MinTrailingZeros coding task - Learn to Code

Matrix A, consisting of N rows and N columns of non-negative integers, is given. Rows are numbered from 0 to N−1 (from top to bottom). Columns are numbered from 0 to N−1 (from left to right). We would like to find a path that starts at the upper-left corner (0, 0) and, moving only right and down, finishes at the bottom-right corner (N−1, N−1). Then, all the numbers on this path will be multiplied together.

Find a path such that the product of all the numbers on the path contain the minimal number of trailing zeros. We assume that 0 has 1 trailing zero.

Write a function:

int solution(int **A, int N);

that, given matrix A, returns the minimal number of trailing zeros.

Examples:

1. Given matrix A below:

The picture describes the first example test.

the function should return 1. The optimal path is: (0,0) → (0,1) → (0,2) → (1,2) → (2,2) → (2,3) → (3,3). The product of numbers 2, 10, 1, 4, 2, 1, 1 is 160, which has one trailing zero. There is no path that yields a product with no trailing zeros.

2. Given matrix A below:

The picture describes the second example test.

the function should return 2. One of the optimal paths is: (0,0) → (1,0) → (1,1) → (1,2) → (2,2) → (3,2) → (3,3). The product of numbers 10, 1, 1, 1, 10, 1, 1 is 100, which has two trailing zeros. There is no path that yields a product with fewer than two trailing zeros.

3. Given matrix A below:

The picture describes the third example test.

the function should return 1. One of the optimal paths is: (0,0) → (0,1) → (1,1) → (1,2) → (2,2). The product of numbers 10, 10, 0, 10, 10 is 0, which has one trailing zero. There is no path that yields a product with no trailing zeros.

Write an efficient algorithm for the following assumptions:

N is an integer within the range [1..500];

each element of matrix A is an integer within the range [0..1,000,000,000].

Matrix A, consisting of N rows and N columns of non-negative integers, is given. Rows are numbered from 0 to N−1 (from top to bottom). Columns are numbered from 0 to N−1 (from left to right). We would like to find a path that starts at the upper-left corner (0, 0) and, moving only right and down, finishes at the bottom-right corner (N−1, N−1). Then, all the numbers on this path will be multiplied together.

Find a path such that the product of all the numbers on the path contain the minimal number of trailing zeros. We assume that 0 has 1 trailing zero.

Write a function:

int solution(vector< vector<int> > &A);

that, given matrix A, returns the minimal number of trailing zeros.

Examples:

1. Given matrix A below:

The picture describes the first example test.

the function should return 1. The optimal path is: (0,0) → (0,1) → (0,2) → (1,2) → (2,2) → (2,3) → (3,3). The product of numbers 2, 10, 1, 4, 2, 1, 1 is 160, which has one trailing zero. There is no path that yields a product with no trailing zeros.

2. Given matrix A below:

The picture describes the second example test.

the function should return 2. One of the optimal paths is: (0,0) → (1,0) → (1,1) → (1,2) → (2,2) → (3,2) → (3,3). The product of numbers 10, 1, 1, 1, 10, 1, 1 is 100, which has two trailing zeros. There is no path that yields a product with fewer than two trailing zeros.

3. Given matrix A below:

The picture describes the third example test.

the function should return 1. One of the optimal paths is: (0,0) → (0,1) → (1,1) → (1,2) → (2,2). The product of numbers 10, 10, 0, 10, 10 is 0, which has one trailing zero. There is no path that yields a product with no trailing zeros.

Write an efficient algorithm for the following assumptions:

N is an integer within the range [1..500];

each element of matrix A is an integer within the range [0..1,000,000,000].

Matrix A, consisting of N rows and N columns of non-negative integers, is given. Rows are numbered from 0 to N−1 (from top to bottom). Columns are numbered from 0 to N−1 (from left to right). We would like to find a path that starts at the upper-left corner (0, 0) and, moving only right and down, finishes at the bottom-right corner (N−1, N−1). Then, all the numbers on this path will be multiplied together.

Find a path such that the product of all the numbers on the path contain the minimal number of trailing zeros. We assume that 0 has 1 trailing zero.

Write a function:

int solution(vector< vector<int> > &A);

that, given matrix A, returns the minimal number of trailing zeros.

Examples:

1. Given matrix A below:

The picture describes the first example test.

the function should return 1. The optimal path is: (0,0) → (0,1) → (0,2) → (1,2) → (2,2) → (2,3) → (3,3). The product of numbers 2, 10, 1, 4, 2, 1, 1 is 160, which has one trailing zero. There is no path that yields a product with no trailing zeros.

