Create: 51-N-Queens.ts

andra961 · andra961 · commit 277fc13b24a4 · 2022-09-15T19:55:20.000+02:00
diff --git a/typescript/51-N-Queens.ts b/typescript/51-N-Queens.ts
@@ -0,0 +1,62 @@
+//check if current state is valid
+const isStateValid = (state: number[], n: number) => {
+    //if there are n queens inserted the state is valid
+    return state.length === n;
+};
+
+//convert given state(valid) to correct answer format(a string)
+const stateToString = (state: number[]) => {
+    let arrs = state.map((col) => {
+        let newArr = new Array(state.length).fill('.');
+        newArr[col] = 'Q';
+        return newArr.join('');
+    });
+
+    return arrs;
+};
+
+//recursive step
+const searchRec = (state: number[], n: number, solutions: string[][]) => {
+    //if current state is valid, add it to the solutions array and return, we go back to previous states (DFS)
+    if (isStateValid(state, n)) return solutions.push(stateToString(state));
+
+    //get new possible candidates (the column in which to place current queen) to add to current State, start with every column
+    let candidates = new Set([...Array(n).keys()]);
+
+    //the row in which next queen will be added
+    let rowToAdd = state.length;
+
+    //iterates previous not empty rows to discard candidates before exploring them
+    for (let row = 0; row < state.length; row++) {
+        //the column in which is placed the queen at current row
+        let col = state[row];
+        let dist = rowToAdd - row;
+        //discard the whole column where queen inserte in "row" is
+        candidates.delete(col);
+        //right diagonal intersection of queen inserted in "row" with the row where to add new queen(new queen cannot be here)
+        candidates.delete(col + dist);
+        //left diagonal intersection of queen inserted in "row" with the row where to add new queen(new queen cannot be here)
+        candidates.delete(col - dist);
+    }
+
+    candidates.forEach((cand) => {
+        //temporarly add candidate to state
+        state.push(cand);
+        //explore new state with that candidate
+        searchRec(state, n, solutions);
+        //explored, remove the candidate to return at previous state
+        state.pop();
+    });
+
+    return;
+};
+
+function solveNQueens(n: number): string[][] {
+    let solutions = [];
+    let start = [];
+
+    //explore starting from empty state
+    searchRec(start, n, solutions);
+
+    return solutions;
+}
