2B. The least round way

一、Problem

There is a square matrix n × n, consisting of non-negative integer numbers. You should find such a way on it that

• starts in the upper left cell of the matrix;
• each following cell is to the right or down from the current cell;
• the way ends in the bottom right cell.

Moreover, if we multiply together all the numbers along the way, the result should be the least “round”. In other words, it should end in the least possible number of zeros.

Input
The first line contains an integer number n (2 ≤ n ≤ 1000), n is the size of the matrix. Then follow n lines containing the matrix elements (non-negative integer numbers not exceeding 109).

Output
In the first line print the least number of trailing zeros. In the second line print the correspondent way itself.

二、Example

input

3
1 2 3
4 5 6
7 8 9

output

0
DDRR

三、Code

package com.codeforces.problemset;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class TheLeastRoundWay {
    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        StringBuilder out = new StringBuilder();

        int matrixSize = Integer.valueOf(in.readLine());
        int[][] checker1 = new int[matrixSize][matrixSize];
        int[][] checker2 = new int[matrixSize][matrixSize];
        int k = -1;
        String[] matrixArray = new String[matrixSize];
        for (int i = 0; i < matrixSize; i++) {
            matrixArray = in.readLine().split(" ");
            for (int j = 0; j < matrixSize; j++) {
                int temp = Integer.parseInt(matrixArray[j]);
                if (temp == 0) {
                    k = i;
                    checker1[i][j] = 10;
                    checker2[i][j] = 10;
                }
                checker1[i][j] = factor(temp, 2);// get factors instead of trying to mod every number
                checker2[i][j] = factor(temp, 5);
            }
        }

        for (int i = 1; i < matrixSize; i++) {
            checker1[0][i] += checker1[0][i-1];
            checker1[i][0] += checker1[i-1][0];
            checker2[0][i] += checker2[0][i-1];
            checker2[i][0] += checker2[i-1][0];
        }

        for (int i = 1; i < matrixSize; i++){
            for (int j = 1; j < matrixSize; j++){
                checker1[i][j] += min(checker1[i][j-1], checker1[i-1][j]);
                checker2[i][j] += min(checker2[i][j-1], checker2[i-1][j]);
            }
        }

        int first = matrixSize - 1; // row
        int second = matrixSize - 1; // column

        int choose1 = checker1[matrixSize - 1][matrixSize - 1];
        int choose2 = checker2[matrixSize - 1][matrixSize - 1];
        int[][] choice;

        if (choose1 < choose2){
            choice = checker1;
        }
        else {
            choice = checker2;
        }

        int trailingZeros = min(choose1, choose2);// 尾随0
        if (k != -1 && trailingZeros > 1) {// different path
            out = new StringBuilder();
            trailingZeros = 1;
            for (int i = 0; i < k; i++) {
                out.append("D");
            }
            for (int i = 0; i < matrixSize - 1; i++) {
                out.append("R");
            }
            for (int i = k; i < matrixSize - 1; i++) {
                out.append("D");
            }
        } else {
            while (!(first == 0 && second == 0)) {
                if (first == 0) {
                    second--;
                    out.insert(0, "R");
                } else if (second == 0) {
                    first--;
                    out.insert(0, "D");
                } else {
                    if (choice[first][second - 1] <= choice[first - 1][second]) {
                        second--;
                        out.insert(0, "R");
                    } else {
                        first--;
                        out.insert(0, "D");
                    }
                }
            }
        }
        System.out.print(trailingZeros + "\n" + out);
    }

    public static int min(int left, int right){
        if (left < right){
            return left;
        }
        else{
            return right;
        }
    }

    static int factor(int num, int factorer) {
        if (num == 0){
            return num;
        }
        int val = 0;
        while (num % factorer == 0) {
            val++;
            num /= factorer;
        }
        return val;
    }
}