2. Given matrix A below:

The picture describes the second example test.

the function should return 2. One of the optimal paths is: (0,0) → (1,0) → (1,1) → (1,2) → (2,2) → (3,2) → (3,3). The product of numbers 10, 1, 1, 1, 10, 1, 1 is 100, which has two trailing zeros. There is no path that yields a product with fewer than two trailing zeros.

3. Given matrix A below:

The picture describes the third example test.

the function should return 1. One of the optimal paths is: (0,0) → (0,1) → (1,1) → (1,2) → (2,2). The product of numbers 10, 10, 0, 10, 10 is 0, which has one trailing zero. There is no path that yields a product with no trailing zeros.

Write an efficient algorithm for the following assumptions:

N is an integer within the range [1..500];

each element of matrix A is an integer within the range [0..1,000,000,000].

Matrix A, consisting of N rows and N columns of non-negative integers, is given. Rows are numbered from 0 to N−1 (from top to bottom). Columns are numbered from 0 to N−1 (from left to right). We would like to find a path that starts at the upper-left corner (0, 0) and, moving only right and down, finishes at the bottom-right corner (N−1, N−1). Then, all the numbers on this path will be multiplied together.

Find a path such that the product of all the numbers on the path contain the minimal number of trailing zeros. We assume that 0 has 1 trailing zero.

Write a function:

class Solution { public int solution(int[][] A); }

that, given matrix A, returns the minimal number of trailing zeros.

Examples:

1. Given matrix A below:

The picture describes the first example test.

the function should return 1. The optimal path is: (0,0) → (0,1) → (0,2) → (1,2) → (2,2) → (2,3) → (3,3). The product of numbers 2, 10, 1, 4, 2, 1, 1 is 160, which has one trailing zero. There is no path that yields a product with no trailing zeros.

2. Given matrix A below:

The picture describes the second example test.

the function should return 2. One of the optimal paths is: (0,0) → (1,0) → (1,1) → (1,2) → (2,2) → (3,2) → (3,3). The product of numbers 10, 1, 1, 1, 10, 1, 1 is 100, which has two trailing zeros. There is no path that yields a product with fewer than two trailing zeros.

3. Given matrix A below:

The picture describes the third example test.

the function should return 1. One of the optimal paths is: (0,0) → (0,1) → (1,1) → (1,2) → (2,2). The product of numbers 10, 10, 0, 10, 10 is 0, which has one trailing zero. There is no path that yields a product with no trailing zeros.

Write an efficient algorithm for the following assumptions:

N is an integer within the range [1..500];

each element of matrix A is an integer within the range [0..1,000,000,000].

Matrix A, consisting of N rows and N columns of non-negative integers, is given. Rows are numbered from 0 to N−1 (from top to bottom). Columns are numbered from 0 to N−1 (from left to right). We would like to find a path that starts at the upper-left corner (0, 0) and, moving only right and down, finishes at the bottom-right corner (N−1, N−1). Then, all the numbers on this path will be multiplied together.

Find a path such that the product of all the numbers on the path contain the minimal number of trailing zeros. We assume that 0 has 1 trailing zero.

Write a function:

int solution(List<List<int>> A);

that, given matrix A, returns the minimal number of trailing zeros.

Examples:

1. Given matrix A below:

The picture describes the first example test.

the function should return 1. The optimal path is: (0,0) → (0,1) → (0,2) → (1,2) → (2,2) → (2,3) → (3,3). The product of numbers 2, 10, 1, 4, 2, 1, 1 is 160, which has one trailing zero. There is no path that yields a product with no trailing zeros.

2. Given matrix A below:

The picture describes the second example test.

the function should return 2. One of the optimal paths is: (0,0) → (1,0) → (1,1) → (1,2) → (2,2) → (3,2) → (3,3). The product of numbers 10, 1, 1, 1, 10, 1, 1 is 100, which has two trailing zeros. There is no path that yields a product with fewer than two trailing zeros.

3. Given matrix A below:

The picture describes the third example test.

the function should return 1. One of the optimal paths is: (0,0) → (0,1) → (1,1) → (1,2) → (2,2). The product of numbers 10, 10, 0, 10, 10 is 0, which has one trailing zero. There is no path that yields a product with no trailing zeros.

Write an efficient algorithm for the following assumptions:

N is an integer within the range [1..500];

each element of matrix A is an integer within the range [0..1,000,000,000].

Matrix A, consisting of N rows and N columns of non-negative integers, is given. Rows are numbered from 0 to N−1 (from top to bottom). Columns are numbered from 0 to N−1 (from left to right). We would like to find a path that starts at the upper-left corner (0, 0) and, moving only right and down, finishes at the bottom-right corner (N−1, N−1). Then, all the numbers on this path will be multiplied together.

Find a path such that the product of all the numbers on the path contain the minimal number of trailing zeros. We assume that 0 has 1 trailing zero.

