2019-07-15 - 兵

题目：

地上有一个m行n列的方格，一个机器人从坐标（0，0）的格子出发，开始移动，他每次可以向左、右、上、下移动一格，但是不能进入行坐标和列坐标的数位之和大于k的格子。例如，当k=18时，机器人能够进入方格（35，37），因为3+5+3+7=18，但是不能进入方格（35，38），因为3+5+3+8=19。请问该机器人能到达多少个格子？

解题思路：

451563168895_.pic.jpg

解题代码：
1、<swift>

var visited: [Bool] = [Bool]()

func movingCount(threshold:Int, rows:Int, cols:Int) -> Int {
    if(threshold < 0 || rows <= 0 || cols <= 0) {
        return 0
    }
    for i in 0...rows*cols {
        visited[i] = false
    }
    let count = movingCountCore(threshold: threshold, rows: rows, cols: cols, row: 0, col: 0)
    return count;
}

func movingCountCore(threshold:Int, rows:Int, cols:Int, row:Int, col:Int) -> Int {
    var count = 0
    if(check(threshold: threshold, rows: rows, cols: cols, row: row, col: col)) {
        visited[row * cols + col] = true
        count = 1 + movingCountCore(threshold: threshold, rows: rows, cols: cols, row: row - 1, col: col) + movingCountCore(threshold: threshold, rows: rows, cols: cols, row: row, col: col - 1) + movingCountCore(threshold: threshold, rows: rows, cols: cols, row: row + 1, col: col) + movingCountCore(threshold: threshold, rows: rows, cols: cols, row: row, col: col + 1)
    }
    return count;
}


func check(threshold:Int, rows:Int, cols:Int, row:Int, col:Int) -> Bool {
    if(row >= 0 && row < rows && col >= 0 && col < cols && getDigitSum(number: row) + getDigitSum(number: col) <= threshold && !visited[row * cols + col]) {
        return true;
    }
    
    return false;
}

func getDigitSum(number originNumber: Int) -> Int {
    var sum = 0
    var number = originNumber
    while(number > 0) {
        sum += number % 10
        number = number / 10
    }
    return sum
}

// ====================测试代码====================
func test(testName: String, threshold:Int, rows:Int, cols:Int, expected:Int) {
    print("\(testName) begins: ")
    if(movingCount(threshold: threshold, rows: rows, cols: cols) == expected) {
        print("Passed.\n")
    } else {
        print("FAILED.\n")
    }
}

// 方格多行多列
func test1() {
    test(testName: "Test1", threshold: 5, rows: 10, cols: 10, expected: 21)
}

2、<C++>

#include <cstdio>

int movingCountCore(int threshold, int rows, int cols, int row, int col, bool* visited);
bool check(int threshold, int rows, int cols, int row, int col, bool* visited);
int getDigitSum(int number);

int movingCount(int threshold, int rows, int cols)
{
    if(threshold < 0 || rows <= 0 || cols <= 0)
        return 0;

    bool *visited = new bool[rows * cols];
    for(int i = 0; i < rows * cols; ++i)
        visited[i] = false;

    int count = movingCountCore(threshold, rows, cols,
        0, 0, visited);

    delete[] visited;

    return count;
}

int movingCountCore(int threshold, int rows, int cols, int row,
    int col, bool* visited)
{
    int count = 0;
    if(check(threshold, rows, cols, row, col, visited))
    {
        visited[row * cols + col] = true;

        count = 1 + movingCountCore(threshold, rows, cols,
            row - 1, col, visited)
            + movingCountCore(threshold, rows, cols,
                row, col - 1, visited)
            + movingCountCore(threshold, rows, cols,
                row + 1, col, visited)
            + movingCountCore(threshold, rows, cols,
                row, col + 1, visited);
    }

    return count;
}

bool check(int threshold, int rows, int cols, int row, int col,
    bool* visited)
{
    if(row >= 0 && row < rows && col >= 0 && col < cols
        && getDigitSum(row) + getDigitSum(col) <= threshold
        && !visited[row* cols + col])
        return true;

    return false;
}

int getDigitSum(int number)
{
    int sum = 0;
    while(number > 0)
    {
        sum += number % 10;
        number /= 10;
    }

    return sum;
}

// ====================测试代码====================
void test(char* testName, int threshold, int rows, int cols, int expected)
{
    if(testName != nullptr)
        printf("%s begins: ", testName);

    if(movingCount(threshold, rows, cols) == expected)
        printf("Passed.\n");
    else
        printf("FAILED.\n");
}

// 方格多行多列
void test1()
{
    test("Test1", 5, 10, 10, 21);
}

// 方格多行多列
void test2()
{
    test("Test2", 15, 20, 20, 359);
}

// 方格只有一行，机器人只能到达部分方格
void test3()
{
    test("Test3", 10, 1, 100, 29);
}

// 方格只有一行，机器人能到达所有方格
void test4()
{
    test("Test4", 10, 1, 10, 10);
}

// 方格只有一列，机器人只能到达部分方格
void test5()
{
    test("Test5", 15, 100, 1, 79);
}

// 方格只有一列，机器人能到达所有方格
void test6()
{
    test("Test6", 15, 10, 1, 10);
}

// 方格只有一行一列
void test7()
{
    test("Test7", 15, 1, 1, 1);
}

// 方格只有一行一列
void test8()
{
    test("Test8", 0, 1, 1, 1);
}

// 机器人不能进入任意一个方格
void test9()
{
    test("Test9", -10, 10, 10, 0);
}

int main(int agrc, char* argv[])
{
    test1();
    test2();
    test3();
    test4();
    test5();
    test6();
    test7();
    test8();
    test9();

    return 0;
}