经典DP之投资者问题

转载请注明作者与出处： franciscolv http://www.cnblogs.com/franciscolv/archive/2011/11/20/2256154.html

package SortSet;


/**
 * 投资问题 m万元，n项投资计划  计算最大盈利和
 * 示例中行表示m万元，列从第一列开始表示n想投资计划
 * @author franciscolv
 *
 */
public class InvestProblem {
    
    public static void main(String[] args) {
        int[][] a = { { 0, 0, 0, 0, 0 },
                { 1, 11, 0, 2, 20 },
                { 2, 12, 5, 10, 21 }, 
                { 3, 13, 10, 30, 22 },
                { 4, 14, 15, 32, 23 },
                { 5, 15, 20, 40, 24 } };
        System.out.println(getMaxProfits(a, 5, 4));
    }
    /**
     * n*m个问题个子问题  每个问题m种选择 故O(n*m^2)
     */
    public static int getMaxProfits(int[][] a, int m, int n) {
        int[][] f = new int[m + 1][n + 1];
        for(int i=0;i<=m;i++)
            f[i][0]=i;
        for (int i = 1; i <= m; i++)
            for (int j = 1; j <= n; j++) {
                if (i == 1&&j==1)
                    f[i][j] = a[1][1];
                else {
                    f[i][j] = findmax(i, j, a, f);
                }
            }
        for (int i = 0; i <= m; i++) {
            for (int j = 0; j <= n; j++)
                System.out.print(f[i][j] + " ");
            System.out.println();
        }
        
        return f[m][n];
    }
    /**
     * o(m)
     */
    private static int findmax(int i, int j, int[][] a, int[][] f) {
        int max = -1;
        for (int k = 0; k <= i; k++) {
            if (a[k][j] + f[i - k][j - 1] > max)
                max = a[k][j] + f[i - k][j - 1];
        }
        return max;
    }
}