Write a function:

func Solution(A [][]int) int

that, given matrix A, returns the minimal number of trailing zeros.

Examples:

1. Given matrix A below:

The picture describes the first example test.

the function should return 1. The optimal path is: (0,0) → (0,1) → (0,2) → (1,2) → (2,2) → (2,3) → (3,3). The product of numbers 2, 10, 1, 4, 2, 1, 1 is 160, which has one trailing zero. There is no path that yields a product with no trailing zeros.

2. Given matrix A below:

The picture describes the second example test.

the function should return 2. One of the optimal paths is: (0,0) → (1,0) → (1,1) → (1,2) → (2,2) → (3,2) → (3,3). The product of numbers 10, 1, 1, 1, 10, 1, 1 is 100, which has two trailing zeros. There is no path that yields a product with fewer than two trailing zeros.

3. Given matrix A below:

The picture describes the third example test.

the function should return 1. One of the optimal paths is: (0,0) → (0,1) → (1,1) → (1,2) → (2,2). The product of numbers 10, 10, 0, 10, 10 is 0, which has one trailing zero. There is no path that yields a product with no trailing zeros.

Write an efficient algorithm for the following assumptions:

N is an integer within the range [1..500];

each element of matrix A is an integer within the range [0..1,000,000,000].

Matrix A, consisting of N rows and N columns of non-negative integers, is given. Rows are numbered from 0 to N−1 (from top to bottom). Columns are numbered from 0 to N−1 (from left to right). We would like to find a path that starts at the upper-left corner (0, 0) and, moving only right and down, finishes at the bottom-right corner (N−1, N−1). Then, all the numbers on this path will be multiplied together.

Find a path such that the product of all the numbers on the path contain the minimal number of trailing zeros. We assume that 0 has 1 trailing zero.

Write a function:

class Solution { public int solution(int[][] A); }

that, given matrix A, returns the minimal number of trailing zeros.

Examples:

1. Given matrix A below:

The picture describes the first example test.

the function should return 1. The optimal path is: (0,0) → (0,1) → (0,2) → (1,2) → (2,2) → (2,3) → (3,3). The product of numbers 2, 10, 1, 4, 2, 1, 1 is 160, which has one trailing zero. There is no path that yields a product with no trailing zeros.

2. Given matrix A below:

The picture describes the second example test.

the function should return 2. One of the optimal paths is: (0,0) → (1,0) → (1,1) → (1,2) → (2,2) → (3,2) → (3,3). The product of numbers 10, 1, 1, 1, 10, 1, 1 is 100, which has two trailing zeros. There is no path that yields a product with fewer than two trailing zeros.

3. Given matrix A below:

The picture describes the third example test.

the function should return 1. One of the optimal paths is: (0,0) → (0,1) → (1,1) → (1,2) → (2,2). The product of numbers 10, 10, 0, 10, 10 is 0, which has one trailing zero. There is no path that yields a product with no trailing zeros.

Write an efficient algorithm for the following assumptions:

N is an integer within the range [1..500];

each element of matrix A is an integer within the range [0..1,000,000,000].

Matrix A, consisting of N rows and N columns of non-negative integers, is given. Rows are numbered from 0 to N−1 (from top to bottom). Columns are numbered from 0 to N−1 (from left to right). We would like to find a path that starts at the upper-left corner (0, 0) and, moving only right and down, finishes at the bottom-right corner (N−1, N−1). Then, all the numbers on this path will be multiplied together.

Find a path such that the product of all the numbers on the path contain the minimal number of trailing zeros. We assume that 0 has 1 trailing zero.

Write a function:

class Solution { public int solution(int[][] A); }

that, given matrix A, returns the minimal number of trailing zeros.

Examples:

1. Given matrix A below:

The picture describes the first example test.

the function should return 1. The optimal path is: (0,0) → (0,1) → (0,2) → (1,2) → (2,2) → (2,3) → (3,3). The product of numbers 2, 10, 1, 4, 2, 1, 1 is 160, which has one trailing zero. There is no path that yields a product with no trailing zeros.

2. Given matrix A below:

The picture describes the second example test.

the function should return 2. One of the optimal paths is: (0,0) → (1,0) → (1,1) → (1,2) → (2,2) → (3,2) → (3,3). The product of numbers 10, 1, 1, 1, 10, 1, 1 is 100, which has two trailing zeros. There is no path that yields a product with fewer than two trailing zeros.

3. Given matrix A below:

The picture describes the third example test.

the function should return 1. One of the optimal paths is: (0,0) → (0,1) → (1,1) → (1,2) → (2,2). The product of numbers 10, 10, 0, 10, 10 is 0, which has one trailing zero. There is no path that yields a product with no trailing zeros.

