101 lines
3.2 KiB
C++
101 lines
3.2 KiB
C++
// Source : https://leetcode.com/problems/unique-paths-iii/
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// Author : Hao Chen
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// Date : 2019-02-03
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/*****************************************************************************************************
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*
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* On a 2-dimensional grid, there are 4 types of squares:
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*
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* 1 represents the starting square. There is exactly one starting square.
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* 2 represents the ending square. There is exactly one ending square.
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* 0 represents empty squares we can walk over.
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* -1 represents obstacles that we cannot walk over.
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*
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* Return the number of 4-directional walks from the starting square to the ending square, that walk
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* over every non-obstacle square exactly once.
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*
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* Example 1:
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*
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* Input: [[1,0,0,0],[0,0,0,0],[0,0,2,-1]]
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* Output: 2
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* Explanation: We have the following two paths:
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* 1. (0,0),(0,1),(0,2),(0,3),(1,3),(1,2),(1,1),(1,0),(2,0),(2,1),(2,2)
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* 2. (0,0),(1,0),(2,0),(2,1),(1,1),(0,1),(0,2),(0,3),(1,3),(1,2),(2,2)
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*
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* Example 2:
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*
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* Input: [[1,0,0,0],[0,0,0,0],[0,0,0,2]]
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* Output: 4
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* Explanation: We have the following four paths:
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* 1. (0,0),(0,1),(0,2),(0,3),(1,3),(1,2),(1,1),(1,0),(2,0),(2,1),(2,2),(2,3)
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* 2. (0,0),(0,1),(1,1),(1,0),(2,0),(2,1),(2,2),(1,2),(0,2),(0,3),(1,3),(2,3)
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* 3. (0,0),(1,0),(2,0),(2,1),(2,2),(1,2),(1,1),(0,1),(0,2),(0,3),(1,3),(2,3)
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* 4. (0,0),(1,0),(2,0),(2,1),(1,1),(0,1),(0,2),(0,3),(1,3),(1,2),(2,2),(2,3)
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*
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* Example 3:
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*
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* Input: [[0,1],[2,0]]
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* Output: 0
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* Explanation:
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* There is no path that walks over every empty square exactly once.
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* Note that the starting and ending square can be anywhere in the grid.
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*
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* Note:
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*
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* 1 <= grid.length * grid[0].length <= 20
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*
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******************************************************************************************************/
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class Solution {
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public:
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int uniquePathsIII(vector<vector<int>>& grid) {
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int path = 0;
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int startX, startY;
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if (!findStartPoint( grid, startX, startY)) return 0;
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uniquePathsHelper(grid, startX, startY, path);
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return path;
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}
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bool findStartPoint(vector<vector<int>> &grid, int& x, int& y) {
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for(int i=0; i<grid.size(); i++) {
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for(int j=0; j<grid[0].size(); j++) {
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if (grid[i][j] == 1) {
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x = i; y =j;
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return true;
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}
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}
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}
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return false;
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}
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bool check(vector<vector<int>> &grid ) {
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for(int i=0; i<grid.size(); i++) {
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for(int j=0; j<grid[0].size(); j++) {
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if (grid[i][j] == 0 ) return false;
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}
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}
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return true;
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}
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void uniquePathsHelper(vector<vector<int>> &grid, int x, int y, int& path ) {
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if (x < 0 || y < 0 || x>= grid.size() || y>=grid[0].size()) return;
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if ( grid[x][y] < 0) return;
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if ( grid[x][y] == 2) {
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if (check(grid)) path++;
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return;
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}
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//back tracing - mark -2 means already passed.
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grid[x][y] = -2;
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uniquePathsHelper(grid, x, y-1, path); // up
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uniquePathsHelper(grid, x, y+1, path); // down
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uniquePathsHelper(grid, x+1, y, path); // right
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uniquePathsHelper(grid, x-1, y, path); // left
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grid[x][y] = 0;
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}
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};
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