2*N (N is the number of cells per side) into some cells so that each number is in exactly one cell, and no cell has more than one number. Each row and each column must contain exactly two numbers. Numbers outside the grid are 1 more or 1 less than the product of the two numbers in that row or column. 9. Addends Select Specified quantity of numbers from a given number set. Each number can not selected more than once. The sum of selected numbers must same as the given value. 10. Equality Delete Specified quantity of squares so that what remains is a correct equation. Use standard order of precedence (multiplication and division before addition and subtraction). 11. Alphametic Square Each letter represents a different digit. Figure out which letter corresponds to which digit so that all equations are true. Multi-digit numbers cannot start with the digit 0. 12. Matches Arithmetic Remove, Add or Move one to three matches so that the matches express a correct arithmetic equality. Click the match to remove it. Click the empty position to add the match. 13. Digit Twins Two numbers are connected by up to three line segments, and the two numbers are divided by their greatest common divisor at the same time. If the quotient is 1, the number will be eliminated. All numbers on the board need to be eliminated. 14. Divisor and multiple Numbers are added to 2 queues alternately. 2 groups of numbers are divided by their greatest common divisor in turn. Eliminate the number If the quotient is 1. 15. Numeric Factor Path On the board, if any two adjacent numbers have a common divisor greater than 1, they can be connected, and only one line can be connected between the two adjacent numbers. The final goal is to connect all the numbers into a non-intersecting path.

Refer to The third edition of the book, covering content [need full version]: 2. Getting Started: Insertion sort, Merge sort; 4. Divide-and-Conquer: Maximum-subarray, Matrix Multiplication[normal, recursive, Strassen’s algorithm]; 6. Heapsort: Heapsort[max-heap, min-heap]; 7. Quicksort: Quicksort; 8. Sorting in Linear Time: Counting sort; 12. Binary Search Trees: Binary search tree[Inorder Walk, Search Recursive, Search Iterative, Minimum Iterative, Maximum Iterative, Successor, Predecessor, Insert, Delete]; 13. Red-Black Trees: Red Black Tree[Insert, Delete]; 15. Dynamic Programming: Rod cutting[Recursive, Top_down, Bottom_up, Print],Longest common subsequence; 16. Greedy Algorithms: Acitivity selection[Recursive, Iterative],Huffman codes; 22. Elementary Graph: Breadth-first search, Depth-first search, Topological sort, Strongly connected components; 23. Minimum Spanning Trees: Minimum spanning tree[Kruskal’s algorithm，Prim’s algorithm]; 24. Single-Source Shortest Paths: The Bellman-Ford algorithm，DAG algorithm，Dijkstra’s algorithm; 25. All-pairs Shortest Paths: All-pairs Shortest paths algorithms[Slow，Faster，The Floyd-Warshall algorithm]; 26. Maximum Flow: The Ford-Fulkerson algorithm; Addition: Tower of Hanoi，N Queens Problem，Comparison of sorting algorithms; The primary features: You can run the pseudo-code single step or continuous, observe the change of parameters and data structures，it can help you to understand the design thought of the algorithm; You can set breakpoints in program and ovserve the status of breakpoint, it can help you to understand why this algorithm is corrcet by using loop invariants; With running-time function stacks and the returning positions，you can track the running process of recursive functions easily, and understand the operation mechanism of computer programs; By recording the performed times of the pseudo-codes can help you to understand the running time of algorithms; I wish this app can be helpful to you;