Write an efficient algorithm for the following assumptions:

N is an integer within the range [1..500];

each element of matrix A is an integer within the range [0..1,000,000,000].

Matrix A, consisting of N rows and N columns of non-negative integers, is given. Rows are numbered from 0 to N−1 (from top to bottom). Columns are numbered from 0 to N−1 (from left to right). We would like to find a path that starts at the upper-left corner (0, 0) and, moving only right and down, finishes at the bottom-right corner (N−1, N−1). Then, all the numbers on this path will be multiplied together.

Find a path such that the product of all the numbers on the path contain the minimal number of trailing zeros. We assume that 0 has 1 trailing zero.

Write a function:

function solution(A);

that, given matrix A, returns the minimal number of trailing zeros.

Examples:

1. Given matrix A below:

The picture describes the first example test.

the function should return 1. The optimal path is: (0,0) → (0,1) → (0,2) → (1,2) → (2,2) → (2,3) → (3,3). The product of numbers 2, 10, 1, 4, 2, 1, 1 is 160, which has one trailing zero. There is no path that yields a product with no trailing zeros.

2. Given matrix A below:

The picture describes the second example test.

the function should return 2. One of the optimal paths is: (0,0) → (1,0) → (1,1) → (1,2) → (2,2) → (3,2) → (3,3). The product of numbers 10, 1, 1, 1, 10, 1, 1 is 100, which has two trailing zeros. There is no path that yields a product with fewer than two trailing zeros.

3. Given matrix A below:

The picture describes the third example test.

the function should return 1. One of the optimal paths is: (0,0) → (0,1) → (1,1) → (1,2) → (2,2). The product of numbers 10, 10, 0, 10, 10 is 0, which has one trailing zero. There is no path that yields a product with no trailing zeros.

Write an efficient algorithm for the following assumptions:

N is an integer within the range [1..500];

each element of matrix A is an integer within the range [0..1,000,000,000].

Matrix A, consisting of N rows and N columns of non-negative integers, is given. Rows are numbered from 0 to N−1 (from top to bottom). Columns are numbered from 0 to N−1 (from left to right). We would like to find a path that starts at the upper-left corner (0, 0) and, moving only right and down, finishes at the bottom-right corner (N−1, N−1). Then, all the numbers on this path will be multiplied together.

Find a path such that the product of all the numbers on the path contain the minimal number of trailing zeros. We assume that 0 has 1 trailing zero.

Write a function:

fun solution(A: Array<IntArray>): Int

that, given matrix A, returns the minimal number of trailing zeros.

Examples:

1. Given matrix A below:

The picture describes the first example test.

the function should return 1. The optimal path is: (0,0) → (0,1) → (0,2) → (1,2) → (2,2) → (2,3) → (3,3). The product of numbers 2, 10, 1, 4, 2, 1, 1 is 160, which has one trailing zero. There is no path that yields a product with no trailing zeros.

2. Given matrix A below:

The picture describes the second example test.

the function should return 2. One of the optimal paths is: (0,0) → (1,0) → (1,1) → (1,2) → (2,2) → (3,2) → (3,3). The product of numbers 10, 1, 1, 1, 10, 1, 1 is 100, which has two trailing zeros. There is no path that yields a product with fewer than two trailing zeros.

3. Given matrix A below:

The picture describes the third example test.

the function should return 1. One of the optimal paths is: (0,0) → (0,1) → (1,1) → (1,2) → (2,2). The product of numbers 10, 10, 0, 10, 10 is 0, which has one trailing zero. There is no path that yields a product with no trailing zeros.

Write an efficient algorithm for the following assumptions:

N is an integer within the range [1..500];

each element of matrix A is an integer within the range [0..1,000,000,000].

Matrix A, consisting of N rows and N columns of non-negative integers, is given. Rows are numbered from 0 to N−1 (from top to bottom). Columns are numbered from 0 to N−1 (from left to right). We would like to find a path that starts at the upper-left corner (0, 0) and, moving only right and down, finishes at the bottom-right corner (N−1, N−1). Then, all the numbers on this path will be multiplied together.

Find a path such that the product of all the numbers on the path contain the minimal number of trailing zeros. We assume that 0 has 1 trailing zero.

Write a function:

function solution(A)

that, given matrix A, returns the minimal number of trailing zeros.

Examples:

1. Given matrix A below:

The picture describes the first example test.

the function should return 1. The optimal path is: (0,0) → (0,1) → (0,2) → (1,2) → (2,2) → (2,3) → (3,3). The product of numbers 2, 10, 1, 4, 2, 1, 1 is 160, which has one trailing zero. There is no path that yields a product with no trailing zeros.

