思路:深度搜索復雜度N!過不了。考慮動態(tài)規(guī)劃:將已經(jīng)選擇的列記為1,未選擇表示0,二進制壓縮,例如110,就表示選擇了第1列和第2列。
d(i, t)表示當前已經(jīng)匹配了i行,選擇了t這些列。狀態(tài)轉(zhuǎn)移:
for(int i = 0; i < n; ++i) { int x = 1 << i; if(x & val) d = max(d, like[row][i] + dfs(row+1, val - x, k-1)); }此時總的狀態(tài)數(shù)就是1<<n,相比N!是極大的優(yōu)化,減少了很多重復情況的搜索。
用記憶化搜索,代碼很好寫。
#include <cstdio>#include <cmath>#include <algorithm>#include <cstring>#include <utility>#include <string>#include <iostream>#include <map>#include <set>#include <vector>#include <queue>#include <stack>using namespace std;#PRagma comment(linker, "/STACK:1024000000,1024000000") #define eps 1e-10#define inf 0x3f3f3f3f#define PI pair<int, int> typedef long long LL;const int maxn = 13 + 5;int like[maxn][maxn], dp[maxn][1<<13];int n, ans;int dfs(int row, int val, int k) { //row表示行,k表示當前選擇了多少列 if(dp[row][val] != -1) return dp[row][val]; int &d = dp[row][val]; if(k == 1) { //邊界 for(int i = 0; i < n; ++i) { int x = 1 << i; if(x & val) return d = like[row][i]; } } for(int i = 0; i < n; ++i) { int x = 1 << i; if(x & val) d = max(d, like[row][i] + dfs(row+1, val - x, k-1)); } return d;}int main() { while(scanf("%d", &n) == 1) { for(int i = 0; i < n; ++i) for(int j = 0; j < n; ++j) { scanf("%d", &like[i][j]); } memset(dp, -1, sizeof(dp)); int start = (1<<n)-1; printf("%d/n", dfs(0, start, n)); } return 0;}如有不當之處歡迎指出!
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