Unique Paths II
2013-07-12 07:34
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Follow up for "Unique Paths":
Now consider if some obstacles are added to the grids. How many unique paths would there be?
An obstacle and empty space is marked as
For example,
There is one obstacle in the middle of a 3x3 grid as illustrated below.
The total number of unique paths is
Note: m and n will be at most 100.
思路:DFS,大数据的TLE,需要进行优化
问题:大数据的时候TLE,问题搜索的时候,走了很多重复的子路径
所以不能进行DFS(DFS本质上是暴力),而应该DP
DP[i,j] = 代表从A[0,0]到A[i,j]的path个数
DP[i,j] = A[i-1,j] is'not obstacle ? DP[i-1,j] + A[i,j-1] is'not obstacle DP[i,j-1]
0 1 0 0 0
1 0 0 0 0
0 0 0 0 0 ==》第一行的时候,需要特殊处理,1之后的初值都是0,1之前的才是1
0 0 0 0 0
Now consider if some obstacles are added to the grids. How many unique paths would there be?
An obstacle and empty space is marked as
1and
0respectively in the grid.
For example,
There is one obstacle in the middle of a 3x3 grid as illustrated below.
[ [0,0,0], [0,1,0], [0,0,0] ]
The total number of unique paths is
2.
Note: m and n will be at most 100.
思路:DFS,大数据的TLE,需要进行优化
class Solution { public: int ans; void dfs(int i, int j, int step,vector<vector<int> > &obstacleGrid){ if (i == obstacleGrid.size() || j == obstacleGrid[0].size()){ return; } if (obstacleGrid[i][j]){ return; } if (step == obstacleGrid.size() + obstacleGrid[0].size() -1){ ans++; return; } dfs(i+1,j,step + 1,obstacleGrid); dfs(i,j+1,step + 1,obstacleGrid); return; } int uniquePathsWithObstacles(vector<vector<int> > &obstacleGrid) { // Start typing your C/C++ solution below // DO NOT write int main() function ans = 0; dfs(0,0,1,obstacleGrid); return ans; } };
问题:大数据的时候TLE,问题搜索的时候,走了很多重复的子路径
所以不能进行DFS(DFS本质上是暴力),而应该DP
DP[i,j] = 代表从A[0,0]到A[i,j]的path个数
DP[i,j] = A[i-1,j] is'not obstacle ? DP[i-1,j] + A[i,j-1] is'not obstacle DP[i,j-1]
0 1 0 0 0
1 0 0 0 0
0 0 0 0 0 ==》第一行的时候,需要特殊处理,1之后的初值都是0,1之前的才是1
0 0 0 0 0
class Solution { public: int dp(vector<vector<int> > &obstacleGrid){ vector<int> dp(obstacleGrid[0].size(),1); int m = obstacleGrid.size(),n = obstacleGrid[0].size(); //第一行需要特殊处理 bool first = false; for(int j = 0; j < n; j++){ if (obstacleGrid[0][j]){ first = true; } if (obstacleGrid[0][j] || first){ dp[j] = 0; }else{ dp[j] = 1; } } for(int i = 1; i < m; i++){ for(int j = 0; j < n; j++){ //dp[i][j] = dp[i-1][j] + dp[i][j-1]; if (obstacleGrid[i][j]){ //是障碍,说明到当前位置的路径个数是0 dp[j] = 0; }else if (j){ dp[j] = dp[j] + dp[j-1]; } } } return dp[dp.size() -1]; } int uniquePathsWithObstacles(vector<vector<int> > &obstacleGrid) { // Start typing your C/C++ solution below // DO NOT write int main() function return dp(obstacleGrid); } };
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