2. Given matrix A below:

The picture describes the second example test.

the function should return 2. One of the optimal paths is: (0,0) → (1,0) → (1,1) → (1,2) → (2,2) → (3,2) → (3,3). The product of numbers 10, 1, 1, 1, 10, 1, 1 is 100, which has two trailing zeros. There is no path that yields a product with fewer than two trailing zeros.

3. Given matrix A below:

The picture describes the third example test.

the function should return 1. One of the optimal paths is: (0,0) → (0,1) → (1,1) → (1,2) → (2,2). The product of numbers 10, 10, 0, 10, 10 is 0, which has one trailing zero. There is no path that yields a product with no trailing zeros.

Note: All arrays in this task are zero-indexed, unlike the common Lua convention. You can use #A to get the length of the array A.

Write an efficient algorithm for the following assumptions:

N is an integer within the range [1..500];

each element of matrix A is an integer within the range [0..1,000,000,000].

Matrix A, consisting of N rows and N columns of non-negative integers, is given. Rows are numbered from 0 to N−1 (from top to bottom). Columns are numbered from 0 to N−1 (from left to right). We would like to find a path that starts at the upper-left corner (0, 0) and, moving only right and down, finishes at the bottom-right corner (N−1, N−1). Then, all the numbers on this path will be multiplied together.

Find a path such that the product of all the numbers on the path contain the minimal number of trailing zeros. We assume that 0 has 1 trailing zero.

Write a function:

int solution(NSMutableArray *A);

that, given matrix A, returns the minimal number of trailing zeros.

Examples:

1. Given matrix A below:

The picture describes the first example test.

the function should return 1. The optimal path is: (0,0) → (0,1) → (0,2) → (1,2) → (2,2) → (2,3) → (3,3). The product of numbers 2, 10, 1, 4, 2, 1, 1 is 160, which has one trailing zero. There is no path that yields a product with no trailing zeros.

2. Given matrix A below:

The picture describes the second example test.

the function should return 2. One of the optimal paths is: (0,0) → (1,0) → (1,1) → (1,2) → (2,2) → (3,2) → (3,3). The product of numbers 10, 1, 1, 1, 10, 1, 1 is 100, which has two trailing zeros. There is no path that yields a product with fewer than two trailing zeros.

3. Given matrix A below:

The picture describes the third example test.

the function should return 1. One of the optimal paths is: (0,0) → (0,1) → (1,1) → (1,2) → (2,2). The product of numbers 10, 10, 0, 10, 10 is 0, which has one trailing zero. There is no path that yields a product with no trailing zeros.

Write an efficient algorithm for the following assumptions:

N is an integer within the range [1..500];

each element of matrix A is an integer within the range [0..1,000,000,000].

Matrix A, consisting of N rows and N columns of non-negative integers, is given. Rows are numbered from 0 to N−1 (from top to bottom). Columns are numbered from 0 to N−1 (from left to right). We would like to find a path that starts at the upper-left corner (0, 0) and, moving only right and down, finishes at the bottom-right corner (N−1, N−1). Then, all the numbers on this path will be multiplied together.

Find a path such that the product of all the numbers on the path contain the minimal number of trailing zeros. We assume that 0 has 1 trailing zero.

Write a function:

function solution(A: TMatrix; N: longint): longint;

that, given matrix A, returns the minimal number of trailing zeros.

Examples:

1. Given matrix A below:

The picture describes the first example test.

the function should return 1. The optimal path is: (0,0) → (0,1) → (0,2) → (1,2) → (2,2) → (2,3) → (3,3). The product of numbers 2, 10, 1, 4, 2, 1, 1 is 160, which has one trailing zero. There is no path that yields a product with no trailing zeros.

2. Given matrix A below:

The picture describes the second example test.

the function should return 2. One of the optimal paths is: (0,0) → (1,0) → (1,1) → (1,2) → (2,2) → (3,2) → (3,3). The product of numbers 10, 1, 1, 1, 10, 1, 1 is 100, which has two trailing zeros. There is no path that yields a product with fewer than two trailing zeros.

3. Given matrix A below:

The picture describes the third example test.

the function should return 1. One of the optimal paths is: (0,0) → (0,1) → (1,1) → (1,2) → (2,2). The product of numbers 10, 10, 0, 10, 10 is 0, which has one trailing zero. There is no path that yields a product with no trailing zeros.

Write an efficient algorithm for the following assumptions:

N is an integer within the range [1..500];

each element of matrix A is an integer within the range [0..1,000,000,000].

