矩阵的最小路径和

package com.hzins.suanfa;

import org.junit.Test;

public class JuzhenMinVarSum {
    /**
     * 空间复杂度o(n^2)
     * 时间复杂度o(n^2)
     * @param array
     * @return
     */
    public static int[][] getdp(int[][] array){
        int[][] dp = new int[array.length][array[0].length];
        dp[0][0] = array[0][0];
        for(int i = 1 ;i < array.length;i ++){
            dp[i][0] = array[i][0] + dp[i-1][0];
        }
        for(int i = 1;i< array[0].length;i ++){
            dp[0][i] = array[0][i] + dp[0][i -1];
        }
        for(int i = 1;i < array.length;i ++){
            for(int j = 1; j<array[0].length;j++){
                dp[i][j] = Math.min(dp[i - 1][j], dp[i][j - 1]) + array[i][j];
            }
        }
        return dp;
    }
    /**
     * 空间复杂度O(n)
     * 时间复杂度o(n^2)
     * @param array
     * @return
     */
    public static int[] getdp1(int[][] array){
        
        int[] dp = new int[array[0].length];
        dp[0] = array[0][0];
        for(int i =1;i<array[0].length;i++){
            dp[i] = array[0][i] + dp[i - 1];
        }
        for(int i = 1; i < array.length;i++){
            dp[0] = array[i][0] + dp[0];
            for (int j = 1;j < array[0].length;j ++){
                int min = Math.min(dp[j], dp[j - 1]);
                dp[j] = min + array[i][j];
            }
        }
        return dp;
    }
    public static void printJuzhen(int[][] a){
        for(int i = 0;i< a.length;i++){
            for (int j = 0;j < a[0].length;j ++){
                System.out.print(a[i][j] + "   ");
            }
            System.out.println();
        }
    }
    @Test
    public void test(){
        int[][] a = new int[3][5];
        for(int i = 0;i < a.length;i ++){
            a[i][0] = 3;
            a[i][1] = 4;
            a[i][2] = 7;
            a[i][3] = 4;
            a[i][4] = 2;
        }
        printJuzhen(a);
        System.out.print("


");
        int[] dp = getdp1(a);
        for(int i : dp){
            System.out.print(i + "  ");
        }
    }
    @Test
    public void test1(){
        int[][] a = new int[3][5];
        for(int i = 0;i < a.length;i ++){
            a[i][0] = 3;
            a[i][1] = 4;
            a[i][2] = 7;
            a[i][3] = 4;
            a[i][4] = 2;
        }
        printJuzhen(a);
        System.out.println("


");
        int[][] dp = getdp(a);
        printJuzhen(dp);
    }
}