zoukankan      html  css  js  c++  java
  • Project Euler Problem 11: Largest product in a grid

    Largest product in a grid

    Problem 11

    In the 20×20 grid below, four numbers along a diagonal line have been marked in red.

    08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
    49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
    81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
    52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
    22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
    24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
    32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
    67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
    24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
    21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
    78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
    16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
    86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
    19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
    04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
    88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
    04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
    20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
    20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
    01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48

    The product of these numbers is 26 × 63 × 78 × 14 = 1788696.

    What is the greatest product of four adjacent numbers in the same direction (up, down, left, right, or diagonally) in the 20×20 grid?


    C++(Faster):

    #include <iostream>
    
    using namespace std;
    
    const int MAXN = 20;
    const int TWO = 2;
    const int FOUR = 4;
    
    int grid[MAXN][MAXN];
    int product2[MAXN][MAXN];
    
    int main()
    {
        int maxproduct = 0, temp;
    
        for(int i=0; i<MAXN; i++)
            for(int j=0; j<MAXN; j++)
                cin >> grid[i][j];
    
        for(int i=0; i<MAXN-TWO; i++)
            for(int j=0; j<MAXN-TWO; j++)
                product2[i][j] = grid[i][j] * grid[i+1][j+1];
        for(int i=0; i<MAXN-FOUR; i++)
            for(int j=0; j<MAXN-FOUR; j++) {
                temp = product2[i][j] * product2[i+2][j+2];
                if(temp > maxproduct)
                    maxproduct = temp;
            }
    
        for(int i=0; i<MAXN-TWO; i++)
            for(int j=0; j<MAXN-TWO; j++)
                product2[i][j] = grid[i][j+3] * grid[i+1][j+2];
        for(int i=0; i<MAXN-FOUR; i++)
            for(int j=0; j<MAXN-FOUR; j++) {
                temp = product2[i][j+3] * product2[i+2][j+1];
                if(temp > maxproduct)
                    maxproduct = temp;
            }
    
        for(int i=0; i<MAXN; i++)
            for(int j=0; j<MAXN-TWO; j++)
                product2[i][j] = grid[i][j] * grid[i][j+1];
        for(int i=0; i<MAXN; i++)
            for(int j=0; j<MAXN-FOUR; j++) {
                temp = product2[i][j] * product2[i][j+2];
                if(temp > maxproduct)
                    maxproduct = temp;
            }
    
        for(int i=0; i<MAXN; i++)
            for(int j=0; j<MAXN-TWO; j++)
                product2[j][i] = grid[j][i] * grid[j][i+1];
        for(int i=0; i<MAXN; i++)
            for(int j=0; j<MAXN-FOUR; j++) {
                temp = product2[j][i] * product2[j][i+2];
                if(temp > maxproduct)
                    maxproduct = temp;
            }
    
        cout << maxproduct << endl;
    
        return 0;
    }



    C++:

    #include <iostream>
    
    using namespace std;
    
    const int MAXN = 20;
    const int FOUR = 4;
    
    int grid[MAXN][MAXN];
    
    int main()
    {
        int maxproduct = 0, temp;
    
        for(int i=0; i<MAXN; i++)
            for(int j=0; j<MAXN; j++)
                cin >> grid[i][j];
    
        for(int i=0; i<MAXN-FOUR; i++)
            for(int j=0; j<MAXN-FOUR; j++) {
                temp = grid[i][j] * grid[i+1][j+1] * grid[i+2][j+2] * grid[i+3][j+3];
                if(temp > maxproduct)
                    maxproduct = temp;
    
                temp = grid[i][j+3] * grid[i+1][j+2] * grid[i+2][j+1] * grid[i+3][j];
                if(temp > maxproduct)
                    maxproduct = temp;
            }
    
        for(int i=0; i<MAXN; i++)
            for(int j=0; j<MAXN-FOUR; j++) {
                temp = grid[i][j] * grid[i][j+1] * grid[i][j+2] * grid[i][j+3];
                if(temp > maxproduct)
                    maxproduct = temp;
    
                temp = grid[j][i] * grid[j][i+1] * grid[j][i+2] * grid[j][i+3];
                if(temp > maxproduct)
                    maxproduct = temp;
            }
    
        cout << maxproduct << endl;
    
        return 0;
    }


    Input data:

    08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
    49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
    81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
    52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
    22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
    24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
    32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
    67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
    24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
    21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
    78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
    16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
    86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
    19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
    04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
    88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
    04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
    20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
    20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
    01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48




  • 相关阅读:
    linux中jdk的安装
    @Transactional 的回滚
    监听器以及在监听类里面获得bean的方法
    list的顺序反转
    iOS 升级到xcode 7和iOS9 问题处理
    iOS 9.0系统策略更新
    iOS 技术分享3
    iOS 技术分享2
    iOS 技术分享
    iOS 面试题
  • 原文地址:https://www.cnblogs.com/tigerisland/p/7564027.html
Copyright © 2011-2022 走看看