Matrix A, consisting of N rows and N columns of non-negative integers, is given. Rows are numbered from 0 to N−1 (from top to bottom). Columns are numbered from 0 to N−1 (from left to right). We would like to find a path that starts at the upper-left corner (0, 0) and, moving only right and down, finishes at the bottom-right corner (N−1, N−1). Then, all the numbers on this path will be multiplied together.

Find a path such that the product of all the numbers on the path contain the minimal number of trailing zeros. We assume that 0 has 1 trailing zero.

Write a function:

function solution($A);

that, given matrix A, returns the minimal number of trailing zeros.

Examples:

1. Given matrix A below:

The picture describes the first example test.

the function should return 1. The optimal path is: (0,0) → (0,1) → (0,2) → (1,2) → (2,2) → (2,3) → (3,3). The product of numbers 2, 10, 1, 4, 2, 1, 1 is 160, which has one trailing zero. There is no path that yields a product with no trailing zeros.

2. Given matrix A below:

The picture describes the second example test.

the function should return 2. One of the optimal paths is: (0,0) → (1,0) → (1,1) → (1,2) → (2,2) → (3,2) → (3,3). The product of numbers 10, 1, 1, 1, 10, 1, 1 is 100, which has two trailing zeros. There is no path that yields a product with fewer than two trailing zeros.

3. Given matrix A below:

The picture describes the third example test.

the function should return 1. One of the optimal paths is: (0,0) → (0,1) → (1,1) → (1,2) → (2,2). The product of numbers 10, 10, 0, 10, 10 is 0, which has one trailing zero. There is no path that yields a product with no trailing zeros.

Write an efficient algorithm for the following assumptions:

N is an integer within the range [1..500];

each element of matrix A is an integer within the range [0..1,000,000,000].

Matrix A, consisting of N rows and N columns of non-negative integers, is given. Rows are numbered from 0 to N−1 (from top to bottom). Columns are numbered from 0 to N−1 (from left to right). We would like to find a path that starts at the upper-left corner (0, 0) and, moving only right and down, finishes at the bottom-right corner (N−1, N−1). Then, all the numbers on this path will be multiplied together.

Find a path such that the product of all the numbers on the path contain the minimal number of trailing zeros. We assume that 0 has 1 trailing zero.

Write a function:

sub solution { my (@A) = @_; ... }

that, given matrix A, returns the minimal number of trailing zeros.

Examples:

1. Given matrix A below:

The picture describes the first example test.

the function should return 1. The optimal path is: (0,0) → (0,1) → (0,2) → (1,2) → (2,2) → (2,3) → (3,3). The product of numbers 2, 10, 1, 4, 2, 1, 1 is 160, which has one trailing zero. There is no path that yields a product with no trailing zeros.

2. Given matrix A below:

The picture describes the second example test.

the function should return 2. One of the optimal paths is: (0,0) → (1,0) → (1,1) → (1,2) → (2,2) → (3,2) → (3,3). The product of numbers 10, 1, 1, 1, 10, 1, 1 is 100, which has two trailing zeros. There is no path that yields a product with fewer than two trailing zeros.

3. Given matrix A below:

The picture describes the third example test.

the function should return 1. One of the optimal paths is: (0,0) → (0,1) → (1,1) → (1,2) → (2,2). The product of numbers 10, 10, 0, 10, 10 is 0, which has one trailing zero. There is no path that yields a product with no trailing zeros.

Write an efficient algorithm for the following assumptions:

N is an integer within the range [1..500];

each element of matrix A is an integer within the range [0..1,000,000,000].

Matrix A, consisting of N rows and N columns of non-negative integers, is given. Rows are numbered from 0 to N−1 (from top to bottom). Columns are numbered from 0 to N−1 (from left to right). We would like to find a path that starts at the upper-left corner (0, 0) and, moving only right and down, finishes at the bottom-right corner (N−1, N−1). Then, all the numbers on this path will be multiplied together.

Find a path such that the product of all the numbers on the path contain the minimal number of trailing zeros. We assume that 0 has 1 trailing zero.

Write a function:

def solution(A)

that, given matrix A, returns the minimal number of trailing zeros.

Examples:

1. Given matrix A below:

The picture describes the first example test.

the function should return 1. The optimal path is: (0,0) → (0,1) → (0,2) → (1,2) → (2,2) → (2,3) → (3,3). The product of numbers 2, 10, 1, 4, 2, 1, 1 is 160, which has one trailing zero. There is no path that yields a product with no trailing zeros.

2. Given matrix A below:

The picture describes the second example test.

the function should return 2. One of the optimal paths is: (0,0) → (1,0) → (1,1) → (1,2) → (2,2) → (3,2) → (3,3). The product of numbers 10, 1, 1, 1, 10, 1, 1 is 100, which has two trailing zeros. There is no path that yields a product with fewer than two trailing zeros.

