UVa 116 - Unidirectional TSP
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题目:在一个二维的平面网格中从左西向右走,每个格子里有个数字每次只能走到本行或者上一行或者下一行;
求一条从西到东的路径,使得路径上的数字和最大,如果都是最大,找到最路径小字典序列。
分析:dp,动态三角形类似物。逆向求解方便找到最小字典序。
状态:f(i,j)为从(i,j)位置开始走到最右侧的最大值;
转移方程:f(i,j)= data(i,j)+ max(f(i+1,j),f(i+1,j-1),f(i+1,j+1));
记录路径后继,用于输出。
说明:使用从后向前计算,得到最小字典序。
#include <iostream>#include <cstdlib>#include <cstring>#include <cstdio>using namespace std;int maps[11][101];int smap[11][101];int fath[11][101];int main(){int n,m;while (~scanf("%d%d",&n,&m)) {for (int i = 1 ; i <= n ; ++ i)for (int j = 1 ; j <= m ; ++ j)scanf("%d",&maps[i][j]);memset(smap, 0, sizeof(smap));for (int i = m ; i >= 1 ; -- i)for (int j = 1 ; j <= n ; ++ j) {smap[j][i] = smap[j][i+1]+maps[j][i];fath[j][i] = j;if (j > 1 && smap[j][i] >= smap[j-1][i+1]+maps[j][i]) {smap[j][i] = smap[j-1][i+1]+maps[j][i];fath[j][i] = j-1;}if (j == n && smap[j][i] >= smap[1][i+1]+maps[j][i]) {smap[j][i] = smap[1][i+1]+maps[j][i];fath[j][i] = 1;}if (j < n && smap[j][i] > smap[j+1][i+1]+maps[j][i]) {smap[j][i] = smap[j+1][i+1]+maps[j][i];fath[j][i] = j+1;}if (j == 1 && smap[j][i] > smap[n][i+1]+maps[j][i]) {smap[j][i] = smap[n][i+1]+maps[j][i];fath[j][i] = n;}}int spa = 1;for (int i = 2 ; i <= n ; ++ i)if (smap[spa][1] > smap[i][1])spa = i;int min = smap[spa][1];for (int i = 1 ; i <= m ; ++ i) {if (i < m) printf("%d ",spa);else printf("%d\n%d\n",spa,min);spa = fath[spa][i];}}return 0;}
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