Re-translate the Japanese version (#1871)

* Retranslate Japanese docs with GPT-5.4

* Retranslate Japanese code with GPT-5.4

ja/codes/c/chapter_backtracking/permutations_i.c

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+/**
+ * File: permutations_i.c
+ * Created Time: 2023-06-04
+ * Author: Gonglja (glj0@outlook.com), krahets (krahets@163.com)
+ */
+
+#include "../utils/common.h"
+
+// 順列は最大 1000 個と仮定
+#define MAX_SIZE 1000
+
+/* バックトラッキング：順列 I */
+void backtrack(int *state, int stateSize, int *choices, int choicesSize, bool *selected, int **res, int *resSize) {
+    // 状態の長さが要素数に等しければ、解を記録
+    if (stateSize == choicesSize) {
+        res[*resSize] = (int *)malloc(choicesSize * sizeof(int));
+        for (int i = 0; i < choicesSize; i++) {
+            res[*resSize][i] = state[i];
+        }
+        (*resSize)++;
+        return;
+    }
+    // すべての選択肢を走査
+    for (int i = 0; i < choicesSize; i++) {
+        int choice = choices[i];
+        // 枝刈り：要素の重複選択を許可しない
+        if (!selected[i]) {
+            // 試行: 選択を行い、状態を更新
+            selected[i] = true;
+            state[stateSize] = choice;
+            // 次の選択へ進む
+            backtrack(state, stateSize + 1, choices, choicesSize, selected, res, resSize);
+            // バックトラック：選択を取り消し、前の状態に戻す
+            selected[i] = false;
+        }
+    }
+}
+
+/* 全順列 I */
+int **permutationsI(int *nums, int numsSize, int *returnSize) {
+    int *state = (int *)malloc(numsSize * sizeof(int));
+    bool *selected = (bool *)malloc(numsSize * sizeof(bool));
+    for (int i = 0; i < numsSize; i++) {
+        selected[i] = false;
+    }
+    int **res = (int **)malloc(MAX_SIZE * sizeof(int *));
+    *returnSize = 0;
+
+    backtrack(state, 0, nums, numsSize, selected, res, returnSize);
+
+    free(state);
+    free(selected);
+
+    return res;
+}
+
+/* Driver Code */
+int main() {
+    int nums[] = {1, 2, 3};
+    int numsSize = sizeof(nums) / sizeof(nums[0]);
+    int returnSize;
+
+    int **res = permutationsI(nums, numsSize, &returnSize);
+
+    printf("入力配列 nums = ");
+    printArray(nums, numsSize);
+    printf("\nすべての順列 res = \n");
+    for (int i = 0; i < returnSize; i++) {
+        printArray(res[i], numsSize);
+    }
+
+    // メモリを解放する
+    for (int i = 0; i < returnSize; i++) {
+        free(res[i]);
+    }
+    free(res);
+
+    return 0;
+}