3. Given matrix A below:

The picture describes the third example test.

the function should return 1. One of the optimal paths is: (0,0) → (0,1) → (1,1) → (1,2) → (2,2). The product of numbers 10, 10, 0, 10, 10 is 0, which has one trailing zero. There is no path that yields a product with no trailing zeros.

Write an efficient algorithm for the following assumptions:

N is an integer within the range [1..500];

each element of matrix A is an integer within the range [0..1,000,000,000].

Matrix A, consisting of N rows and N columns of non-negative integers, is given. Rows are numbered from 0 to N−1 (from top to bottom). Columns are numbered from 0 to N−1 (from left to right). We would like to find a path that starts at the upper-left corner (0, 0) and, moving only right and down, finishes at the bottom-right corner (N−1, N−1). Then, all the numbers on this path will be multiplied together.

Find a path such that the product of all the numbers on the path contain the minimal number of trailing zeros. We assume that 0 has 1 trailing zero.

Write a function:

def solution(a)

that, given matrix A, returns the minimal number of trailing zeros.

Examples:

1. Given matrix A below:

The picture describes the first example test.

the function should return 1. The optimal path is: (0,0) → (0,1) → (0,2) → (1,2) → (2,2) → (2,3) → (3,3). The product of numbers 2, 10, 1, 4, 2, 1, 1 is 160, which has one trailing zero. There is no path that yields a product with no trailing zeros.

2. Given matrix A below:

The picture describes the second example test.

the function should return 2. One of the optimal paths is: (0,0) → (1,0) → (1,1) → (1,2) → (2,2) → (3,2) → (3,3). The product of numbers 10, 1, 1, 1, 10, 1, 1 is 100, which has two trailing zeros. There is no path that yields a product with fewer than two trailing zeros.

3. Given matrix A below:

The picture describes the third example test.

the function should return 1. One of the optimal paths is: (0,0) → (0,1) → (1,1) → (1,2) → (2,2). The product of numbers 10, 10, 0, 10, 10 is 0, which has one trailing zero. There is no path that yields a product with no trailing zeros.

Write an efficient algorithm for the following assumptions:

N is an integer within the range [1..500];

each element of matrix A is an integer within the range [0..1,000,000,000].

Matrix A, consisting of N rows and N columns of non-negative integers, is given. Rows are numbered from 0 to N−1 (from top to bottom). Columns are numbered from 0 to N−1 (from left to right). We would like to find a path that starts at the upper-left corner (0, 0) and, moving only right and down, finishes at the bottom-right corner (N−1, N−1). Then, all the numbers on this path will be multiplied together.

Find a path such that the product of all the numbers on the path contain the minimal number of trailing zeros. We assume that 0 has 1 trailing zero.

Write a function:

object Solution { def solution(a: Array[Array[Int]]): Int }

that, given matrix A, returns the minimal number of trailing zeros.

Examples:

1. Given matrix A below:

The picture describes the first example test.

the function should return 1. The optimal path is: (0,0) → (0,1) → (0,2) → (1,2) → (2,2) → (2,3) → (3,3). The product of numbers 2, 10, 1, 4, 2, 1, 1 is 160, which has one trailing zero. There is no path that yields a product with no trailing zeros.

2. Given matrix A below:

The picture describes the second example test.

the function should return 2. One of the optimal paths is: (0,0) → (1,0) → (1,1) → (1,2) → (2,2) → (3,2) → (3,3). The product of numbers 10, 1, 1, 1, 10, 1, 1 is 100, which has two trailing zeros. There is no path that yields a product with fewer than two trailing zeros.

3. Given matrix A below:

The picture describes the third example test.

the function should return 1. One of the optimal paths is: (0,0) → (0,1) → (1,1) → (1,2) → (2,2). The product of numbers 10, 10, 0, 10, 10 is 0, which has one trailing zero. There is no path that yields a product with no trailing zeros.

Write an efficient algorithm for the following assumptions:

N is an integer within the range [1..500];

each element of matrix A is an integer within the range [0..1,000,000,000].

Matrix A, consisting of N rows and N columns of non-negative integers, is given. Rows are numbered from 0 to N−1 (from top to bottom). Columns are numbered from 0 to N−1 (from left to right). We would like to find a path that starts at the upper-left corner (0, 0) and, moving only right and down, finishes at the bottom-right corner (N−1, N−1). Then, all the numbers on this path will be multiplied together.

Find a path such that the product of all the numbers on the path contain the minimal number of trailing zeros. We assume that 0 has 1 trailing zero.

Write a function:

public func solution(_ A : inout [[Int]]) -> Int

that, given matrix A, returns the minimal number of trailing zeros.

