POJ-1163 The Triangle

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本文介绍了一个算法问题，即在一个三角形数字阵列中找到从顶部到底部的最大路径和。通过递归方法，该算法考虑了每一步可以向左下或右下移动的特点，并实现了高效的求解。

描述

7
3 8
8 1 0
2 7 4 4
4 5 2 6 5

(Figure 1)
Figure 1 shows a number triangle. Write a program that calculates the highest sum of numbers passed on a route that starts at the top and ends somewhere on the base. Each step can go either diagonally down to the left or diagonally down to the right.

输入

Your program is to read from standard input. The first line contains one integer N: the number of rows in the triangle. The following N lines describe the data of the triangle. The number of rows in the triangle is > 1 but <= 100. The numbers in the triangle, all integers, are between 0 and 99.

输出

Your program is to write to standard output. The highest sum is written as an integer.

输入样例

5
7
3 8
8 1 0
2 7 4 4
4 5 2 6 5

输出样例

代码

#include <iostream>
#include <algorithm>
using namespace std;
int D[101][101],m=0,n;
int maxD[101][101];
int maxRoute(int i, int j) {
    if (maxD[i][j] != -1) {
        return maxD[i][j];
    }
    if (i == n) {
        maxD[i][j] = D[i][j];
        return maxD[i][j];
    }
    else {
        int x = maxRoute(i + 1, j);
        int y = maxRoute(i + 1, j + 1);
        maxD[i][j] = max(x, y) + D[i][j];
    }
    return maxD[i][j];

}
int main() {

    cin >> n; //从1,1开始
    for (int i = 1; i <= n; i++) {
        for (int j = 1; j <= i; j++) {
            cin >> D[i][j];
            maxD[i][j] = -1;
        }
    }

    cout << maxRoute(1, 1)<<endl;
    return 0;
}