62. Unique Paths

0062-unique-paths/memo.md

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+### step1
+
+BFSでマスを管理しながら左と上のマスの経路数を足し合わせた。
+
+### step2
+
+ChatGPTを参考に、DPで解く解き方に変更。
+
+### step3
+
+3回通すまで書き直し。

0062-unique-paths/step1.cpp

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+class Solution {
+public:
+    int uniquePaths(int m, int n) {
+        vector<vector<int>> ways(m, vector<int>(n, 0));
+        ways[0][0] = 1;
+
+        queue<pair<int, int>> grids;
+        grids.emplace(0, 0);
+
+        while (!grids.empty()) {
+            auto[row, column] = grids.front();
+            grids.pop();
+
+            if (!(row == 0 && column == 0) && ways[row][column] != 0) {
+                continue;
+            }
+
+            if (row - 1 >= 0) {
+                ways[row][column] += ways[row -  1][column];
+            }
+            if (column - 1 >= 0) {
+                ways[row][column] += ways[row][column - 1];
+            }
+
+            if (row + 1 < m) {
+                grids.emplace(row + 1, column);
+            }
+            if (column + 1 < n) {
+                grids.emplace(row, column + 1);
+            }
+        }
+        return ways[m - 1][n - 1];
+    }
+};

0062-unique-paths/step2.cpp

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+class Solution {
+public:
+    int uniquePaths(int m, int n) {
+        vector<vector<int>> ways(m, vector<int>(n, 1));
+
+        for (int i = 1; i < m; i++) {
+            for (int j = 1; j < n; j++) {
+                ways[i][j] = ways[i - 1][j] + ways[i][j - 1];
+            }
+        }
+
+        return ways[m - 1][n - 1];
+    }
+};

0062-unique-paths/step3.cpp

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+class Solution {
+public:
+    int uniquePaths(int m, int n) {
+        vector<vector<int>> ways(m, vector<int>(n, 1));
+
+        for (int i = 1; i < m; i++) {
+            for (int j = 1; j < n; j++) {
+                ways[i][j] = ways[i - 1][j] + ways[i][j - 1];
+            }
+        }
+
+        return ways[m - 1][n - 1];
+    }
+};