Examples:

1. Given matrix A below:

The picture describes the first example test.

the function should return 1. The optimal path is: (0,0) → (0,1) → (0,2) → (1,2) → (2,2) → (2,3) → (3,3). The product of numbers 2, 10, 1, 4, 2, 1, 1 is 160, which has one trailing zero. There is no path that yields a product with no trailing zeros.

2. Given matrix A below:

The picture describes the second example test.

the function should return 2. One of the optimal paths is: (0,0) → (1,0) → (1,1) → (1,2) → (2,2) → (3,2) → (3,3). The product of numbers 10, 1, 1, 1, 10, 1, 1 is 100, which has two trailing zeros. There is no path that yields a product with fewer than two trailing zeros.

3. Given matrix A below:

The picture describes the third example test.

the function should return 1. One of the optimal paths is: (0,0) → (0,1) → (1,1) → (1,2) → (2,2). The product of numbers 10, 10, 0, 10, 10 is 0, which has one trailing zero. There is no path that yields a product with no trailing zeros.

Write an efficient algorithm for the following assumptions:

N is an integer within the range [1..500];

each element of matrix A is an integer within the range [0..1,000,000,000].

Matrix A, consisting of N rows and N columns of non-negative integers, is given. Rows are numbered from 0 to N−1 (from top to bottom). Columns are numbered from 0 to N−1 (from left to right). We would like to find a path that starts at the upper-left corner (0, 0) and, moving only right and down, finishes at the bottom-right corner (N−1, N−1). Then, all the numbers on this path will be multiplied together.

Find a path such that the product of all the numbers on the path contain the minimal number of trailing zeros. We assume that 0 has 1 trailing zero.

Write a function:

function solution(A: number[][]): number;

that, given matrix A, returns the minimal number of trailing zeros.

Examples:

1. Given matrix A below:

The picture describes the first example test.

the function should return 1. The optimal path is: (0,0) → (0,1) → (0,2) → (1,2) → (2,2) → (2,3) → (3,3). The product of numbers 2, 10, 1, 4, 2, 1, 1 is 160, which has one trailing zero. There is no path that yields a product with no trailing zeros.

2. Given matrix A below:

The picture describes the second example test.

the function should return 2. One of the optimal paths is: (0,0) → (1,0) → (1,1) → (1,2) → (2,2) → (3,2) → (3,3). The product of numbers 10, 1, 1, 1, 10, 1, 1 is 100, which has two trailing zeros. There is no path that yields a product with fewer than two trailing zeros.

3. Given matrix A below:

The picture describes the third example test.

the function should return 1. One of the optimal paths is: (0,0) → (0,1) → (1,1) → (1,2) → (2,2). The product of numbers 10, 10, 0, 10, 10 is 0, which has one trailing zero. There is no path that yields a product with no trailing zeros.

Write an efficient algorithm for the following assumptions:

N is an integer within the range [1..500];

each element of matrix A is an integer within the range [0..1,000,000,000].

Matrix A, consisting of N rows and N columns of non-negative integers, is given. Rows are numbered from 0 to N−1 (from top to bottom). Columns are numbered from 0 to N−1 (from left to right). We would like to find a path that starts at the upper-left corner (0, 0) and, moving only right and down, finishes at the bottom-right corner (N−1, N−1). Then, all the numbers on this path will be multiplied together.

Find a path such that the product of all the numbers on the path contain the minimal number of trailing zeros. We assume that 0 has 1 trailing zero.

Write a function:

Private Function solution(A As Integer()()) As Integer

that, given matrix A, returns the minimal number of trailing zeros.

Examples:

1. Given matrix A below:

The picture describes the first example test.

the function should return 1. The optimal path is: (0,0) → (0,1) → (0,2) → (1,2) → (2,2) → (2,3) → (3,3). The product of numbers 2, 10, 1, 4, 2, 1, 1 is 160, which has one trailing zero. There is no path that yields a product with no trailing zeros.

2. Given matrix A below:

The picture describes the second example test.

the function should return 2. One of the optimal paths is: (0,0) → (1,0) → (1,1) → (1,2) → (2,2) → (3,2) → (3,3). The product of numbers 10, 1, 1, 1, 10, 1, 1 is 100, which has two trailing zeros. There is no path that yields a product with fewer than two trailing zeros.

3. Given matrix A below:

The picture describes the third example test.

the function should return 1. One of the optimal paths is: (0,0) → (0,1) → (1,1) → (1,2) → (2,2). The product of numbers 10, 10, 0, 10, 10 is 0, which has one trailing zero. There is no path that yields a product with no trailing zeros.

Write an efficient algorithm for the following assumptions:

N is an integer within the range [1..500];

each element of matrix A is an integer within the range [0..1,000,000,000].

MinTrailingZeros

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